Symmetry Conserving Dynamical Mappings

TL;DR

This paper introduces two nonperturbative dynamical mapping methods that preserve symmetry, with one surpassing the 1/N-expansion by incorporating Gaussian functional dynamics, enhancing the understanding of symmetry-conserving quantum mappings.

Contribution

It presents two novel symmetry-conserving dynamical mapping approaches, one based on 1/N-expansion and the other on current mappings, with the latter offering a more comprehensive framework.

Findings

The second approach transcends the 1/N-expansion.

The methods preserve symmetry nonperturbatively.

The Gaussian functional approach is integrated into the mapping.

Abstract

Using the concept of dynamical mappings, two symmetry conserving nonperturbative approaches are presented. The first is based on the 1/N-expansion and sorted out using Holstein-Primakoff mapping. The second consists of dynamically mapping the canonical fields into the corresponding currents. It is argued, either by comparing the Fock spaces or the observables, that the latter constitutes a higher approach which transcends the 1/N-expansion and contains the dynamics generated by the Gaussian functional approach.