Abstract
The problem of a relativistic spinning particle interacting with a weak gravitational plane wave in (3+1) dimensions is formulated in the frame work of covariant supersymmetric path integrals. The relative Green function is expressed through a functional integral over bosonic trajectories that describe the external motion and fermionic variables that describe the spin degrees of freedom. The (3+1) dimensional problem is reduced to the (1+1) dimensional one by using an identity. Next, the relative propagator is exactly calculated and the wave functions are extracted.
References
R.P. Feynman, A.R. Hibbs, Quantum Mechanics and Path Integrals (McGraw Hill, New York, 1965)
S.W. Hawking, J.B. Hartle, Phys. Rev. D 13, 2188 (1976)
D.M. Chitre, J.B. Hartle, Phys. Rev. D 16, 251 (1977)
L.S. Schulman, Techniques and Applications of Path Integration (John Wiley, New York, 1981)
H. Kleinert, Path Integral in Quantum Mechanics, Statistics and Polymer Physics (World Scientific, Singapore, 1990)
M. Chaichian, A. Demichev, Path Integrals in Physics, Vol. 1 (IOP Publisher, Bristol UK, 2001)
M. Chaichian, A. Demichev, Stochastic Processes and Quantum Mechanics, Vol. 2 (IOP Publisher, Bristol UK, 2001)
M. Chaichian, A. Demichev, Quantum Field Theory, Statistical Physics and other Modern Applications (IOP Publisher, Bristol UK, 2001)
E.S. Fradkin, D.M. Gitman, Phys. Rev. D 44, 3220 (1991)
C. Alexandrou, R. Rosenfelder, A.W. Schreiber, Phys. Rev. A 59, 3 (1998)
D.M. Gitman, Nucl. Phys. B 488, 490 (1997)
B. Geyer, D.M. Gitman, I.L. Shapiro, Int. J. Mod. Phys. A 15, 3861 (2000)
S. Haouat, L. Chetouani, Int. J. Theor. Phys. 46, 1528 (2007)
S. Haouat, L. Chetouani, J. Phys. A Math. Theor. 40, 1349 (2007)
A. Barducci, R. Giachetti, J. Phys. A Math. Gen. 38, 1615 (2005)
A.N. Vaidya, C. Farina, M.S. Guimaraes, M. Neves, J. Phys. A Math. Theor. 40, 9149 (2007)
L.D. Landau, E.M. Lifshitz, The Classical Theory Fields (Pergamon Press, Oxford, 1987)
V.I. Pustovoit, L.A. Chernozatonskii, JETP 34, 229 (1981)
B.F. Schutz, A first Course in General Relativity (Cambridge University Press, Cambridge, 1995)
S. Weinberg, Gravitation and Cosmology (John Wiley and Sons, New York, 1972)
F.A. Berezin, M.S. Marinov, JETP Lett. 21, 320 (1975)
F.A. Berezin, M.S. Marinov, Ann. Phys. 104, 336 (1977)
L. Brink, S. Deser, B. Zumino, P. Di Vecchia, P. Howe, Phys. Lett. B 64, 435 (1976)
L. Brink, P. Di Vecchia, P. Howe, Nucl. Phys. B 118, 76 (1977)
D.M. Gitman, S.I. Zlatev, Phys. Rev. D 55, 7701 (1997)
D.M. Gitman, S.I. Zlatev, W.D. Cruz, Brazil. J. Phys. 26, 419 (1996)
S. Zeggari, T. Boudjedaa, L. Chetouani, Phys. Scripta 64, 285 (2001)
J.D. Bjorken, S.D. Drell, Relativistic Quantum Fields (McGraw Hill, New York, 1965)
A.M. Polyakov, Gauge Fields and Strings (Harwood Academic, Chur, Switzerland, 1987)
Author information
Authors and Affiliations
Corresponding author
Additional information
PACS
04.30.-w; 03.65.Ca; 03.65.Db; 03.65.Pm
Rights and permissions
About this article
Cite this article
Haouat, S., Chetouani, L. Worldline path integrals for a Dirac particle in a weak gravitational plane wave. Eur. Phys. J. C 53, 289–294 (2008). https://doi.org/10.1140/epjc/s10052-007-0448-7
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1140/epjc/s10052-007-0448-7