On quantization in light-cone variables compatible with wavelet transform

TL;DR

This paper proposes a novel quantization method in light-cone variables that incorporates wavelet transforms to separate space-time scales, aiming to improve the physical consistency of quantum field theories.

Contribution

It introduces a quantization procedure compatible with scale separation using wavelet transforms in light-cone variables, advancing the integration of scale analysis into quantum field theory.

Findings

Demonstrates compatibility of quantization with wavelet-based scale separation.

Provides a framework for divergence-free quantum field theories.

Extends previous wavelet-based approaches to light-cone quantization.

Abstract

Canonical quantization of quantum field theory models is inherently related to the Lorentz invariant partition of classical fields into the positive and the negative frequency parts $u(x) = u^+(x) + u^-(x),$ performed with the help of Fourier transform in Minkowski space. That is the commutation relations are being established between non localized solutions of field equations. At the same time the construction of divergence free physical theory requires the separation of the contributions of different space-time scales. In present paper, using the light-cone variables, we propose a quantization procedure which is compatible with separation of scales using continuous wavelet transform, as described in our previous paper Phys.Rev D 88(2013)025015