Lightfront Hamiltonian Structures for the Nonlinear Sigma Model

TL;DR

This paper derives the Dirac brackets for the O(N) nonlinear sigma model in the lightfront framework, highlighting key subtleties such as boundary condition preferences and their implications.

Contribution

It provides a detailed derivation of the lightfront Hamiltonian structure for the nonlinear sigma model, including the effects of constraints and boundary conditions.

Findings

Anti-periodic boundary conditions are preferred in the lightfront description.

Explicit Dirac brackets are derived for the model with and without constraints.

Subtleties in the lightfront quantization process are elucidated.

Abstract

We derive the Dirac brackets for the O(N) nonlinear sigma model in the lightfront description with and without the constraint. We bring out various subtleties that arise including the fact that anti-periodic boundary condition seems to be preferred.