On the Computation of Mass Spectra and Structure Functions in a Relativistic Hamiltonian Formalism: A Lattice Point of View

TL;DR

This paper introduces a new numerical technique called the large momentum frame (LMF) for solving field theories, combining lattice gauge theory advantages with front form quantisation, and discusses its physical implications and differences from other frames.

Contribution

The paper proposes the LMF as a novel approach that overcomes limitations of the IMF and FF, providing a more physical framework for analyzing distribution functions in deep inelastic scattering.

Findings

LMF differs from IMF and FF in key physical aspects.

IMF violates lattice scaling window and is unphysical.

FF propagators violate micro-causality and causality.

Abstract

Herein we propose a new numerical technique for solving field theories: the large momentum frame (LMF). This technique combines several advantages of lattice gauge theory with the simplicity of front form quantisation. We apply the LMF on QED(1+1) and on the $\phi^4(3+1)$ theory. We demonstrate both analytically and in practical examples (1) that the LMF does neither correspond to the infinite momentum frame (IMF) nor to the front-form (FF) (2) that the LMF is not equivalent to the IMF (3) that the IMF is unphysical since it violates the lattice scaling window and (4) that the FF is even more unphysical because FF propagators violate micro-causality, causality and the finiteness of the speed of light. We argue that distribution functions measured in deep inelastic scattering should be interpreted in the LMF (preferably in the Breit frame) rather than in the FF formalism. In particular, we argue that deep inelastic scattering probes space-like distribution functions.