Algebraic and Dirac-Hestenes spinors and spinor fields

Journal of Mathematical Physics

Volumn 45, Issue 7, 2004, Pages 2908-2944

  Rodrigues Jr , Waldyr A ^a  

^a UNIVERSITY OF CAMPINAS   (Brazil)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 3543081718     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1757037     Document Type: Article

References (171)

1. Ablamowicz, R. and Fauser, B. (eds.), Clifford Algebras and their Applications in Mathematical Physics, Vol. 1; Algebra and Physics (Birkhauser, Boston 2000).
2. Ablamowicz, R. (ed.), Clifford Algebras, Progress in Mathematical Physics 34 (Birkhauser, Boston, 2004).
3. Ablamowicz, R. and Sobczyk, G. (eds.), Lectures on Clifford (Geometric) Algebras and Applications (Birkhauser, Boston, 2004).
4. Adler, S. L., Quaternionic Quantum Mechanics and Quantum Fields (Oxford University Press, Oxford, 1995).
5. Aharonov, Y. and Susskind, L., "Observality of the sign of spinors under a 2π rotation," Phys. Rev. 158, 1237-1238 (1967).
6. Atyah, M. F., Bott, R., and Shapiro, A., "Clifford modules," Topology 3, 3-38 (1964).
7. Ashdown, M. A. J., Somarro, S. S., Gull, S. F., and Doran, C. J. L., "Multilinear representations of rotation groups within geometric algebra," J. Math. Phys. 39, 1566-1588 (1998).
8. Barut, A. O. and Bracken, X., "Zitterbewegung and the internal geometry of the electron," Phys. Rev. D 23, 2454-2463 (1981).
9. Barut, A. O. and Zanghi, N., "Classical model of the Dirac electron," Phys. Rev. Lett. 52, 2009-2012 (1984).
10. Barut, A. O., "Excited states of Zitterbewegung," Phys. Lett. B 237, 436-439 (1990).
11. Baylis, W. E. (ed.), Clifford (Geometric) Algebras with Applications in Physics, Mathematics and Engineering (Birkhäuser, Boston, 1996).
12. Baylis, W., Electrodynamics, A Modern Geometric Approach (Birkhauser, Boston, 1999).
13. Bjorken, J. D. and Drell, S., Relativistic Quantum Mechanics (McGraw-Hill, New York, 1964).
14. Been, I. M. and Tucker, R. W., An Introduction to Spinors and Geometries with Applications in Physics (Hilger, Bristol.
15. Been, I. M. and Tucker, R. W., ''Representing spinors with differential forms," in Spinors in Physics and Geometry, edited by A. Trautman and G. Furlan (World Scientific, Singapore, 1988).
16. Berezin, F. A., The Method of Second Quantization (Academic, New York, 1996).
17. Berezin, F. A. and Marinov, M.S., "Particle spin dynamics as the Grassmann variant of classical mechanics." Ann. Phys. (N.Y.) 104, 336-362 (1997).
18. Bayro-Corrochano, E. and Zhang, Y. A., "The motor extended Kalman filter: A geometrical approach for 3D rigid motion estimation," J. Math. Imaging Vision 13, 205-227 (2000).
19. Bayro-Corrochano, E., Geometrical Computing for Perception Action Systems (Springer, Berlin, 2001).
20. Blaine Lawson, H., Jr. and Michelshon, M. L., Spin Geometry (Princeton University Press, Princeton, NJ, 1989).
21. Bleecker, D., Gauge Theory and Variational Principles (Addison-Wesley Reading, MA, 1981).
22. Brauer, R. and Weyl, H., "Spinors in n dimensions," Am. J. Math. 57, 425-449 (1935).
23. Budinich, P., and Trautman, A., The Spinorial Chessboard (Springer, Berlin, 1998).
24. Cartan, E., The Theory of Spinors (MIT Press, Cambridge, MA, 1996).
25. Castro, C., "Hints of a new relativity principle from p-brane quantum mechanics," Chaos, Solitons Fractals 11, 1721-1737 (2000).
26. Castro, C., "The status and programs of the new relativity theory," Chaos, Solitons Fractals 12, 1585-1606 (2001).
27. Castro, C., "The string uncertainty relations follow from the new relativity principle," Found. Phys. 30, 1301-1316 (2000).
28. Castro, C., "Is quantum spacetime infinite dimensional," Chaos, Solitons Fractals 11, 1663-1670 (2000).
29. Castro, C., Noncommutative quantum mechanics and geometry from quantization in C-spaces, hep-th/0206181.
30. Castro, C., "A derivation of the black-hole area-entropy relation in any dimension," Entropie 3, 12-26 (2001).
31. Castro, C. and Granik, A., "Extended scale relativity, p-loop harmonic oscillator and logarithmic corrections to the black hole entropy," Found. Phys. 33, 445-466 (2003).
32. Castro, C. and Pavsic, M., "Higher derivative gravity and torsion from the geometry of C-spaces," Phys. Lett. B 539, 133-142 (2002).
33. Castro, C., "Generalized p-forms electrodynamics in Clifford space," Mod. Phys. Lett. A 19, 19-29 (2004).
34. Castro, C. and Pavsic, M., "The extended relativity theory in Clifford spaces," Int. J. Mod. Phys. (to be published).
35. Challinor, A., Lasenby, A., Doran, C., and Gull, S., "Massive, non-ghost solutions for the Dirac field coupled self-consistently to gravity," Gen. Relativ. Gravit. 29, 1527-1544 (1997).
36. Challinor, A., Lasenby, A., Somaroo, C., Doran, C., and Gull, S., "Tunnelling times of electrons," Phys. Lett. A 227, 143-152 (1997).
37. Challinor, A., Lasenby, A., and Doran, C., "A relativistic, causal account of spin measurement," Phys. Lett. A 218, 128-138 (1996).
38. Chevalley, C., The Algebraic Theory of Spinors (Columbia University Press, New York, 1954).
39. Chevalley, C., The Algebraic Theory of Spinors and Clifford Algebras. Collect Works Vol. 2 (Springer-Verlag, Berlin, 1997).
40. Choquet-Bruhat, Y., Géométrie Différentielle et Systèmes Extérieurs (Dunod, Paris, 1968).
41. Choquet-Bruhat, Y., DeWitt-Morette, C., and Dillard-Bleick, M., Analysis, Manifolds and Physics, revised edition (North-Holland, Amsterdam, 1982).
42. Colombo, F., Sabadini, I., Sommen, F., and Struppa, D. C. (eds.), Computational Algebraic Analysis, Progress in Mathematical Physics (Birkhauser, Boston, 2004).
43. Crawford, J., "On the algebra of Dirac bispinor densities: Factorization and inversion theorems," J. Math. Phys. 26, 1439-144) (1985).
44. Crummeyrolle, A., Orthogonal and Sympletic Clifford Algebras (Kluwer Academic, Dordrecht, 1991).
45. Daviau, C., Equation de Dirac non Linéaire, Thèse de doctorat, Univ. de Nantes, 1993.
46. Daviau, C., "Solutions of the Dirac equation and a non linear Dirac equation for the hydrogen atom," Adv. Appl. Clifford Algebras 7, 175-194 (1997).
47. Delanghe, R., Sommen, F., and Souček, V., Clifford Algebra and Spinor-Valued Functions: A Function Theory for the Dirac Operator, Mathematics and its Applications 53 (Kluwer Academic, Dordrecht, 1992).
48. De Leo, S. and Rodrigues, W. A., Jr., "Quantum mechanics: From complex to complexified quaternions," Int. J. Theor. Phys. 36, 2725-2757 (1997).
49. De Leo, S. and Rodrigues, W. A., Jr., "Quaternionic electron theory: Dirac's equation," Int. J. Theor. Phys. 37, 1511-1529 (1998).
50. De Leo, S. and Rodrigues, W. A., Jr., "Quaternionic electron theory: Geometry, algebra and Dirac's spinors," Int. J. Theor. Phys. 37, 1707-1720 (1998).
51. De Leo, S., Rodrigues, W. A., Jr., and Vaz, J., Jr., "Complex geometry and Dirac equation," Int. J. Theor. Phys. 37, 2415-2431 (1998).
52. De Leo, S., Rodrigues, W. A., Jr., and Vaz, J., Jr., "Dirac-Hestenes Lagrangian," Int. J. Theor. Phys. 38, 2349-2369 (1999).
53. Dirac, P. A. M., "The quantum theory of the electron," Proc. R. Soc. London, Ser. A 117, 610-624 (1928).
54. Doran, C. J. L., Lasenby, A., Challinor, A., and Gull, S., "Effects of spin-torsion in gauge theory gravity," J. Math. Phys. 39, 3303-3321 (1998).
55. Doran, C. J. L., Lasenby, A., and Gull, S., "The physics of rotating cylindrical strings," Phys. Rev. D 54, 6021-6031 (1996).
56. Doran, C. J. L., Lasenby, A., Somaroo, S., and Challinor, A., "Spacetime algebra and electron physics," Adv. Imaging Electron Phys. 95, 271-386 (1996).
57. Doran, C. J. L., "New form of the Kerr solution," Phys. Rev. D 61, 067503 (2000).
58. Doran, C. and Lasenby, A., Geometric Algebra for Physicists (Cambridge University Press, Cambridge, 2003).
59. Dorst, L., Doran, C., and Lasenby, J. (eds.), Applications of Geometric Algebra in Computer Science and Engineering (Birkhauser, Boston, 2002).
60. Fauser, B., "A treatise on quantum Clifford algebras," math.QA/022059.
61. Felzenwalb, B., Álgebras de Dimensão Finita [Instituto de Matemática Pura e Aplicada (IMPA), Rio de Janeiro, 1979].
62. Fernández, V. V., Moya, A. M., and Rodrigues, W. A., Jr., "Covariant Derivatives on Minkowski Manifolds," in Clifford Algebras and their Applications in Mathematical Physics, Vol. 1: Algebra and Physics, edited by R. Ablamowicz and B. Fauser (Birkhauser, Boston, 2000).
63. Fernández, V. V., Moya, A. M., and Rodrigues, W. A., Jr., "Euclidean Clifford Algebra Space," Adv. Appl. Clifford Algebras 11, 1-21 (2001).
64. Fernández, V. V., Moya, A. M., and Rodrigues, W. A., Jr., "Extensors," Adv. Appl. Clifford Algebras 11, 23-43 (2001).
65. Fernández, V. V., Moya, A. M., and Rodrigues, W. A., Jr., "Metric tensor vs metric extensor," Adv. Appl. Clifford Algebras 11, 43-51 (2001).
66. Fierz, M., "Zur FermischenTheorie des β-zerfals," Z. Phys. 104, 553-565 (1937).
67. Figueiredo, V. L., Rodrigues, W. A., Jr., and Oliveira, E. C., "Covariant, algebraic and operator spinors," Int. J. Theor. Phys. 29, 371-395 (1990).
68. Figueiredo, V. L., Rodrigues, W. A., Jr., and Oliveira, E. C., "Clifford algebras and the hidden geometrical nature of spinors," Algebras, Groups Geom. 7, 153-198 (1990).
69. Frankel, T., The Geometry of Physics (Cambridge University Press, Cambridge, 1997).
70. Furuta, S., Doran, C. J. L., and Havel, S.-G. "Measurement with SAW-guided electrons," Proceedings, Sixth International Conference on Clifford Algebras and their Applications, Tennessee, 2002.
71. Gsponer, A., "On the 'Equivalence' of Maxwell and Dirac equations," Int. J. Theor. Phys. 41, 689-694 (2002).
72. Geroch, R., "Spinor structure of spacetimes in general relativity. I," J. Math. Phys. 9, 1739-1744 (1968).
73. Graf, W., "Differential forms as spinors," Ann. Inst. Henri Poincare, Sect. A 29, 85-109 (1978).
74. Gull, S. F., Lasenby, A. N., and Doran, C. J. L., "Electron paths tunnelling and diffraction in the spacetime algebra," Found. Phys. 23, 1329-1356 (1993).
75. Gurtler, R. and Hestenes, D., "Consistency in the formulation of Dirac, Pauli and Schrodinger theories," J. Math. Phys. 16, 573-583 (1975).
76. Harvey, F. R., Spinors and Calibrations (Academic, San Diego, 1990).
77. Havel, T. F., Doran, C. J. L., and Furuta, S., "Density operators in the multiparticle spacetime algebra," Proc. R. Soc. (to be published).
78. Hermann, R., Spinors, Clifford and Caley Algebras, Interdisciplinariy Mathematics Vol. VII (Rutgers University, New Brunswick, NJ, 1974).
79. Hestenes, D., Space-Time Algebra (Gordon and Breach, New York, 1966, 1987, 1992).
80. Hestenes, D., "Real spinor fields," J. Math. Phys. 8, 798-808 (1967).
81. Hestenes, D., "Observables, operators, and complex numbers in Dirac theory," J. Math. Phys. 16, 556-571 (1975).
82. Hestenes, D., "Local observables in Dirac theory," J. Math. Phys. 14, 893-905 (1973).
83. Hestenes, D., "Proper particle mechanics," J. Math. Phys. 15, 1768-1777 (1974).
84. Hestenes, D., "Proper dynamics of a rigid point particle," J. Math. Phys. 15, 1778-1786 (1974).
85. Hestenes, D., "Observables operators and complex numbers in the Dirac theory," J. Math. Phys. 16, 556-572 (1975).
86. Hestenes, D. and Sobczyk, G., Clifford Algebra to Geometrical Calculus (Reidel, Dordrecht, 1984, 1987).
87. Hestenes, D., "Space-time structure of weak and electromagnetic interactions," Found. Phys. 12, 153-168 (1982).
88. Hestenes, D., "Quantum mechanics from self-interaction," Found. Phys. 15, 63-87 (1985).
89. Hestenes, D., "The Zitterbewegung interpretation of quantum mechanics," Found. Phys. 20, 1213-1232 (1990).
90. Hestenes, D., "A spinor approach to gravitational motion and precession," Int. J. Theor. Phys. 25, 1013-1028 (1986).
91. Hestenes, D., "Invariant body kinematics I: Saccadic and compensatory eye movements," Neural Networks 7, 65-77 (1993).
92. Hestenes, D., "Invariant body kinematics II: Reaching and neurogeometry," Neural Networks 7, 79-88 (1993).
93. Hladik, J., Spinors in Physics (Springer-Verlag, Berlin, 1999).
94. Hurley, D. J. and Vandyck, M. A., Geometry, Spinors and Applications (Springer-Verlag, Berlin, 1999).
95. Ivanenko, D. and Obukov, N. Yu., "Gravitational interaction of fermion antisymmetric connection in general relativitiy," Ann. Phys. (N.Y.) 17, 59-70 (1985).
96. Jancewicz, B., Multivectors and Clifford Algebra in Electrodynamics (World Scientific, Singapore, 1989).
97. Kähler, E., "Der innere differentialkalkül," Rediconti Matematica Appl 21, 425-523 (1962).
98. Knus, M. A., Quadratic forms, Clifford Algebras and Spinors [Univ. Estadual de Campinas (UNICAMP), Campinas, 1988].
99. Lasenby, J., Bayro-Corrochano, E. J., Lasenby, A., and Sommer, G., "A new methodology for computing invariants in computer vison," in IEEE Proc. of the International Conf. on Pattern Recognition, ICPR' 96, Viena, Austria, vol. 1, 93-397 (1996).
100. Lasenby, J. and Bayro-Corrochano, E. J., "Computing 3D projective invariants from points and lines," in Computer Analysis of Images and Patterns, edited by G. Sommer, K. Daniilisis, and X. Pauli, 7th Int. Conf., CAIP' 97, Kiel (Springer-Verlag, Berlin, 1997), pp. 82-89.
101. Lasenby, J. and Bayro-Corrochano, E. J., "Analysis and computation of projective invariants from multiple views in the geometrical algebra framework," Int. J. Pattern Recognit. Artif. Intell. 13, 1105-1121 (1999).
102. Lasenby, A. and Doran, C., ''Grassmann calculus, pseudoclassical mechanics and geometric algebra," J. Math. Phys. 34, 3683-3712 (1993).
103. Lasenby, A., Doran, C., and Gull, S., "Gravity, gauge theories and geometric algebra," Philos. Trans. R. Soc. London, Ser. A 356, 487-582 (1998).
104. Lasenby, J., Lasenby, A. N., and Doran, C. J. L., "A unified mathematical language for physics and engineering in the 21st century," Philos. Trans. R. Soc. London, Ser. A 358, 21-39 (2000).
105. Lasenby, A. and Doran, C. J. L., "Geometric algebra, Dirac wavefunctions and black holes," in Advances in the Interplay Between Quantum and Gravity Physics, edited by P. G. Borgmann and V. de Sabbata (Kluwer Academic, Dordrecht, 2002), pp. 251-283.
106. Lichnerowicz, A., "Champs spinoriales et propagateurs en relativité générale," Ann. Inst. Henri Poincare, Sect. A 13, 233-20 (1964).
107. Lewis, A., Doran, C., and Lasenby, A., "Electron scattering without spin sums," Int. J. Theor. Phys. 40, 363-375 (2001).
108. Lichnerowicz, A., "Champ de Dirac, Champ du neutrino et transformations C, P, T sur un espace temps courbe," Bull. Soc. Math. France 92, 11-100 (1984).
109. Lounesto, P., Clifford Algebras and Spinors, 2nd ed. (Cambridge University Press, Cambridge, 2001).
110. Marchuck, N., "A Concept of Dirac-type tensor equations," math-ph/0212006.
111. Marchuck, N., "Dirac-type tensor equations with non Abelian gauge symmetries on pseudo-Riemannian space,"Nuovo Cimento Soc. Ital. Fis., B 117B, 613-614 (2002).
112. Marchuck, N., "The Dirac equation vs. the Dirac type tensor equation," Nuovo Cimento Soc. Ital. Fis., B 117B, 511-520 (2002).
113. Marchuck, N., "Dirac-type equations on a parallelisable manifolds," math-ph/0211072.
114. Marchuck, N., "Dirac-type tensor equations with non-Abelian gauge symmetries on pseudo-Riemannian space," Nuovo Cimento Soc. Ital. Fis., B 117B, 95-120 (2002).
115. Marchuck, N., "The tensor Dirac equation in Riemannian space," math-ph/0010045.
116. Marchuck, N., "A tensor form of the Dirac equation," math-ph/0007025.
117. Marchuck, N., "A gauge model with spinor group for a description of a local interaction of a Fermion with electromagnetic and gravitational fields," Nuovo Cimento Soc. Ital. Fis., B 115B, 11-25 (2000).
118. Marchuck, N., "Dirac gamma-equation, classical gauge fields and Clifford algebra," math-ph/9811022.
119. Matteuci, P., "Gravity, spinors and gauge natural bundles," Ph.D. thesis, Univ. Southampton (2003). http:// www.maths.soton.ac.uk/~pnm/ phdthesis.pdf
120. Miller, W., Jr., Symmetry Groups and their Applications (Academic, New York, 1972).
121. Miralles, D. E., "Noves Applications de l'Algebra Geomètrica a la Física Matemàtica," Ph.D. thesis, Department de Física Fonamental, Universitat de Barcelona, 2001.
122. Misner, C. W. and Wheeler, J. A., "Classical physics as geometry-gravitation, electromagnetism, unquantized charge, and mass as properties of curved empty space," Ann. Phys. (N.Y.) 2, 525-603 (1957).
123. 2-gradings Clifford algebras," Int. J. Theor. Phys. 41, 1651-1671 (2002).
124. 2- gradings on Clifford algebras and multivector structures," J. Phys. A 36, 4395-4405 (2003).
125. Mosna, R. A. and Vaz, J., Jr., "Quantum tomography for Dirac spinors," Phys. Lett. A 315, 418-425 (2003).
126. Mosna, R. A. and Rodrigues, W. A., Jr., "The bundles of algebraic and Dirac-Hestenes spinor fields," J. Math. Phys. (in press).
127. Moya, A. M., Fernández, V. V., and Rodrigues, W. A., Jr., "Metric Clifford algebra," Adv. Appl. Clifford Algebras 11, 53-73 (2001).
128. Moya, A.M., Fernández, V. V., and Rodrigues, W. A., Jr., "Multivector functions of a real variable," Adv. Appl. Clifford Algebras 11, 75-83 (2001).
129. Moya, A. M., Fernández, V. V., and Rodrigues, W. A., Jr., "Multivector functions of mutivector variable," Adv. Appl. Clifford Algebras 11, 85-98 (2001).
130. Moya, A. M., Fernández, V. V., and Rodrigues, W. A., Jr., "Multivector Functional," Adv. Appl. Clifford Algebras 11, 99-109 (2001).
131. Naber, G. L., "Topology," Geometry and Gauge Fields. Interactions, Appl. Math. Sci. 141 (Springer-Verlag, New York, 2000).
132. Nakahara M., "Geometry," Topology and Physics (Institute of Physics, Bristol, 1990).
133. Nicolescu, L. I., Notes on Seiberg-Witten Theory, Graduate Studies in Mathematics 28 (AMS, Providence, RI, 2000).
134. Oliveira, E. C. and Rodrigues, W. A., Jr., "Clifford valued differential forms, algebraic spinor fields, gravitation, electromagnetism and "Unified" theories," math-ph/0311001.
135. Pavšic, M., Recami, E., Rodrigues, W. A., Jr., Macarrone, G. D., Racciti, F., and Salesi, G., "Spin and Electron Structure," Phys. Lett. B 318, 481-488 (1993).
136. Pav̌sic, M., The Landscape of Theoretical Physics: A Global View-From Point Particles to the Brane World and Beyond in Search of a Unifying Principle, Fundamental Theories of Physics 119 (Kluwer Academic, Dordrecht, 2001).
137. Pav̌sic, M., "Clifford algebra based polydimensional relativity and relativistic dynamics," Found. Phys. 31, 1185-1209 (2001).
138. Pav̌sic, M., "How the geometric calculus resolves the ordering ambiguity of quantum theory in curved space," Class. Quantum Grav. 20, 2697-2714 (2003).
139. Penrose, R. and Rindler, W., Spinors and Spacetitne (Cambridge University Press, Cambridge, 1986), Vol. 1.
140. Pezzaglia, W. M., Jr., "Dimensionality democratic calculus and principles of polydimensional physics," in Clifford Algebras and their Applications in Mathematical Physics, Vol 1: Algebras and Physics, edited by R. Ablamowicz and B. Fauser (Birkhauser, Boston, 2000).
141. Porteous, I. R., Topological Geometry, 2nd ed. (Cambridge University Press, Cambridge, 1981).
142. Porteous, I. R., Clifford Algebras and the Classical Groups, 2nd ed. (Cambridge University Press, Cambridge, 2001).
143. Rainich, G. Y., "Electromagnetism in general relativity," Trans. Am. Math. Soc. 27, 106-136 (1925).
144. Raševskil, P. K., "The theory of spinors," Usp. Mat. Nauk 10, 3-110 (1955).
145. Ryan, J. and Sproessig, W., Clifford Algebras and their Applications in Mathematical Physics, Vol 2: Clifford Analysis (Birkhauser, Boston, 2000).
146. Riesz, M., Clifford Numbers and Spinors, The Institute for Fluid Mechanics and Applied Mathematics, Lecture Series 28, Univ. Maryland, 1958. Reprinted as facsimile, E. F. Bolinder, and P. Lounesto (eds.) (Kluwer Academic, Dordrecht, 1993).
147. Riesz, M., "L' equation de Dirac en relativité générale," Skandinaviska Matematikerkongressen i Lund 1953, pp. 241-259, Håkan Ohlssons Boktryckeri, Lund, 1954. Reprinted in L. Gårdening and L. Hömander (eds.), Marcel Riez, Collected Papers (Springer, New York, 1988), pp. 814-832.
148. Riesz, M., "L' equation de Dirac en relativité générale," Skandinaviska Matematikerkongressen i Lund 1953, pp. 241-259, Håkan Ohlssons Boktryckeri, Lund, 1954. Reprinted in L. Gårdening and L. Hömander (eds.), Marcel Riez, Collected Papers (Springer, New York, 1988), pp. 814-832.
149. Rodrigues, W. A., Jr. and Oliveira, E. C., "Dirac and Maxwell equations in the Clifford and spin-Clifford bundles," Int. J. Theor. Phys. 29, 397-411 (1990).
150. Rodrigues, W. A., Jr., and Vaz, J., Jr., "About Zitterbewegung and electron structure," Phys. Lett. B 318, 623-628 (1993).
151. Rodrigues, W. A., Jr., Souza, Q. A. G., Vaz, J., Jr., and Lounesto, P., "Dirac-Hestenes spinor fields on Riemann-Cartan manifolds," Int. J. Theor. Phys. 35, 1854-1900 (1995).
152. Rodrigues, W. A., Jr., Souza, Q. A. G., and Vaz, J., "Spinor fields and superfields as equivalence classes of exterior algebra fields," in Clifford Algebras and Spinor Structures, edited by R. Abramovicz and P. Lounesto (Kluwer Academic Dordrecht, 1995), pp. 177-198.
153. Rodrigues, W. A., Jr., Vaz, J., Jr., and Pavšic, M., "The Clifford bundle and the dynamics of the superparticle," Banach Cent Publ. 37, 295-314 (1996).
154. Rodrigues, W. A., Jr., and Vaz, J., Jr., "From electromagnetism to relativistic quantum mechanics," Found. Phys. 28, 789-814 (1998).
155. Rodrigues, W. A., Jr., and Souza, Q. A. G., "The Clifford bundle and the nature of the gravitational field," Found. Phys. 23, 1465-1490 (1993).
156. Rodrigues, W. A., Jr., "Maxwell-Dirac equivalences of the first and second kinds and the Seiberg-Witten equations," Int. J. Math. Math. Sci. 2003, 2707-2734 (2003).
157. Rodrigues, W. A., Jr., and Sharif, M., "Rotating frames in SRT: The Sagnac effect and related issues," Found. Phys. 31, 1785-1783 (2001).
158. Rodrigues, W. A., Jr., and Sharif, M., "Equivalence principle and the principle of local Lorentz invariance," Found. Phys. 31, 1785-186 (2001).
159. Sachs, R. K. and Wu, H., General Relativity for Mathematicians (Springer-Verlag, New York, 1997).
160. Seiberg, N. and Witten, E., "Monopoles, duality and chiral symmetry breaking in N=2 QCD," Nucl. Phys. B 431, 581-640 (1994).
161. Somaroo, S. S., Lasenby, A., and Doran, C., "Geometric algebra and the causal approach to multiparticle quantum mechanics," J. Math. Phys. 40, 3327-3340 (1999).
162. Sommer, G. (ed.), Geometric Computing with Clifford Algebra (Springer-Verlag, Heidelberg, 2000).
163. Streater, R. F. and Wightman, A. S., PCT, Spin & Statistics, And All That (Benjamin, New York, 1964).
164. Trayling, G. and Baylis, W., "A geometric basis for the standard-model gauge group," J. Phys. A 34, 3309-3324 (2001).
165. Vaz, J., Jr., and Rodrigues, W. A., Jr., "Equivalence of Dirac and Maxwell equations and quantum mechanics," Int. J. Theor. Phys. 32, 945-949 (1993).
166. Vaz, J. Jr., and Rodrigues, W. A. Jr., "Zitterbewegung and the electromagnetic field of the electron," Phys. Lett. B 319, 203-208 (1993).
167. Vaz, J., Jr., "The Barut and Zanghi model, and some generalizations," Phys. Lett. B 344, 149-164 (1995).
168. Vaz, J., Jr., "A spinning particle model including radiation reaction," Phys. Lett. B 345, 448-451 (1995).
169. Vaz, J. Jr., "Clifford algebras and Witten monoples equations," in Geometry, Topology and Physics, edited by B. N. Apanasov, S. B. Bradlow, W. A. Rodrigues, Jr., and K. K. Uhlenbeck (Walter de Gruyter, Berlin, 1997).
170. Witten, E., "A note on the antibracket formalism," Mod. Phys. Lett. A 5, 487-494 (1990).
171. Zeni, J. R. and Rodrigues, W. A., Jr., "A thoughtful study of Lorentz transformations by Clifford algebras," Int. J. Mod. Phys. A 7, 1793-1817 (1992).