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Representation of permutation operators in quantum mechanics Seagraves, Paul Henry

Abstract

A simple method is presented for writing the matrix elements of transposition operators for discrete sets of quantum numbers. A proper product of these leads to easy computation of general permutation operators. It is shown how these operators may be constructed with operators defined in angular momentum space. Results agree with Dirac for transposition of two particles of spin ½ and with Kaempffer for spin 1. The calculations are performed to extend the results to spin 3/2 and 2 along with alternate representations. Special considerations are required for fermion creation and annihilation operators.

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