Non-standard Schwinger fermionic representation of unitary group

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.

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