Artículos de revistas
Multivector Dirac Equation And ℤ2-gradings Of Clifford Algebras
Registro en:
International Journal Of Theoretical Physics. , v. 41, n. 9, p. 1651 - 1671, 2002.
207748
10.1023/A:1021003016189
2-s2.0-0141563531
Autor
Mosna R.A.
Miralles D.
Vaz Jr. J.
Institución
Resumen
We generalize certain aspects of Hestenes's approach to Dirac theory to obtain multivector Dirac equations associated to a large class of representations of the gamma matrices. This is done by replacing the usual even/odd decomposition of the space-time algebra with more general ℤ 2-gradings. Some examples are given and the chiral case, which is not addressed by the usual approach, is considered in detail. A Lagrangian formulation is briefly discussed. A relationship between this work and certain quaternionic models of the (usual) quantum mechanics is obtained. Finally, we discuss under what conditions the Hestenes's form can be recovered and we suggest a geometrical interpretation for the corresponding situation. 41 9 1651 1671 Adler, S.L., (1995) Quaternionic Quantum Mechanics and Quantum Fields, , Oxford University Press, London Becher, P., Joos, H., The Divac-Kähler equation and fermions on the lattice (1982) Zeitschrift für Physikalische Chemic, 15, pp. 343-365 Benn, I.M., Tucker, R.W., (1987) An Introduction to Spinors and Geometry with Applications in Physics, , Adam Hilger, Bristol, CT Bjorken, D., Drell, S., (1964) Relativistic Quantum Mechanics, , McGraw-Hill, New York Chisholm, J.S.R., Farwell, R.S., Gauge transformations of spinors within a Clifford algebraic structure (1999) Journal of Physics A: Mathematical and General, 32, pp. 2085-2823 Dimakis, A., A new representation of Clifford algebras (1989) Journal of Physics A: Mathematical and General, 22, pp. 3171-3193 Emch, G.G., "Mécanique quantique quaternionienne et relativité restreinte I (1963) Helvetica Physica Acta, 36, pp. 739-769 Emch, G.G., "Mécanique quantique quaternionienne et relativité restreinte II (1963) Helvetica Physica Acta, 36, pp. 770-769 Fauser, B., On the equivalence of Daviau's space Clifford algebraic, Hestenes' and Parra's formulations of (real) Dirac theory (2001) International Journal of Theoretical Physics, 40, pp. 441-453. , Also hep-th/9908200 Fauser, B., Ablamowicz, R., On the decomposition of Clifford algebras of arbitrary bilinear form (2000) Clifford Algebras and Their Applications in Mathematical Physic - Vol. 1. Algebra and Physics, 1, pp. 341-366. , R. Ablmowicz and B. Fauser eds., Birkhauser, Boston. (Also math. QA/9911180) Finkelstein, D., Jauch, J.M., Schiminovich, S., Speiser, D., Foundations of quaternion quantum mechanics (1962) Journal of Mathematical Physics, 3, p. 207 Gull, S., Doran, C., Lasenby, A., Electron physics I and II (1996) Clifford (Geometric) Algebras with Applications in Physics, Mathematics, and Engineering, , W. E. Baylis. ed., Birkhauser, Boston Harvey, F.R., (1990) Spinors and Calibrations, , Academic Press, New York Hestenes, D., Real spinor fields (1967) Journal of Mathematical Physics, 8, p. 798 Hestenes, D., Space-time structure of weak and electromagnetic interactions (1982) Foundations of Physics, 12, pp. 153-168 Hestenes, D., Real dirac theory (1995) Advances in Applied Clifford Algebras, 7, p. 97 Itzykson, C., Zuber, J., (1980) Quantum Field Theory, , McGraw-Hill, New York De Leo, S., Quaternionic Lorentz group and dirac equation (2001) Foundation of Physics Letters, 14, pp. 37-50. , Also hep-th/0103129 Lounesto, P., (1996) Clifford Algebras and Spinors, , Cambridge University Press, Cambridge, MA Messiah, A., (1961) Quantum Mechanics, Vol. II, 2. , North-Holland, Amsterdam Mosna, R.A., Miralles, D., Vaz, J., ℤ2-Gradings of Clifford Algebras and Multivector Structures, , in preparation Pezzaglia, W.M., Dimensionally democratic calculus and principles of polydimensional physics (2000) Clifford Algebras and Their Applications in Mathematical Physics - Vol. 1: Algebra and Physics, 1, pp. 101-123. , R. Ablamowicz and B. Fauser, eds., Birkhauser, Boston. (Also gr-qc/9912025) Rabin, J.M., Homology theory of lattice fermion doubling (1982) Nuclear Physics B, 201, pp. 315-332 Rotelli, P., The Dirac equation on the quaternion field (1989) Modern Physics Letters A, 4, pp. 933-934