UV Finite Field Theories on Noncommutative Spacetimes: the Quantum Wick Product and Time Independent Perturbation Theory

TL;DR

This paper calculates energy corrections in a noncommutative quantum field theory using a regularised Hamiltonian, revealing invariance under some symmetries but Lorentz symmetry breaking, and recovers standard theory when noncommutativity vanishes.

Contribution

It introduces a method to compute energy corrections in noncommutative spacetime with ultraviolet finiteness and explores symmetry properties and dispersion relations.

Findings

Energy correction is invariant under rotation and translation.

Lorentz covariance is broken, leading to dispersion relation distortion.

Standard quantum field theory is recovered when noncommutativity is removed.

Abstract

In this article an energy correction is calculated in the time independent perturbation setup using a regularised ultraviolet finite Hamiltonian on the noncommutative Minkowski space. The correction to the energy is invariant under rotation and translation but is not Lorentz covariant and this leads to a distortion of the dispersion relation. In the limit where the noncommutativity vanishes the common quantum field theory on the commutative Minkowski space is reobtained.