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Physica Scripta

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

Tahar Boudjedaa, L. Chétouani, Larbi Guechi, Théophile F. Hammann

Published Oct 1, 1992• 22 citations
Publisher

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.

DOI
10.1088/0031-8949/46/4/001

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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.
Abstract The dynamics of relativistic particles of spin 0 and 1/2, interacting with an external electromagnetic field and a quantized plane wave, is studied using the path integral framework. We take advantage of the existing properties of the interaction to introduce a delta functional in order to calculate Green's functions. This simply reduces the problem to two coupled oscillators. The energy spectrum and wave functions are calculated for the spin 0 case and the analogy with Jaynes‐Cummings model is made to derive the energy spectrum for the spin 1/2 case.
is discussed. A new method is proposed for approximations of the corresponding path integral. It is shown that calculation of this integral does not give the Green's function of the Klein-Gordon equation but leads to the propagator of a scalar field in the twocomponent Feshbach-Villars formalism. The difficulties in calculating path integrals in the presence of nontrivial external fields are discussed. 1. In the present paper, we consider some methodological questions of relativistic quantum mechanics associated with quantization of the classical Hamtltonian of a relativistic charged particle with rest mass m in external fields: electromagnetic Au(r, t) (p = 0, 1, 2, 3) and scalar V(r, t):
Exact Green’s function related to a Dirac particle submitted to the combination of Aharonov–Bohm and Coulomb potentials in [Formula: see text]) coordinate space is analytically calculated via path integral formalism. The Pauli matrices which describe the spin dynamics are replaced by two fermionic oscillators via the Schwinger model. The energy spectrum as well as the corresponding normalized wave functions are extracted following this approach. The interesting properties of the spinors are thus deduced after symmetrization. According to the symmetric form for Green’s function, it is shown that the non-relativistic limit of the Dirac particle is undertaken with much ease.
Using the coherent states representation and the Schwinger boson model, the propagator of a spinning particle in interaction with an arbitrary magnetic field is derived in the framework of the path integral formalism. To show the relevance of the formalism to some applications, the Green function of spinning particle s=1/2 in special configuration of magnetic field is calculated. The transition amplitude and Berry’s phase for an arbitrary spin and time dependent magnetic field are deduced. The case of half integer spin is also considered.