Multiresolution Quantum Field Theory in Light-Front Coordinates

We analyse the use of wavelet transform in quantum field theory models written in lightfront coordinates. In a recent paper (Phys. Rev. D 101: 096004 2020) 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 lightfront variables (x(+), x(-)). The definition of a spacetime event in our generalization is very much like the definition of event in probability theory.

Automated summary

This paper analyzes the use of wavelet transform in quantum field theory models written in lightfront coordinates. By generalizing the concept of continuous causal path to sequences of causally ordered spacetime regions and using wavelet transform, the evaluation rules for Feynman path integrals over such sequences are presented.