Multiresolution quantum field theory in light-front coordinates

TL;DR

This paper develops a symmetric wavelet-based approach to quantum field theory in light-front coordinates, generalizing path integrals over causally ordered regions to improve the mathematical framework.

Contribution

It introduces a symmetric wavelet transform framework for light-front quantum field theory, extending previous asymmetric models and defining causally ordered spacetime regions for path integrals.

Findings

Wavelet transform applied symmetrically to light-front variables.

Generalization of causal path concepts to spacetime regions.

Evaluation rules for Feynman path integrals using wavelets.

Abstract

We analyse the use of wavelet transform in quantum field theory models written in light-front coordinates. In a recent paper [W.N Polyzou, Phys. Rev. D 101(2020) 096004] W.N.Polyzou used $x^+$ variable as 'time', and applied wavelet transform to the 'spatial' coordinates only. This makes the theory asymmetric with respect to space and time coordinates. In present paper we generalise the concept of continuous causal path, which is the basis of path integration, to the sequences of causally ordered spacetime regions, and present evaluation rules for Feynman path integrals over such sequences in terms of wavelet transform. Both the path integrals and the wavelet transform in our model are symmetric with respect to the light-front variables ($x^+,x^-$). The definition of a spacetime event in our generalization is very much like the definition of event in probability theory.