Quantum field theory of degenerate systems

TL;DR

This paper develops a quantum field theory framework for degenerate systems using density matrices and Hopf algebra techniques, revealing modified Schwinger-Dyson equations and deriving Green function hierarchies.

Contribution

It introduces a self-consistent quantum field theory for degenerate systems employing density matrices and Hopf algebra methods, extending traditional approaches.

Findings

Modified Schwinger-Dyson equations for degenerate systems

Hierarchy of Green functions derived for these systems

Explicit calculation for a single electron in a two-fold degenerate orbital

Abstract

To set up a self-consistent quantum field theory of degenerate systems, the unperturbed state should be described by a density matrix instead of a pure state. This increases the combinatorial complexity of the many-body equations. Hopf algebraic techniques are used to deal with this complexity and show that the Schwinger-Dyson equations are modified in a non-trivial way. The hierarchy of Green functions is derived for degenerate systems, and the case of a single electron in a two-fold degenerate orbital is calculated in detail.