Fine-Tuning Renormalization and Two-particle States in Nonrelativistic Four-fermion Model

TL;DR

This paper explores exact solutions for two-particle states in a nonrelativistic four-fermion model, examining renormalization, self-adjoint extensions, and Goldstone modes to deepen understanding of the model's quantum behavior.

Contribution

It introduces a novel connection between renormalization procedures and self-adjoint extensions in the context of nonrelativistic four-fermion interactions.

Findings

Derived exact two-particle eigenstates.

Analyzed the Goldstone mode characteristics.

Linked renormalization with self-adjoint extensions.

Abstract

Various exact solutions of two-particle eigenvalue problems for nonrelativistic contact four-fermion current-current interaction are obtained. Specifics of Goldstone mode is investigated. The connection between a renormalization procedure and construction of self-adjoint extensions is revealed.