The path integral quantization and the construction of the S-matrix operator in the Abelian and non-Abelian Chern-Simons theories


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Fainberg V., Pak N., Shikakhwa M.

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, cilt.30, ss.3947-3965, 1997 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 30 Konu: 11
  • Basım Tarihi: 1997
  • Doi Numarası: 10.1088/0305-4470/30/11/022
  • Dergi Adı: JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL
  • Sayfa Sayıları: ss.3947-3965

Özet

The covariant path integral quantization of the theory of the scalar and spinor fields interacting through the Abelian and non-Abelian Chern-Simons gauge fields in 2 + 1 dimensions is carried out using the De Witt-Fadeev-Popov method. The mathematical ill-definiteness of the path integral of theories with pure Chern-Simons' fields is remedied by the introduction of the Maxwell or Maxwell-type (in the non-Abelian case) terms, which make the resulting theories super-renormalizable and guarantees their gauge-invariant regularization and renormalization. The generating functionals are constructed and shown to be the same as those of quantum electrodynamics (quantum chromodynamics) in 2 + 1 dimensions with the substitution of the Chern-Simons propagator for the photon (gluon) propagator. By constructing the propagator in the general case, the existence of two limits; pure Chern-Simons and quantum electrodynamics (quantum chromodynamics) after renormalization is demonstrated.