Spin in the path integral: anti-commuting versus commuting variables

We discuss the equivalence between the path integral representations of spin dynamics for anti-commuting (Grassmann) and commuting variables and establish a bosonization dictionary for both generators of spin and single fermion operators. The content of this construction in terms of the representati...

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Bibliographic Details
Published in:Physics letters. B 1995-02, Vol.345 (3), p.242-247
Main Authors: Scholtz, F.G., Theron, A.N., Geyer, H.B.
Format: Article
Language:English
Subjects:
Bosonization
Dyson mapping
Free field realization
Grassmann variables
Path integral
Spin dynamics
Vertex operator
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Summary:We discuss the equivalence between the path integral representations of spin dynamics for anti-commuting (Grassmann) and commuting variables and establish a bosonization dictionary for both generators of spin and single fermion operators. The content of this construction in terms of the representations of the spin algebra is discussed in the path integral setting. Finally it is shown how a ‘free field realization’ (Dyson mapping) can be constructed in the path integral.
ISSN:0370-2693
1873-2445
DOI:10.1016/0370-2693(94)01635-P