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Name: Waldyr Alves Rodrigues Jr.
Status: married, five childreen
born: 03/14/1946 at Araraquara, SP, Brazil
Address: Rua Luverci Pereira de Souza, 1172
13084-032 Campinas, SP
fone: 55 19 32893266
e-mail: walrod@ime.unicamp.br
or walrod@mpc.com.br
TITLES
B. Sc. Physics, University of São Paulo
(USP), São Paulo, SP, Brazil, 1968.
Ph.D. Physics, University of Torino,
Italy, 1971.
Full Professor of Mathematical Physics, State
University of Campinas (UNICAMP), Campinas, SP, Brazil, 1986.
PRESENT
POSITION:
Invited Professor
at the Institute of Mathematics, Statistics and Scientific Computation,
IMECC-UNICAMP.
·
Director of the Institute of Mathematics,
Statistics and Scientific Computation, State University of Campinas
(IMECC-UNICAMP), 1994-1998.
·
Vice President of the Foundation for the
Development of UNICAMP (FUNCAMP), 1998-2000.
·
Dean of Graduate
Studies in
Applied Mathematics, IMECC-UNICAMP, 1998-1999.
· Full Professor of Mathematical
Physics,
IMECC-UNICAMP, 1986. Retired at November 1999.
· Visiting Scientist at MIT (USA), 1976-1978.
· Visiting Scientist at CERN-Geneve, 1979.
· Visiting Professor, University of Trento, Italy, 1987/1988.
· Visiting Professor, University of Perugia, Italy, 1999.
· Visiting Professor, Department of Mathematical Sciences, Univ. Liverpool, UK,
08/2001-02/2002.
FAPESP
06/1967 ‑ 12/1968 - Scientific Initiation.
FAPESP
04/1969 ‑ 06/1969 ‑
Research
FAPESP
01/1970 ‑ 12/1971
-Ph.D. fellowship
INFN
Itália:
Participation at the International School of Sub-Nuclear Physics Ettore Majorana 07/1971, Erice, Sicilia.
CNPq
1973 TC 16.626, US$ 50.000
CNPq
1973 TC 12.323 , US$ 50.000
CNPq
1974 TC 17.143, US$ 100.000
FAPESP
07/1976 ‑
01/1978 - Pos-Doc Fellowship (MIT ‑ USA)
CNPq
03/1979 ‑ 06/1979 - fellowship CERN/CNPq
CNPq
1980 - senior research fellowship
CNPq
1981 - senior research fellowship
ICTP
1981
- fellowship to participate at the “Spring School and Workshop on on Supegravity’’ (22 April ‑
06 May 1981)
IILA/CNR (Itália) ‑ 1982 – research fellowship, Univ. Catania, Catania, Italy
CNPq
1982 ‑ senior research fellowship
CNPq
1983 ‑ senior research fellowship
CNPq
1984 ‑ senior research fellowship
CNPq
1985 ‑ senior research fellowship
CNPq
1986 ‑ senior research fellowship
CNR (Itália) 1987 - research
fellowship, Univ. Trento, Italy
CNPq
1987 ‑ senior research fellowship
CNPq
1988 ‑ 1989 ‑ senior research fellowship
FAPESP
01/01/88 ‑ 30/10/88 – senior research fellowship to do research at the
University of Trento, Italy
FAPESP
September/89 - grant to participate at a meeting at London
CNPq
1989 ‑ senior research fellowship
FAPESP
1990 - grant for a
two months visit of Prof. J. F. Pommaret at IMECC
CNPq
1990 ‑ senior research fellowship
CNPq
1991- senior research fellowship
CNPq
1992 - grant for acquisition of a Sun Workstation
CNPq
1992 ‑1993
senior research fellowship
FAEP
1992 - personal computer
CNPq
1993 - grant to participate at the III
Workshop on Clifford Algebras and their Applications in Mathematical Physics, Deinze, Belgium, May 1993.
CNPq
1994 ‑1995 senior research fellowship
CNPq
1994 – grant for a nine months visit of
Prof. Matej Pavsic
FAPESP
1994 – grant for visit of Prof. Matej Pavsic (air thickets)
CNPq
1994 – grant for a visit of Prof. Andrey
Grib- US$ 50,000
FAPESP
1995 – grant for acquisition of computational equipments (US$ 60,000)
FAPESP
1995 – grant for a two months visit of Prof. Ian R. Porteous
at IMECC- US$ 10,400
FAPESP
1996 – grant for a six months visit of Prof. A .A .Grib
- US$ 26,200
FAPESP
1996 – research grant for several projects at IMECC-UNICAMP - US$ 120,000
CNPq
1996 - senior research fellowship
FAPESP
1997 – research grant for several projects at IMECC-UNICAMP - US$ 150,000
CNPq
1998
- senior research fellowship
FAPESP 1998-
grant for a ten months visit of Prof. Andrey Grib- US$ 34,400
CNPq/ TWAS 2000- grant for a
three months visit of Dr. M. Sharif- US$ 6,500
FAPESP 2000/2002- pos-doc fellowship for Dr. Bolivar Alves Oliveira
MOTOROLA 2001-research grant to
develop an antenna for launching (finite aperture approximations) to X waves.
CNPq 2001/2002- senior research
fellowship (Department of Mathematical Sciences, University of Liverpool
In the last 40 years I lectured more
than 70 courses at graduated and pos-graduated levels at Physics and
Mathematical Departments, as, e.g.:
·
General Physics
·
Electrodynamics
·
Special and General
Relativity
·
Mathematical Methods of
Physics
·
Applied Mathematics
·
Partial Differential
Equations
·
Elementary Particle
Theory
·
Differential Geometry
·
Theory of Connections
and Gauge Theory
·
Quantum Mechanics
·
Quantum Theory of
Fields
·
Calculus, Linear
Algebra and Analytic Geometry
·
Clifford, Algebras, Multivetor and Extensor Calculus.
MEMBER OF
EDITORIAL BOARD AND REFEREE OF JOURNALS
Member of the editorial board: Advances in Applied Clifford
Algebras, Random Operators and Stochastic Equations.
Referee: Found. Phys.,
N. Cimento, J. Math.
Phys., Int. J. Theor.
Phys., Brazilian Journal of Phys., Phys. Letters A and B, Journal
of Physics: Mathematical and General, Classical and Quantum Gravity,
Advances in Applied Clifford Algebras, Phys. Rev. A, D ,E, etc.
Reviewer: Mathematics Reviews and Zentralblatt für Mathematik.
Master
and PhD. thesis Advised
·
Title: Mutiple
Production of Mesons Induced by Cosmic Ray (Elab>240 TeV) and Comparison with IRS‑CERN
Data.
Ph.D. thesis of Armando Turtelli
Junior, presented to the “Instituto de Física "Gleb Wataghin” (IFGW),
UNICAMP, at 06/03/ 1974
·
Title: The Theory of Groups and the
Concept of Mass.
M. Sc. thesis (Pure Mathematics) of Afonso Augusto Lopes, presented to IMECC‑UNICAMP
at 08/ 23/1983.
·
Title: Covariance, Invariance and the
Principle of Relativity.
Ph. D. thesis (Pure Mathematics) of Miriam E.
F. Scanavini, presented
to IMECC‑UNICAMP, 08/21/1986
·
Title: Symmetry Laws in Spacetime in Spacetime Theories.
M. Sc.
thesis (Physics) of Quintino A. Gomes de Souza,
presented to IFGW- UNICAMP,
05/1986.
·
Title: Generalized Potentials and dual
Charges: An Essay about Magnetic Monopoles.
Ph. D. thesis (Physics) of Adolfo Maia Jr.,
presented to IFGW-UNICAMP, 08/1987.
·
Title: Spinorial
Structures in Lorentzian Manifolds.
Ph.D. thesis (Pure Mathematics) ofVera Lúcia Figueiredo,
presented to IMECC‑UNICAMP, 10/02/1986
·
Title: Geometrical Algebras, Rotations
and Classic Electrodynamics.
M.Sc. thesis (Physics) of
José Roberto Zeni presented to IFGW-UNICAMP,
10/14/1987.
·
Title: Aplications
of Principal Fiber Bundles and Spacetime Theories to
some Physical Theories
Ph.D. thesis (Physics) of Márcio
A. Faria‑Rosa, presented to IFGW-UNICAMP,
10/1987.
·
Title: Mathematical Foundations of Gauge
Theories.
M. Sc. thesis (Pure Mathematics) of Alexandre Trovon de Carvalho, presented to IMECC-UNICAMP
, 02/20/1992 .
·
Title: Lorentz Transformations, Clifford
Algebras and the Motion Of Charged Particles.
Ph. D. thesis (Physics) of José Ricardo Rezende Zeni, presented to IFGW-UNICAMP,
01/1992.
·
Title: Dirac Operators on Riemann-Cartan-Weyl Spacetimes
and the Nature of the Gravitational Field.
Ph. D. thesis of Quintino
Augusto Gomes de Souza, presented to IFGW-UNICAMP, 06/1992.
·
Title: The Spacetime
Algebra, the Dirac-Hestenes Spinor
and the Theory of the Electron.
Ph. D. thesis (Applied Mathematics) of Jayme Vaz Jr., presented to IMECC‑UNICAMP, 12/1993.
·
Title: A Model of a Classical
Particle with Spin.
M. Sc. thesis (Physics) of Virgínia
Fernandez, presented to IFGW-UNICAMP,
06/08/1995.
·
Title: Lagrangian Formalism for Multivectorial
Fields.
Ph. D. thesis (Apllied
Mathematics) of Antonio Manuel Moya, presented to IMECC-UNICAMP,
05/26/1999.
·
Title: Superluminal Solutions of the
Relativistic Wave Equations and the Principle
of
Relativity.
Ph. D. thesis (Physics) of José Emilio Maiorino, presented to IFGW-UNICAMP, 06/26/1999.
·
Title: The Role of Algebraic Operators in
the Lagrangian Formalism.
Ph. D. thesis (Pure Mathematics) of Alexandre Luis Trovon de Carvalho, presented to IMECC-UNICAMP,
05/05/2000.
·
Title: Distortion and Rotation Extensors
in the Gravitational Theories.
Ph. D. thesis (Physics) of Virginia Velma Fernández,
presented to IFGW-UNICAMP, 11/29/2000.
· Dr. Edmundo Capelas de Oliveira (88/89)
· Dr. Quintino A. Gomes de Souza (92/94)
· Dr. Yuri Bozkhov (94/95)
· Dr. Rodolfo Monaco (1993/1994)
· Dr. Alberto Saa (1996/1997)
· Dr. Bolivar Alves Oliveira (2000/2002).
· Dr. Bolivar Alves Oliveira (2005)
· Dr. Eduardo A. Notte-Cuello (2007)
·
Zeferino Vaz Prize of Academic Merit in
Mathematics,1992.
·
Ordinary member da Lódz Society of Sciences, Polonia,
since 29/05/95.
·
Member of the Editorial
Board of the Journal "Advances in Applied Clifford Algebras".
·
Member of the Editorial
Board of the Journal "Random Operator and Stochastic Equations".
·
Member of the New York Academy
of Sciences.
·
Zeferino Vaz Prize of Academic Merits in
Mathematics, 1998.
·
Listed in several ‘Who
is Who?’ since 1997.
MEMBER OF SCIENTIFIC SOCIETIES
· Sociedade Brasileira de Física
· Sociedade Brasileira de Matemática Aplicada e Computacional
· Sociedade Brasileira de Matemática.
· American Mathematical Society
·
New York Academy of
Sciences
·
Lódz Society of Sciences, Poland
· Chairman of the International
Conference: The Mind‑Matter Interaction,
Hotel Transamerica, São Paulo, SP, July, 1985.
Sponsors: UNICAMP, IBM‑Brasil, Banco Real.
·
Co-Chairman of the
Workshop: Gravitação, Partículas
e Cosmologia, IMECC‑UNICAMP,
2‑5 May 1989.
Sponsors: CNPq, CAPES.
·
Co-Chairman of the
International Conference: 8th Latin American Symposium on Relativity and
Gravitation (SILARG VIII) Águas de Lindóia, 25‑30 de junho de
1993.
Sponsors: CNPq, FAPESP.
·
Member of the Org.
Com.: Banach Center Symposium on
Generalizations of Complex Analysis and The Applications on Mathematical
Physics.("Seminar on Deformations of Mathematical Structures Applied
to Physics), Warsaw, May 30 – July 1,1994.
Sponsor: Polish Academy of Sciences
· Member of the Org. Com. First Brasil/USA
Workshop on Geometry, Topology and Physics, July 1996.
Sponsor: CNPq, FAPESP, FINEP, FAEP
·
Member of the Org. Com.
of the V Friedmann Seminar on Gravitation and Cosmology,
St. Petersburg, Russia, June 1998.
Sponsor: Univ. St. Petersburg, Friedmann Lab. Theor. Physics
· Member of the Scientific. Com. of the VI Int. Conference
on Clifford Algebras, Cookville, TN, May 2002
Sponsors: Americam Mathematical Society, National
Science Foundation
· Member of the Scientific. Com. of the VII Int. Conference
on Clifford Algebras, Toulouse, France, May 2005
Sponsor: Univ. Paul Sabatier,
Toulouse, France.
·
Chairman of the VIII
Int. Conference on Clifford Algebras, Campinas, Brazil, May 2007
Sponsor: University of Campinas
PARTICIPATION
IN CONGRESS, SUMMERS SCHOOLS, ETC.
1.
International School in Sub‑Nuclear Physics ‑
Ettore Majorana ‑
July 1971‑ Erice, Sicília
(Italy).
2. XXIV Reunião da SBPC ‑ (contributed papers) July 1972 ‑ São Paulo.
3. XXV Reunião da SBPC ‑ (contributed papers) July 1973 ‑ Guanabara.
4. 3º Simpósio Nacional de Física do Estado Sólido e Ciência dos Materiais ‑ (contributed papers) July 1973 ‑ Campinas.
5.
XV Scottish Universities Summer School ‑ August 1973 ‑ Edinburg ‑
Scotland.
6.
XXVI Reunião da SBPC ‑ (contributed papers)
July 1974 ‑ Recife.
7.
XVII International Conference on High Energy Physics,
(invited Delegate) London, 1974.
8.
March Meeting of the American Physical Society (contributed
papers),Washington, 1978.
9.
Spring School and Workshop on Supergravity,
ICTP, Trieste, 04/22-06/06, 1981.
10. III Encontro Nacional de Física de Partículas e Campos (contributed papers), Cambuquira, MG, September1981.
11. II Escola de Gravitação e Cosmologia do CBPF ‑ João Pessoa-Pb (1980).
12. III Escola de Gravitação e Cosmologia do CBPF ‑ Rio de Janeiro ‑ RJ (1982).
13. 7º Congresso Nacional de Matemática Aplicada e Computacional, (invited lecturer) Campinas, SP, 24- 28 September 1984.
14.
First International Conference on the Mind‑Matter
Interaction, (organizer) July 1985, São Paulo, Brasil.
15.
XVIII International Cosmic Ray Conference, (contributed paper, 1983, India).
16.
XVII International
Conference on High Energy Physics, (contributed paper), July, 1986, Berkeley,
USA.
17.
Conference: "300
Years of the Discovery of the Law of Gravitation, Brazilian Society for the
Philosophy of Science (invited lecturer), August, 1986, Campinas, Brasil.
18.
Global Conference on
Mathematical Physics (invited lecturer), October, 1987, Nagpur, India.
19.
The Return of the
Galilean Method in Science (invited lecturer), Universitá
di Bologna and Consiglio Nazionale Ricerca (CNR), May
1988, Bologna, Italy.
20.
Conference on the
Status of Experimental and Theoretical Physics, Dep. of Mathematics, (invited
lecturer), Universita di
Perugia, Maio de 1988, Itália.
21.
VII Convegno
Nazionale di Relativita e Fisica della Gravitazione,
Italian Physical Society (lecturer), September, 1988, Cavalese,
Itália.
22.
Conference:
"Physical Interpretations of Relativity Theory", British Society for
the Philosophy of Science, (contributed paper), September, 1988, London, UK.
23.
Conference: Foundations
of the Mathematics and Physics in the XX Century. Renounce to Intuition. (invited lecturer), Univ. di
Perugia, Itália, 27‑29, September, 1989.
24. VII Simposio Latino Americano de Relatividade e Gravitação, México City, November 1990.
25. XII Encontro Nacional de Física de Partículas e Campos, Caxambú, MG, 1991.
26.
III Workshop on
Clifford Algebras and their Applications in Mathematical Physics (invited
lecturer) Deinze, Belgium, May 1993.
27. SILARG VIII "8th Latin American
Symposium on Relativity and Gravitation" (invited lecturer) Águas de Lindóia, July 25‑30,
1995.
28.
International
Conference on the Theory of the Electron (invited lecturer), Univ. Nac. Aut. Mexico, Mexico City, September 27-29, (1995).
29.
IV Workshop
"Clifford Algebras and their Applications in Mathematical Physics,
(invited lecturer) Aachen, Germany, May 1995.
30.
Conference: Physical
Interpretations of Relativity Theory (invited lecturer) London, September 1996.
31.
Conference: Covegno Cartesiano, (invited
lecturer) Univ. Perugia, Italia, September 1996.
32.
Conference:
Superluminal (?) Velocities, (invited lecturer) Univ. Kohln, Germany, 04 - 07 June 1998.
33.
Conference: V Friedmann Seminar on Gravitation and Cosmology, (invited lecturer)
Friedmann Lab. Theor.
Phys., St. Petersburg, Russia, June 16 - 25, 1998.
34.
Bohm Symposium, University of São Paulo,
September 1998.
35.
V Conference on
Clifford Algebras and their Applications in Mathematical Physics (invited lecturer),
México, 27/06-04/07, 1999.
36.
Paulo L. Ferreira
Symposium, Institute of Theoretical Physics, Univ. Estadual
Paulista (UNESP), October 1999.
37. VI
Conference on Clifford Algebras and their Applications in Mathematical Physics,
Cookvile,
USA, May 2002.
38.
VII Conference on
Clifford Algebras and their Applications in Mathematical Physics, Toulouse,
France, May 2005.
1.
Calculation of the
Form Factors in the Soft
Pion Formalism, Atti delle
Accademia delle
Scienze di
Torino 106, 173‑180 (1972).
2.
On the Theory of
Disordered Alloys (with N. J. Parada and A.R. Lopes),
Braz. J. Phys. 4, 263‑281 (1974).
3.
Commentary about
the Large Transverse Secondary Momenta Observed at
the ISR‑CERN (with A. Turtelli Jr. and M. Luksys), Anais da
Acad. Bras. de Ciências 46, 197‑201 (1974).
4.
Pion Inclusive Distributions at Cosmic
Ray Energies and Comparison with ISR Data(with A. Turtelli Jr,), N. Cimento A 23, 227‑236 (1974).
5.
A Comment on a
Proposed Crucial Experiment to Test Einstein's Special Theory of Relativity
(with V. Buonomano), N.
Cimento B 34, 240‑244 (1976).
6.
Discrete “Fireball”
Masses in High Energy Collisions (with C. A. P. Ceneviva), Acta Phys.
Polon.
B 8, 457‑467 (1977).
7.
Single Particle
Green’s Functions Calculations of the Electrical Conductivity of Strong
Correlated Systems, Braz. J. Phys. 9, 109‑122
(1979).
8.
Electronic
Correlations in Narrow‑Band Solids (with Ellen
J. Yoffa and David Adler), Phys. Rev. B
19, 1203‑1212 (1979).
9.
A New Type of
Nuclear Interaction in the
, (with C.M.G. Lattes, Y. Fujimoto et al.) Brazil‑Japan Emulsion Chamber Collaboration, AIP Conference Proc.
49, Particles and Fields 16, 317‑333
(1979).
10.
Multiple Meson
Production in the
Region,
(with C.M.G. Lattes, Y. Fujimoto et al.). Brasil‑Japan Emulsion Chamber Collaboration, AIP Conference Proc.
49, Particles and Fields 16, 94‑109
(1979).
11.
Baryon Pair Production
with Large Decay Q‑value, (Brazil‑Japan
Emulsion Chamber Collaboration, (with C. M. G. Lattes, Y. Fujimoto et al), AIP Conference Proc. 49,
Particles and Fields 16, 145-151 (1979).
12.
Centauro, Geminion
and Multi‑Pion Events (with J. Dias de Deus), N.
Cimento A
55, 34‑44 (1980).
13.
Antiparticles from
Special Relativity with Orthochronous and Antichronous Lorentz
Transformations (with E. Recami), Found. Phys. 12, 709‑718
(1982). MR 831:83006 and MR 87B:83007
14. Objetividade, Convencionalismo e a Teoria da Relatividade (with C.A.P. Ceneviva), Cadernos de História e Filosofia da Ciência 3, 59‑832 (1982).
15.
The Standard of Lenght in the Theory of Relativity and Ehrenfest
Paradox, N. Cimento B 74, 199‑211
(1983).
16.
Chirons, Centauros,
Geminions, Pion
Production: A Phenomenological and Theoretical Analysis (with P. Ammiraju and E.Recami),
N. Cimento
A 78, 172‑204 (1983).
17.
Some Applications
of Non‑Hermitian Operators in Quantum Mechanics
and Quantum Field Theory (with E. Recami and P. Smrz). Hadronic Journal 6, 1773‑1789 (1983).
18.
Einstein's Special
Relativity Versus Lorentz's Aether Theory, (with J.Tiomno), Braz. J. Phys. 14 (volume
dedicated to Mário Schönberg),
450‑465 (1984).
19.
Is Lorentz
Invariance an Exact Symmetry of Nature? Hadronic Journal 7, 436‑455 (1984). MR
87i:83007
20.
On Experiments to
Detect Failures of Relativity Theory (with J. Tiomno),
Found. Phys. 15,
945‑961 (1985).
21.
Lorentz Invariant
Clocks do not Exist, Lett. Nuovo Cimento 44, 510‑512
(1985). MR 87d:83008
22.
Theory of the
Michelson ‑ Morley Experiment in a Gravitational Field (with M.A.F.
Rosa), Lett. Nuovo Cimento 44, 437‑441 (1985).
23.
Tachyons: May They
Have a Role in Elementary Particle Physics?, (with E. Recami), Progress in Particles and Nuclear Physics
15, 499‑517 (1985).
24.
A Comment on the
Null Geodesics Equation in the Schwarzchild Geometry
(with M.A.F. Rosa), Braz. J. Phys. 16, 535‑540 (1986).
25.
A Satisfactory
Formalism for Magnetic Monopoles by Clifford Algebras (with M.A. de Faria Rosa and E. Recami), Phys.Letters
B 173, 233‑236 (1986); P.L. B 188,
511E (1987). MR 87j:81267 and MR 88c:81126
26.
A Comment on the
Proof of Noether’s Theorem in Smooth Manifolds (with
Q.A.G. de Souza), Braz. J. Phys. 16, 541‑549 (1986).
27. Os Taquions (with E. Recami and M. Fracastoro‑Decker), Ciência Hoje 5, 48‑50 (1986).
28.
The Meaning of Time
in Relativity and Einstein’s Later View of the Twin Paradox (with M. A. Faria
Rosa), Found. Phys. 19,
705‑724 (1989). MR 90k:83006
29.
Grassmann’s Fields and Generalized Magnetic
Monopoles (with A. Maia Jr.), Braz. J. Phys. 19, 292‑305
(1989).
30.
A Geometrical
Theory of Non Topological Magnetic Monopoles (with M. A. Faria Rosa), Mod.
Phys. Lett. A 4,
175‑184 (1989). MR 91b:53091
31.
A Comment on the
Twin Paradox and the Hafele‑Keating Experiment
(with E. C. de Oliveira), Phys. Letters A 140, 479‑484 (1989). MR
90m:83007
32.
Physico-Mathematical Approach to
Generalized Monopoles without String (with M. A. Faria
Rosa, A. Maia Jr. and E. Recami), Hadronic
Journal 12, 187‑212 (1989). MR 91f:81240
34.
Magnetic Monopoles
without String by Kahler‑Clifford Algebras
(with M.A. Faria Rosa, A. Maia, Jr., and E. Recami), Mod. Phys. Lett.
A 5, 543‑549 (1990). MR
91i:81106 31.
35.
A Comment on
Generalized Electrodynamics and Dirac Algebras, Found. Phys. Lett. 3, 95‑99
(1990). MR 91d:81106
36.
Dirac and Maxwell
Equations in the Clifford and Spin‑Clifford
Bundles (with E. C. de Oliveira), Int. J. Theor. Phys. 29, 397‑412 (1990). MR
91d:53021
37.
Covariant,
Algebraic and Operator Spinors (with V.L. Figueiredo and E. C. de Oliveira), Int.
J. Theor. Phys. 29,
371‑396 (1990). MR 91d:5302
38.
Magnetic Monopoles
without String in the Kähler‑Clifford Algebra
Bundle: A Geometrical Interpretation (with A. Maia Jr., E. Recami, and M. A. Faria Rosa),
J. Math. Phys. 31,
502‑505 (1990). MR 91d:81158
and MR 92b:81225
39.
Finite Form of a
Generic Proper Orthocronous Lorentz Transformation
and its Dynamical Interpretation (with J. R.R.Zeni), Braz.
J. Phys. 20, 377‑384
(1990).
40.
Formal Structures,
the Concepts of Covariance, Invariance, Equivalent Reference Frames, and the Principle
of Relativity (with M. Scanavini and L. P. Alcantara), Found. Phys. Lett.
3, 59‑79 (1990). MR 91b:83005
41.
Real Spin Clifford
Bundle and the Spinor Structure of Space‑Time (with V. L. Figueiredo),
Int. J. Theor. Phys.
29, 413‑424 (1990). MR 91d:53022
42.
Clifford Algebras
and the Hidden Geometrical Nature of Spinors (with V.
L. Figueiredo and E.C.de Oliveira), Algebras,
Groups and Geom. 7, 153‑198 (1990). MR 92f:15015
43.
The Exponential of
the Generators of the Lorentz Group and the Solution of the Lorentz Force,
(with J. R.R. Zeni), Hadronic
Journal 13, 317‑327 (1990). MR 92b:83007
44.
On Magnetic
Monopoles (without a String) and the Clifford Bundle Formalism, (with E. Recami), Ann. de la Fond. L. de Broglie 16, 1‑12
(1991).
45.
Hadronic Mass Spectra in a Unifield Approach of Strong and Gravitational Theory (with
P. Ammiraju, E. Recami, J. Roversi,
and V.T. Zanchin), Hadronic
Journal 14, 441‑457 (1991).
46.
A Thougthful Study of Proper Orthocronous
Lorentz Transformations by Clifford Algebras (with J. R. R. Zeni), Int. J. Mod. Phys. A 7, 1793‑1817 (1992). MR
93d:15041
47.
Equivalence
of Dirac and Maxwell Equations and Quantum Mechanics, (with J. Vaz, Jr.), Int. J. Theor. Phys. 32, 945‑955
(1993). MR 94h:81051
48.
Comments on Fryberger’s Approach to Generalized Electromagnetism (with
J. Vaz, Jr.), Adv. in Appl. Clifford Alg.
3, 139‑146 (1993). MR 94c:78004
49.
A Generalization of
Dirac Non Linear Electrodynamics, and Spinning Charged Particles (with E. Recami and J. Vaz, Jr.), Found
Phys. 23, 469‑481 (1993). MR 94c:83054
50.
The Clifford Bundle
and the Nature of the Gravitational Field, (with
Q. A. G. de Souza), Found. Phys. 23, 1465‑1490 (1993).
MR 95c:83054
51.
The Relation
between 2‑Spinors and Rotations, (with J. E. Maiorino
and J. R. R. Zeni). Alg. Groups
and Geom. 10, 53‑72 (1993). MR 94i:15023
52.
A Spinor Representation of Maxwell Equations and the Dirac
Equation, (with J.Vaz, Jr.), Hadronic
Journal 16, 129‑135 (1993). MR 94a:81049
53.
Spin and Electron
Structure (with M. Pavsic, E. Recami,
D. G. Maccarrone, F.Raciti
and G. Salesi), Phys. Lett.
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94h:81163
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About Zitterbewegung
and Electron Structure, (with J. Vaz Jr., E.Recami and G.Salesi), Phys. Lett. B 318, 623‑628
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55.
Zitterbewegung and the Electromagnetic Field of
the Electron, (with J. Vaz Jr.), Phys. Lett. B 319, 203‑208
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56.
New Integral
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Arbitrary Potential (with R. L. Monaco), Phys. Lett.
A 179, 235‑238 (1993). MR
94h:81026
57.
Do Neutron Interferometric Experiments Implies that the Neutron Wave Function
is a Covariant Pauli Spinor (with J. E. Maiorino and J. R. Zeni). Adv. in Appl. Clifford Alg. 3, 21‑28 (1993).
58.
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Magnetic Monopoles (with A. Maia Jr.), Mod. Phys. Lett.
A 9, 81‑88 (1994). MR
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The Effective Riemann‑Cartan‑Weyl Space Generated by a Dirac‑Hestenes Spinor
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Q. A. G. de Souza and J. Vaz Jr.), Algebras,
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60.
Electron Structure,
Zitterbewegung and a New Non‑Linear
Dirac‑Like Equation (with M. Pavsic and E. Recami), Hadronic Journal 18, 97-118 (1995).
61.
The Mathematical
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de Souza and Y. Bozhkov), Found. Phys. 25, 871-924 (1995).
MR 95f:53101
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63.
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Fluctuation Double Well. Part B (with A. J. R. Madureira,
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64.
Mass and Energy in
General Relativity (with Y. Bohzkov), Gen. Rel.
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A Riemann Integral
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66.
Taquiones (with E. Recami
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67.
On the Problem of Conformal Coupling in
Field Theory in Curved Spacetime (with A. A. Grib). Cosmol. Grav. 1, 273-276 (1995).
68.
Dirac‑Hestenes Spinor
Fields, in Riemann‑Cartan Spacetimes
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MR 94j:53073
69.
A Unified Theory
for Construction of Arbitrary Speeds 0 £ v < ¥ Solutions of the Relativistic Wave Equations
(with J. E. Maiorino), Random Oper.
Stoch.
Equs. 4, 355-400 (1996). MR 98c:81089
70.
Clifford Algebraical Approach to Particle Lifetimes, (with J. Lawrinowicz), Bull. Soc. Sci. Lódz
XXI, 1-7 (1996). MR 1475 302
71. The Clifford Bundle and the Dynamics of the Superparticle (with J. Vaz, Jr and M Pavsic), Banach Center Publications. Polish Acad. Sci. 37, 295-314 (1996). MR 98i:81091
72. Uma
Topologia mais Fina para o Espaço-Tempo de Minkowski
(with A.L.T. de Carvalho), Bol. Soc. Paran. Mat. 16, 23-38 (1996).
73.
On the Existence of Undistorted
Progressive Waves (UPWs) of Arbitrary Speeds 0 £ v < ¥ in Nature” (with Jian-Yu Lu). Found. Phys. 27, 435-508, (1997)
MR 98f:35144
74.
Subluminal and
Superluminal Solutions in Vacuum of Maxwell and the Massless
Dirac Equation.(with J.Vaz
Jr.). Advances Appl. Clifford Algebras 7(S), 453-462 (1997). MR
98k:81100
75.
Maxwell and Dirac
Theories an Already Unified Theory (with J. Vaz Jr.),
Advances Appl. Clifford Algebras.
7(S), 369-386 (1997). MR 99k:81100
76.
The Exact Bohr-Sommerfeld Quantization Rule (with R. L. Monaco), Random
Oper. Stoch. Equs. 5, 197-202 (1997).
MR 98c:81064
77.
The Geometry of Spacetime with Superluminal Phenomena (with T. Matolcsi), Algebras, Groups and Geom. 15,
1-15 (1997). MR 2000a:83005
78.
Quantum Mechanics
from Complex to Complexified Quaternions
(with S. De Leo), Int. J. Theor. Phys. 36, 2725-2757 (1997). MR
99f:81118
79.
New Solutions of
the Main Relativistic Wave Equations (with J. E. Maiorino
and Y. D. Bozhkov), Seminari di
Geometria, Univ. Bologna 11, 202-229
(1997). MR 99h:81073
80.
Launching of
Non-Dispersive Sub and Superluminal Beams, (with V. Barashenkov),
N. Cimento B 113 (3),
329-338 (1998).
81. On the equation Ñ´ a = k a (with J. Vaz, Jr). Bol. Soc. Par. Matemática 17 (1/2), 19-24 (1998). MR 99j:78011
82.
From
Electromagnetism to Relativistic Quantum Mechanics (with J. Vaz
Jr.), Found. Phys.
28 (5), 789-814 (1998). MR 99i:81073
83.
Quaternionic Electron Theory: Dirac’s Equation
(with S. De Leo), Int. J. Theor. Phys. 37 (5), 1511-1529
(1998). MR 99f:81079
84.
Complex Geometry
and Dirac Equation, (with S. De Leo and J. Vaz, Jr), Int. J. Theor. Phys. 37 (9), 2479-2495 (1998). MR
2000g:81082
85.
Quaternionic Electron Theory: Geometry, Algebra
and Dirac’s Spinors, (with S. De Leo), Int. J. Theor. Phys.,
37 (6), 1707-1720 (1998). MR 99j:81060
86.
Superluminal
Electromagnetic Waves in Free Space (with E. C. Oliveira), Annalen
der Physik
7, 654-659 (1998).
87.
The Electric Field
Outside a Stationary Resistive Wire Carreging a
Constant-Current, (with A. K.T. Assis and A. J.
Mania), Found. Phys. 29
(5), 729-753 (1999). MR 2000e:78002
88.
The Dirac-Hestenes Lagrangian, (with S. De
Leo, Z. Oziewicz and J. Vaz,
Jr), Int. J. Theor.
Phys. 38, 2347-2378
(1999). MR 2002m:81075
89.
What is
Superluminal Wave Motion (with J. E. Maiorino), Sci.
and Tech. Mag. 2 (4), 167 pages, (1999), http://www.ime.unicamp.br/rel_pesq/1999/rp59-99.html
90.
Lagrangian Formalism for Multiform Fields on Minkowski Spacetime (with A. M. Moya and V. V. Fernández), Int.
J. Theor. Phys. 40 (1), 299-313 (2001). MR
2002d: 58025
91.
The non Sequitur
Mathematics and Physics of the ‘New Electrodynamics’ Proposed by
the AIAS Group (with A. L. Trovon de Carvalho), Random Oper. Stoch. Equs.
9 (3), 161-206 (2001). MR 2002d:78002,
http://arxiv.org/abs/physics/0302016
92.
Causal Explanation
of Observed Superluminal Behavior of Microwave Propagation in Free Space (with
D.S. Thober and A.L. Xavier, Jr.), Phys. Lett. A 284(6), 217-224 (2001).
93.
Thoughtful Comments
on ‘Bessel Beams and Signal Propagation’ (with E.C. de Oliveira, D. S. Thober and A.L. Xavier, Jr., Phys. Lett.
A 284(6), 296-303
(2001). MR 2002d:78007
94.
Rotating Frames in RT:
Sagnac’s Effect in SRT and other
Related Issues, (with M. Sharif), Found. Phys. 31(12), 1767-1784 (2001). MR
2003a:83005
95.
Equivalence
Principle and the Principle of Local Lorentz Invariance (with M.Sharif), Found. Phys. 31(12), 1785-1806 (2001). MR
2003a:83006
96.
Finite Energy Superluminal Solutions of Maxwell Equations (with E. C. de
Oliveira), Phys. Lett. A 296(6),
367-370 (2001). MR 1917688
97.
Euclidean
Clifford Algebra (with V. V. Fernández and A.
M. Moya), Advances in Applied Clifford
Algebras 11(S3), 1-21 (2001).
98.
Extensors (with V.
V. Fernández and A. M. Moya),
Advances in Applied Clifford Algebras 11(S3), 23-40 (2001).
99.
Metric Tensor Vs. Metric Extensor (with V. V. Fernández
and A. M. Moya), Advances in Applied Clifford
Algebras 11(S3), 41-48 (2001).
100.
Metric Clifford
Algebra (with V. V. Fernández and A. M. Moya), Advances in Applied Clifford Algebras 11(S3)
49-68, (2001).
101. Multivector Functions of Real Variable (with V.
V. Fernández and A. M. Moya),
Advances in Applied Clifford Algebras 11(S3), 69-77, (2001).
102. Multivector Functions of Mutivector
Variable (with V. V. Fernández and A. M. Moya), Advances in Applied Clifford Algebras 11
(S3), 79-91 (2001).
103. Multivector Functionals
(with V. V. Fernández and A. M. Moya), Advances in Applied Clifford Algebras 11
(S3), 93-103 (2001).
104.
The Relation
between Maxwell, Dirac and the Seiberg-Witten
Equations, International Journal of Mathematics and Mathematical Siciences 2003, 2707-2734 (2003), RP
61/02 IMECC-UNICAMP, math-phys/0212034. MR 2005f:81110
105. Stochastical Electrodynamics in Clifford-Analytical Formulation Related to
Entropy-Depending Strucutres, Bulletin Soc. des
Sci. et Lettres de Lódz,
LIII, series Recherches sur
les Deformations XL1, 69-87 (2003). MR 2006k:78003
106.
Algebraic and Dirac-Hestenes Spinors and Spinor Fields, J. Math. Phys. 45 (7), 2908-2994 (2004). MR
2006B:61113
107.
The Bundles of
Algebraic and Dirac-Hestenes Spinor
Fields (with R. A. Mosna). J. Math. Phys. 45(7), 2945-2966
(2004). MR 2006b:61114
108. Dotted and Undotted
Algebraic Spinor Fields in General Relativity (with
E. Capelas de Oliveira, Int. J. Mod. Phys. D 13(8), 1637-1659
(2004). MR 2005g:83081 and
MR 2133771
109. Clifford Valued Differential Forms
and Some Issues on Gravitation, Electromagnetism and
“Unified” Theories (with E. Capelas de Oliveira), Int.
J. Mod. Phys. D 13(9),
1879-1915 (2004). MR 2005m:83110
and MR 2346632
110.
Hidden Consequence
of Active Local Lorentz Invariance (with R. da Rocha and J. Vaz
Jr.), Int. J. Geom. Meth. Mod. Phys. 2, 305-357 (2005). MR
2006g:81070
111. An Ambiguous Statement Called
‘Tetrad Postulate’ and the Correct Field Equations Satisfied by the Tetrad
Fields (with Q. A. G. de Souza) Int. J. Mod. Phys. D 14(12),
2095-2150 (2005), MR 2007a:83003 [http://arxiv.org/abs/math-ph/0411085]
112.
Where are Elko Spinor fields in Lounesto Spinor Field Classification? (with
R. da Rocha), Mod. Phys. Lett. A
21 (1),
65-74 (2006). MR 2006i:81091 [http://arxiv.org/abs/math-ph/0506075]
113.
The
Einstein-Hilbert Lagrangian Density in a
2-dimensional Spacetime is an Exact Differential
(with R. da Rocha), Mod. Phys. Lett. A 21 (19),
1519-1527 (2006).MR 2007b:83140 [http://arxiv.org/abs/hep-th/0512168]
114.
The Dirac–Hestenes Equation for Spherical Symmetric Potentials in the
Spherical and Cartesian Gauges (with R. da Rocha), Int. J. Mod. Phys. A 21, (19-20), 4071-4082 (2006). MR
2007f:81124 [http://arxiv.org/abs/math-ph/0601018]
115.
A Comment on "On
Some Contradictory Computations in Multi-dimensional Mathematics" (with E.
Capelas de Oliveira), Nonlinear Analysis: Theory,
Methods & Applications 67 (7), 2316-2320 (2007). MR 2331882 [http://arxiv.org/abs/math.GM/0603599]
116.
A Maxwell Like Formulation of Gravitational Theory in Minkowski Spacetime (with E.
Notte-Cuello), Int. J. Mod. Phys. D 16, 1027-1041 (2007), MR 2008g:83065
[http://arxiv.org/abs/math-ph/0608017]
117.
Geometric Algebras
and Extensors (with V. V. Fernández and A. M. Moya), Int. J.
Geom. Meth. Math. Phys 4 (6),
927-964(2007). MR 2352860 [http://arxiv.org/abs/math.DG/0703090]
118.
Multivector and Extensor Fields in Smooth
Manifolds (with V. V. Fernández and A. M. Moya), Int. J. Geom. Meth. Math.
Phys. 4 (6), 965-985 (2007). MR
2352861 [http://arxiv.org/abs/math.DG/0501559]
119.
Geometric and and Extensor Algebras in the Study of the Differential
Geometry of Arbitrary Manifolds (with V. V. Fernández
and A. M. Moya), Int. J. Geom. Meth. Math. Phys. 4 (7),1117-1158 (2007). MR 2371936 [http://arxiv.org/abs/math.DG/0703094]
120.
Clifford and
Extensor Calculus and the Riemann and Ricci Extensor Fields of Deformed
Structures (M,∇′,
η) and (M,∇,g)
(with V. V. Fernández , A. M. Moya and R. da Rocha), Int.
J. Geom. Meth. Math. Phys. 4 (7),
1159-1172 (2007). MR 2371937 [http://arxiv.org/abs/math.DG/0502003]
121.
Conservation Laws on
Riemann-Cartan, Lorentzian
and Teleparallel Spacetimes
I. Conservation Laws, (with Q. A. G. de Souza and R. da Rocha), Bulletin Soc. des
Sci. et Lettres de Lódz 57 , Ser. Recherches sur les Deformations
52, 37-65 (2007) [http://arxiv.org/abs/math-ph/0605008]
122.
Conservation Laws on
Riemann-Cartan, Lorentzian
and Teleparallel Spacetimes
II. Appendix on Clifford Bundles, Maxwell Theory and Teleparallel
Spacetimes, (with Q. A. G. de Souza and R. da Rocha),
Bulletin Soc. des
Sci. et Lettres de Lódz 57, Ser. Recherches sur les Deformations
52, 66-77 (2007) [http://arxiv.org/abs/math-ph/0605008]
123.
The Hyperbolic
Clifford Algebra of Multivecfors (with Q. A. G.
Souza), Algebras, Groups and Geometries 24 (1), 1-24
(2007), MR 2008h:15025 [http://arxiv.org/abs/math-ph/0703053]
124.
Duality Products of
Multivectors and Multiforms
and Extensors (with V. V. Fernández, A. M. Moya and E. A. Notte-Cuello), Algebras, Groups and
Geometries 24 (1), 25-54 (2007), MR 2008f:15095 [http://arxiv.org/abs/math-ph/0703054]
125.
Parallelism Structure
on a Smooth Manifold, (with V. V. Fernández, A. M. Moya and E. A. Notte-Cuello), Algebras, Groups and
Geometries 24 (2), 129-155 (2007), MR
2008g:53022 [http://arxiv.org/abs/math-ph/0703055]
126. Covariant Derivatives of Multivector and Multiform Fields, (with V. V. Fernández, A. M. Moya and E. A.
Notte-Cuello), Algebras, Groups and Geometries 24 (2), 221-237
(2007), MR 2345853 [http://arxiv.org/abs/math-ph/0703056]
127. Covariant Derivatives of Extensor
Fields, (with V. V. Fernández, A. M. Moya and E. A. Notte-Cuello), Algebras, Groups and
Geometries 24 (3), 255-267 (2007). MR 2384680
[http://arxiv.org/abs/math-ph/0703057v1]
128. The
Square of the Dirac and spin-Dirac Operators on a Riemann-Cartan
Space(time) (with E. A. Notte-Cuello and Q. A. G. de
Souza), Rep. Math. Phys. 60,
135-157 (2007). [http://arxiv.org/abs/math-ph/0703052]
129. Differential Forms on
Riemannian (Lorentzian) and Riemann-Cartan Structures and Some Applications to Physics, Ann. Fond. L. de Broglie 32 (4), 425-478 (2007). [http://arxiv.org/abs/0712.3067v3.pdf]
130.
Freud's Identity of Differential Geometry, the Einstein-Hilbert Equations and the
Vexatious Problem of the Energy-Momentum
Conservation in GR (with E. Notte-Cuello) Advances in Applied Clifford Algebras
19 (1), 113-145, (2009).[http://arxiv.org/abs/0801.2559]
131. Diffeomorphism Invariance and Local Lorentz Invariance
(with R. da Rocha), Advances in Applied Clifford Algebras 18 (3-4), 945-961
(2008).[http://arxiv.org/abs/math-ph/0510026]
132. The
Effective Lorentzian and Teleparallel
Spacetimes Generated by a Free
Electromagnetic Field (with E. Notte-Cuello and R. da Rocha),
Rep. Math. Phys. 62(3),
69-89 (2008). [http://arxiv.org/abs/gr-qc/0612098]
133. Superposition Principle and the Problem of the
Additivity of the Energies and Momenta
of Distinct Electromagnetic Fields (with E. Notte-Cuello), Rep. Math.
Phys. 62(3), 91-101 (2008).[http://arxiv.org/abs/math-ph/0612036]
B. BOOK CHAPTERS