Multiresolution quantum field theory in light-front coordinates

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.

arXiv commentrevtex, 29 pages, 8 eps figures

References in corpus (16)

• Exact evolution equation for the effective potential
• Non-Perturbative Renormalization Flow in Quantum Field Theory and Statistical Physics
• QCD thermalization: Ab initio approaches and interdisciplinary connections
• From Path Integrals to Tensor Networks for AdS/CFT
• Light Rays, Singularities, and All That
• Quantum field theory without divergences
• Continuous Wavelet Transform in Quantum Field Theory
• Causal sites as quantum geometry
• Algebraic Classical and Quantum Field Theory on Causal Sets
• Wavelet representation of light-front quantum field theory
• Heavy quarkonia production at LHC and EIC using Basis Light-Front Quantization wavefunctions
• Transitioning from equal-time to light-front quantization in ${\varphi }_2^4$ theory
• Unifying renormalization group and the continuous wavelet transform
• Wavelet based regularization for Euclidean field theory
• Renormalization of viscosity in wavelet-based model of turbulence
• Wavelet regularization of Euclidean QED