An asymptotic formula for models with caustics

TL;DR

This paper presents an asymptotic formula that improves the accuracy of quantum models with caustics by suppressing divergences, ensuring the validity of the mean field approximation.

Contribution

It introduces a novel asymptotic formula with an extra term to handle caustics in quantum models, extending the WKB approximation.

Findings

The formula effectively suppresses divergences caused by caustics.

It guarantees the validity of the mean field approximation in models with caustics.

Applicable to models like the Nambu--Jona-Lasinio (NJL) model.

Abstract

We introduce an asymptotic formula for calculating quantum mechanical and quantum theoretical models with caustics, like the Nambu--Jona-Lasinio(NJL) model. This asymptotic formula is given by the form attached the extra term, which suppresses the divergence induced because of caustics, to the leading term of the WKB approximation. This formula guarantees validity of the mean field approximation of models with caustics.