The Vacuum in Light-Cone Field Theory

TL;DR

This paper discusses the nature of the vacuum in light-cone field theory, proposing methods to reconcile its trivial appearance with the complex vacuum physics, and introduces a framework to incorporate vacuum effects into the light-cone formalism.

Contribution

It presents a way to formulate quantum field theory on null planes that aligns with traditional formulations and simplifies vacuum physics analysis.

Findings

Light-cone vacuum is 'trivial' but can encode complex vacuum physics.

A construction method for equivalent light-cone and equal-time theories.

Effective Hamiltonians can include vacuum effects in a simple vacuum Hilbert space.

Abstract

This is an overview of the problem of the vacuum in light-cone field theory, stressing its close connection to other puzzles regarding light-cone quantization. I explain the sense in which the light-cone vacuum is ``trivial,'' and describe a way of setting up a quantum field theory on null planes so that it is equivalent to the usual equal-time formulation. This construction is quite helpful in resolving the puzzling aspects of the light-cone formalism. It furthermore allows the extraction of effective Hamiltonians that incorporate vacuum physics, but that act in a Hilbert space in which the vacuum state is simple. The discussion is fairly informal, and focuses mainly on the conceptual issues. [Talk presented at {\sc Orbis Scientiae 1996}, Miami Beach, FL, January 25--28, 1996. To appear in the proceedings.]