Proper time and path integral representations for the commutation function

TL;DR

This paper develops proper time and path integral representations for the commutation function of a quantized spinor field interacting with external electromagnetic fields, generalizing known formulas and explicitly analyzing light cone singularities.

Contribution

It introduces a proper time representation valid in any dimension and constructs a path integral form for the commutation function, extending the Fock formula to arbitrary dimensions.

Findings

Explicit light cone singularities are derived.

Proper time representation is established in all dimensions.

A new path integral representation for the commutation function is constructed.

Abstract

On the example of the quantized spinor field, interacting with arbitrary external electromagnetic field, the commutation function is studied. It is shown that a proper time representation is available in any dimensions. Using it, all the light cone singularities of the function are found explicitly, generalizing the Fock formula in four dimensions, and a path integral representation is constructed.