Non-Canonical Perturbation Theory of Non-Linear Sigma Models

TL;DR

This paper develops a novel perturbation theory for the O(N)-invariant Non-Linear Sigma Model using non-canonical commutation relations that incorporate the model's geometric and topological features.

Contribution

It introduces a non-canonical perturbative approach tailored to the geometry and topology of the target manifold in NLSMs, differing from traditional methods.

Findings

New perturbation framework for NLSMs

Accounts for target space geometry and topology

Potential applications in non-perturbative regimes

Abstract

We explore the O(N)-invariant Non-Linear Sigma Model (NLSM) in a different perturbative regime from the usual relativistic-free-field one, by using non-canonical basic commutation relations adapted to the underlying O(N) symmetry of the system, which also account for the non-trivial (non-flat) geometry and topology of the target manifold.