Deformation quantization for fermionic fields

I. Galaviz

Departamento de Física, Centro de Investigación y de Estudios Avanzados del IPN, P.O. Box 14–740, 07000 México D.F., México, e–mail: igalaviz@fis.cinvestav.mx

Recibido el 1 de mayo de 2006
Aceptado el 1 de noviembre de 2006

Abstract

The deformation quantization of any Grassmann free field, or fermionic free field, in particular, the Dirac free field is discussed. Stratonovich–Weyl quantizer, Moyal product and Wigner functionals are obtained for this field by deforming suitable Fermi oscillator variables. In addition the propagator of the Dirac field is computed in this context.

Keywords: Deformation quantization; Weyl–Wigner–Moyal formalism; Dirac field.

Resumen

Se discute la cuantización por deformación de un campo libre de Grassmann, o campo fermiónico libre; en particular, el formalismo es aplicado al campo libre de Dirac. El cuantizador de Stratonovich–Weyl, el producto de Moyal y las funcionales de Wigner son obtenidos para este campo, deformando las variables apropiadas del oscilador de Fermi. Ademas, el propagador del campo de Dirac es calculado en este contexto.

Descriptores: Cuantización por deformación; formalismo de Weyl–Wigner–Moyal; campo de Dirac.

PACS: 03.70.+k;11.10.–z

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Acknowledgements

I am indebted with G. Dito, H. García–Compeán, C. Maldonado–Mercado, M. Przanowski and F. Turrubiantes for intensive discussions and useful suggestions. This review was partially supported by the CONACyT graduate fellowship and the CONACyT grant 45713–F I want to thank the CINVESTAV–Monterrey for their warm hospitality.

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