Quantum Newtonian Dynamics on a Light Front

TL;DR

This paper explores the unique features of quantum dynamics on a light-front, highlighting the differences between string and field theories, and proposes a novel way to recast field theory as a Newtonian system for nonperturbative analysis.

Contribution

It introduces a new approach to reformulate field theories as Newtonian systems inspired by string theory, facilitating nonperturbative studies.

Findings

String dynamics on a light-front resemble Newtonian many-particle systems.

Field theory can be viewed as a limit of string theory with infinite tension.

Simple quantum systems demonstrate the feasibility of the proposed reformulation.

Abstract

We recall the special features of quantum dynamics on a light-front (in an infinite momentum frame) in string and field theory. The reason this approach is more effective for string than for fields is stressed: the light-front dynamics for string is that of a true Newtonian many particle system, since a string bit has a fixed Newtonian mass. In contrast, each particle of a field theory has a variable Newtonian mass P^+, so the Newtonian analogy actually requires an infinite number of species of elementary Newtonian particles. This complication substantially weakens the value of the Newtonian analogy in applying light-front dynamics to nonperturbative problems. Motivated by the fact that conventional field theories can be obtained as infinite tension limits of string theories, we propose a way to recast field theory as a standard Newtonian system. We devise and analyze some simple quantum mechanical systems that display the essence of the proposal, and we discuss prospects for applying these ideas to large N_c QCD.