Noncommutative field theory in formalism of first quantization

TL;DR

This paper develops a first-quantized approach to quadratic non-commutative field theory in abelian gauge backgrounds, revealing non-trivial momentum dependence and providing exact propagator representations for scalar and spinning particles, with applications to pair-production processes.

Contribution

It introduces a novel first-quantized formalism for non-commutative field theory that captures non-trivial momentum dependence and exact propagators.

Findings

Exact propagator representations for scalar and spinning particles.

Non-trivial momentum dependence prevents local second-order formalism.

Application to Schwinger-type pair-production processes.

Abstract

We present a first-quantized formulation of the quadratic non-commutative field theory in the background of abelian (gauge) field. Even in this simple case the Hamiltonian of a propagating particle depends non-trivially on the momentum (since external fields depend on location of the Landau orbit) so that one can not integrate out momentum to obtain a local theory in the second order formalism. The cases of scalar and spinning particles are considered. A representation for exact propagators is found and the result is applied to description of the Schwinger-type processes (pair-production in homogenous external field).