Generating functions for canonical systems of fermions

TL;DR

This paper introduces a generating function approach to derive recursion relations for systems of degenerate fermions, extending Pratt's diagrammatic method to include multiple conservation laws without restrictions.

Contribution

It presents a novel generating function method for deriving recursion relations in fermionic systems, removing previous limitations on conservation laws.

Findings

Recursion relations can be derived from generating functions for fermionic systems.

The method accommodates multiple conservation laws simultaneously.

It offers an efficient alternative to diagrammatic techniques.

Abstract

The method proposed by Pratt to derive recursion relations for systems of degenerate fermions [Phys. Rev. Lett. 84, 4255 (2000), arXiv:nucl-th/9905055] relies on diagrammatic techniques. This efficient formalism assumes no explicit two-body interactions, makes possible the inclusion of conservation laws and requires low computational time. In this brief report, we show that such recursion relations can be obtained from generating functions, without any restriction as concerns the number of conservation laws (e.g. total energy or angular momentum).