https://doi.org/10.1140/epjc/s10052-007-0448-7
Regular Article - Theoretical Physics
Worldline path integrals for a Dirac particle in a weak gravitational plane wave
1
Laboratoire de Physique Théorique, Université de Jijel, BP 98, Ouled Aissa, Jijel, 18000, Algérie
2
Département de Physique, Faculté de Sciences Exactes, Université Mentouri, Route Ain El-Bey, Constantine, 25000, Algérie
* e-mail: chetoua1@carameil.com
Received:
31
May
2007
Revised:
6
October
2007
Published online:
10
November
2007
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.
© Springer-Verlag , 2008
