Path Integral for Dirac Particle in Plane Wave Field

Abstract

The problem of a relativistic spinning particle in interaction with an electromagnetic plane wave field is treated via path integrals. The dynamics of the spin of the particle is described using the supersymmetric action proposed by Fradkin and Gitman. The problem has been solved by using two identities, one bosonic and the other fermionic, which are related directly to the classical equations of motion. The exact expression of the relative Green's function is given and the result agrees with those of the literature. Further, the suitably normalized wave functions are also extracted.

Green’s Function for Dirac Particle in a Non-Abelian Field: A Path Integral Approach

“…In order to determine the Green function, we follow the usual construction method [11] of path integral form.…”

“…First, we put = and = , and then the variables and are rendered, respectively, independent of and of by introducing the following three identities [11,12]:…”

“…So if we put = Ψ , these new variables are rendered independent [11,12] by the introduction of the following relation:…”

“…We can cite, for example, the simple cases such as the constant field [4], the plane wave [5,6], the crossed electric and magnetic fields [7,8], and the combination of constant homogeneous electromagnetic field with a plane wave field [9,10]. With the path integral formalism, we can cite [11][12][13][14], where the interactions have classical form.…”

Dirac particle in the presence of a plane waveand constant magnetic fields: path integral approach

“…In the third section, we compute the (GF) by adopting the fluctuation analysis performed on both, real and Grassmann variables [9] and inserting the known identities [7] into this formulation.…”