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Comments on spin operators and spin-polarization states of 2+1 fermions

S. P. Gavrilov·D. M. Gitman·J. L. Tomazelli
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Abstract

In this brief article we discuss spin polarization operators and spin polarization states of 2+1 massive Dirac fermions and find a convenient representation by the help of 4-spinors for their description. We stress that in particular the use of such a representation allows us to introduce the conserved covariant spin operator in the 2+1 field theory. Another advantage of this representation is related to the pseudoclassical limit of the theory. Indeed, quantization of the pseudoclassical model of a spinning particle in 2+1 dimensions leads to the 4-spinor representation as the adequate realization of the operator algebra, where the corresponding operator of a first-class constraint, which cannot be gauged out by imposing the gauge condition, is just the covariant operator previously introduced in the quantum theory.

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S. P. Gavrilov, D. M. Gitman, J. L. Tomazelli. 2007-01-08. Comments on spin operators and spin-polarization states of 2+1 fermions. https://doi.org/10.1140/epjc%2Fs2004-02026-9

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