Canonical quantization of non-local field equations

TL;DR

This paper develops a consistent method for quantizing relativistic non-local field equations, analyzing their algebraic structure, gauge quantization, and physical state properties.

Contribution

It introduces a novel quantization approach for non-local fields, including gauge fields, and explores their Poincare representations and propagator structures.

Findings

Field operators generally form reducible Poincare representations

Quantization of non-local gauge fields is achieved via Gupta-Bleuler method

The theory's propagators and physical states are characterized

Abstract

We consistently quantize a class of relativistic non-local field equations characterized by a non-local kinetic term in the lagrangian. We solve the classical non-local equations of motion for a scalar field and evaluate the on-shell hamiltonian. The quantization is realized by imposing Heisenberg's equation which leads to the commutator algebra obeyed by the Fourier components of the field. We show that the field operator carries, in general, a reducible representation of the Poincare group. We also consider the Gupta-Bleuler quantization of a non-local gauge field and analyze the propagators and the physical states of the theory.