Deformation Quantization of Classical Fields

F.J. Turrubiates; H. Garcia-Compean; J.F. Plebanski; M. Przanowski

Deformation Quantization of Classical Fields

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arxiv hep-th/9909206 v3 pith:JWZTU4KM submitted 1999-09-29 hep-th math.QAquant-ph

H. Garcia-Compean , J.F. Plebanski , M. Przanowski , F.J. Turrubiates This is my paper · ORCID

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keywords deformationquantizationabelianclassicalfieldsgaugewignerconsidered

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We study the deformation quantization of scalar and abelian gauge classical free fields. Stratonovich-Weyl quantizer, star-products and Wigner functionals are obtained in field and oscillator variables. Abelian gauge theory is particularly intriguing since Wigner functional is factorized into a physical part and other one containing the constraints only. Some effects of non-trivial topology within deformation quantization formalism are also considered.

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The Polymer representation for the scalar field: A Wigner functional approach
gr-qc 2019-08 conditional novelty 6.0 of 10

The polymer Wigner functional for a real scalar field is derived as a weak covariance limit of the Gaussian-measure Wigner functional, reproducing earlier GNS and Fock results.

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