Deformation Quantization of Fermi Fields

Details Deformation Quantization of Fermi Fields Deformation Quantization of Fermi Fields

2007-03-14

arxiv.org/abs/hep-th/0703125v1

Annals Phys.323:827-844,2008

Physics

High Energy Physics

High Energy Physics - Theory

19+1 pages, no figures, revtex4 file style

Scientific paper

10.1016/j.aop.2007.05.006

Deformation quantization for any Grassmann scalar free field is described via the Weyl-Wigner-Moyal formalism. The Stratonovich-Weyl quantizer, the Moyal $\star$-product and the Wigner functional are obtained by extending the formalism proposed recently in [35] to the fermionic systems of infinite number of degrees of freedom. In particular, this formalism is applied to quantize the Dirac free field. It is observed that the use of suitable oscillator variables facilitates considerably the procedure. The Stratonovich-Weyl quantizer, the Moyal $\star$-product, the Wigner functional, the normal ordering operator, and finally, the Dirac propagator have been found with the use of these variables.

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