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

Download

index.pdf

Date

1997-06-07

Author

Fainberg, VY
Pak, Namık Kemal
Shikakhwa, MS

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

315
views

56
downloads

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.

Subject Keywords

Mathematical Physics, General Physics and Astronomy, Statistical and Nonlinear Physics

URI

https://hdl.handle.net/11511/62741

Journal

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL

DOI

https://doi.org/10.1088/0305-4470/30/11/022

Collections

Department of Physics, Article

Suggestions

OpenMETU
Core

The discrete harmonic oscillator, Harper's equation, and the discrete fractional Fourier transform BARKER, L; Candan, Çağatay; HAKIOGLU, T; KUTAY, MA; OZAKTAS, HM (IOP Publishing, 2000-03-24) Certain solutions to Harper's equation are discrete analogues of (and approximations to) the Hermite-Gaussian functions. They are the energy eigenfunctions of a-discrete algebraic analogue of the harmonic oscillator, and they lead to a definition of a discrete fractional Fourier transform (FT). The discrete fractional FT is essentially the time-evolution operator of the discrete harmonic oscillator.
The Lie algebra sl(2,R) and so-called Kepler-Ermakov systems Leach, PGL; Karasu, Emine Ayşe (Informa UK Limited, 2004-05-01) A recent paper by Karasu (Kalkanli) and Yildirim (Journal of Nonlinear Mathematical Physics 9 (2002) 475-482) presented a study of the Kepler-Ermakov system in the context of determining the form of an arbitrary function in the system which was compatible with the presence of the sl(2, R) algebra characteristic of Ermakov systems and the existence of a Lagrangian for a subset of the systems. We supplement that analysis by correcting some results.
An alternative simple solution of the sextic anharmonic oscillator and perturbed coulomb problems IKHDAİR, SAMEER; Sever, Ramazan (World Scientific Pub Co Pte Lt, 2007-10-01) Utilizing an appropriate ansatz to the wave function, we reproduce the exact bound-state solutions of the radial Schrodinger equation to various exactly solvable sextic an-harmonic oscillator and confining perturbed Coulomb models in D-dimensions. We show that the perturbed Coulomb problem with eigenvalue E can be transformed to a sextic anharmonic oscillator problem with eigenvalue P. We also check the explicit relevance of these two related problems in higher-space dimensions. It is shown that exact solut...
Gardner's deformations of the Boussinesq equations Karasu, Atalay (IOP Publishing, 2006-09-15) Using the algebraic method of Gardner's deformations for completely integrable systems, we construct recurrence relations for densities of the Hamiltonians for the Boussinesq and the Kaup-Boussinesq equations. By extending the Magri schemes for these equations, we obtain new integrable systems adjoint with respect to the initial ones and describe their Hamiltonian structures and symmetry properties.
FIRST-PRINCIPLES CALCULATIONS FOR THE STRUCTURAL AND ELECTRONIC PROPERTIES OF ScxAl1-xN ALLOYS Mohammad, Rezek; Katırcıoğlu, Şenay (World Scientific Pub Co Pte Lt, 2013-10-01) The first-principles calculations based on Density Functional Theory (DFT) within generalized gradient approximation (GGA) of Engel-Vosko-Perdew-Wang and modified exact exchange potential of Becke-Johnson have been introduced for the structural and electronic properties of the ScxAl1-xN alloys, respectively. The present lattice constants calculated for the ScAlN alloys and the end compounds (AlN and ScN) are found to be in very good agreement with the available experimental and theoretical ones. The stable ...

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: https://hdl.handle.net/11511/62741.