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

Fainberg, VY
Pak, Namık Kemal
Shikakhwa, MS
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.


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Citation Formats
V. Fainberg, N. K. Pak, and M. Shikakhwa, “The path integral quantization and the construction of the S-matrix operator in the Abelian and non-Abelian Chern-Simons theories,” JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, pp. 3947–3965, 1997, Accessed: 00, 2020. [Online]. Available: