Path integral for particles of spin zero and 1/2 in the field of an electromagnetic plane wave

Abstract

The Green's functions for charged particles of spin zero and 1/2, which are subjected to the action of the field of an electromagnetic plane wave, are calculated in the path integral formalism. It is also shown that in the case of spin 0, the semi-classical Green's function obtained via a canonical transformation, is accurate. These Green's functions are obtained under a compact form. The waves in the case of spin 0 and the wave functions in the case of spin 1/2 are then deduced.

Stochastic quantization for spinless particle subjected to the field of a plane wave: Case of local gauge

“…This result agrees exactly with that of reference [8]. Moreover, our Green's function is the same one as that determined by the approach of the phase space.…”

“…Firstly, it was studied by Schwinger [6] by his formalism, then it was considered within the algebraic point of view [7] and also by the path integral approach [8]. The solutions of the KleinGordon equation obtained, thanks to the properties of this wave, are analytical.…”

Quasiclassical propagator of a relativistic particle via the path-dependent gauge potential

“…Another case where the quasiclassical approximation yields the exact result is the interaction of a charged particle with a plane electromagnetic wave [7][8][9][10][11]. The corresponding propagator for this case is called Volkov propagator.…”

“…In fact, if the Lagrangian of a point particle is a quadratic function of the coordinate and the velocity, then the corresponding exact propagator coincides with the quasiclassical propagator, i.e., the classical path dominates the Feynman path integral [3][4][5][6]. It is interesting that the exact Volkov propagator, the propagator of a charged particle interacting with a plane electromagnetic wave, is also given by its quasiclassical limit [7][8][9][10][11], though the Lagrangian is not quadratic. Furthermore, there are many cases where the quasiclassical propagator is a good approximation.…”

Green’s function for an electron model with a plane wave

“…The plane wave being characterized by the quantity φ = , it seems complicated to perform the D integration. However, if we introduce the following identity [8]:…”