Hamiltonian Formalism for Space-time Non-commutative Theories

TL;DR

This paper develops a Hamiltonian formalism for space-time non-commutative theories, enabling local treatment of non-local actions via auxiliary dimensions, and derives Feynman rules for quantization.

Contribution

It introduces a Hamiltonian approach for non-local space-time theories using auxiliary dimensions, facilitating quantization and analysis of non-commutative field theories.

Findings

Hamiltonian formalism for non-local theories established

Feynman rules derived for non-commutative  theory

Framework applicable to various non-local space-time models

Abstract

Space-time non-commutative theories are non-local in time. We develop the Hamiltonian formalism for non-local field theories in d space-time dimensions by considering auxiliary d+1 dimensional field theories which are local with respect to the evolution time. The Hamiltonian path integral quantization is considered and the Feynman rules in the Lagrangian formalism are derived. The case of non-commutative \phi^3 theory is considered as an example.