Non-standard Schwinger fermionic representation of unitary group

TL;DR

This paper explores a non-standard fermionic representation of the unitary group U(n), revealing its non-uniqueness for n≥3 and establishing a uniform approach using n-fermion operators.

Contribution

It introduces a novel non-standard Schwinger fermionic representation for U(n) groups, highlighting its non-uniqueness and providing a unified construction method.

Findings

The representation is not unique for n≥3.

A uniform approach to construct the representation is proposed.

Discussion of the representation for U(C(m,n)) groups.

Abstract

The non-standard Schwinger fermionic representation of the unitary group is studied by using $n$-fermion operators. One finds that the Schwinger fermionic representation of the U(n) group is not unique when $n\ge 3$. In general, based on $n$-fermion operators, the non-standard Schwinger fermionic representation of the U(n) group can be established in a uniform approach, where all the generators commute with the total number operators. The Schwinger fermionic representation of $U(C^{m}_{n})$ group is also discussed.