Existence, degeneracy and stability of ground states by logarithmic Sobolev inequalities on Clifford algebras

TL;DR

This paper establishes the existence, degeneracy, and stability of ground states in Clifford algebra energy forms satisfying logarithmic Sobolev inequalities, with applications to quantum field theory.

Contribution

It introduces a novel approach using logarithmic Sobolev inequalities to analyze ground states in Clifford algebras, extending to quantum field theory models.

Findings

Proves existence and finite degeneracy of ground states.

Shows stability under certain unbounded perturbations.

Provides an infinitesimal method for ground state analysis in QFT.

Abstract

We prove existence and finite degeneracy of ground states of energy forms satisfying logarithmic Sobolev inequalities with respect to non vacuum states of Clifford algebras. We then derive the stability of the ground state with respect to certain unbounded perturbations of the energy form. Finally, we show how this provides an infinitesimal approach to existence and uniqueness of the ground state of Hamiltonians considered by L. Gross in QFT, describing spin $1/2$ Dirac particles subject to interactions with an external scalar field.