Massive renormalizable Abelian gauge theory in 2+1 dimensions

Dilkes, F. A.; McKeon, D. G. C.

doi:10.1103/physrevd.52.4668

Cited by 7 publications

(7 citation statements)

References 43 publications

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“…It would therefore be of interest to examine an alternative regularization scheme that preserves gauge invariance without the need to dimensionally continue the antisymmetric tensor. One excellent candidate is operator regularization, which was shown to greatly facilitate two-loop calculations in Chern-Simons theory [20].…”

Section: Discussionmentioning

confidence: 99%

Two-loop quantum corrections of scalar QED with nonminimal Chern-Simons coupling

et al. 1999

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We investigate two-loop quantum corrections to non-minimally coupled Maxwell-Chern-Simons theory. The non-minimal gauge interaction represents the magnetic moment interaction between the charged scalar and the electromagnetic field. We show that one-loop renormalizability of the theory found in previous work does not survive to the two-loop level. However, with an appropriate choice of the non-minimal coupling constant, it is possible to renormalize the two-loop effective potential and hence render it potentially useful for a detailed analysis of spontaneous symmetry breaking induced by radiative corrections. ͓S0556-2821͑99͒05024-9͔

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Section: Discussionmentioning

confidence: 99%

Two-loop quantum corrections of scalar QED with nonminimal Chern-Simons coupling

et al. 1999

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“…as follows from [2], [6] and [7]. Since K 0 (x) ∼ − log x and K 1 (x) ∼ 1 x near x = 0, we see that the energy…”

Section: The Modelmentioning

confidence: 90%

“…Setting β = 0 in order to ensure that A 0 (r) vanishes at infinity, we see from [6] and [4b] that A(r) = −αr K 1 (µr) .…”

Section: The Modelmentioning

confidence: 99%

“…The constant of integration α in [6] and [7] is not fixed by considerations related to the equations [4]. (In (2-4), the constant of integration analogous to α is determined by requiring finiteness at r = 0; this is not possible here.…”

Section: The Modelmentioning

confidence: 99%

“…This motivates us to consider vortex solutions in a 2 + 1 dimensional model in which there is both a Chern-Simons and Stuekelberg mass term for the U(1) gauge field. This theory has been shown to be a renormalizable model for a massive vector field (6). The matter field to which this vector field couples is taken to be a scalar with quadratic and quartic self-interactions.…”

Section: Introductionmentioning

confidence: 99%

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Vortex solutions in the Chern-Simons Stuekelberg model

McKeon¹

1998

Can. J. Phys.

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Vortex solutions to the classical field equations in a massive, renormalizable U(1) gauge model are considered in (2+1) dimensions. A vector field whose kinetic term consists of a Chern-Simons term plus a Stuekelberg mass term is coupled to a scalar field. If the classical scalar field is set equal to zero, then there are classical configurations of the vector field in which the magnetic flux is non-vanishing and finite. In contrast to the Nielsen-Olesen vortex, the magnetic field vanishes exponentially at large distances and diverges logarithmicly at short distances. This divergence, although not so severe as to cause the flux to diverge, results in the Hamiltonian becoming infinite. If the classical scalar field is no longer equal to zero, then the magnetic flux is not only finite, but quantized and the asymptotic behaviour of the field is altered so that the Hamiltonian no longer suffers from a divergence due to the field configuration at the origin. Furthermore, the asymptotic behaviour at infinity is dependent on the magnitude of the Stuekelberg mass term.

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Off-diagonal elements of the DeWitt expansion from the quantum-mechanical path integral

Dilkes

McKeon

1996

Phys. Rev. D

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The DeWitt expansion of the matrix element M xy = x| exp −[ 1 2 (p − A) 2 + V ]t |y , (p = −i∂) in powers of t can be made in a number of ways. For x = y (the case of interest when doing one-loop calculations) numerous approaches have been employed to determine this expansion to very high order; when x = y (relevant for doing calculations beyond one-loop) there appear to be but two examples of performing the DeWitt expansion. In this paper we compute the off-diagonal elements of the DeWitt expansion coefficients using the Fock-Schwinger gauge. Our technique is based on representing M xy by a quantum mechanical path integral. We also generalize our method to the case of curved space, allowing us to determine the DeWitt expansion ofM xy = x| exp 1t|y by use of normal coordinates. By comparison with results for the DeWitt expansion of this matrix element obtained by the iterative solution of the diffusion equation, the relative merit of different approaches to the representation of M xy as a quantum mechanical path integral can be assessed. Furthermore, the exact dependence ofM xy on some geometric scalars can be determined. In two appendices, we discuss boundary effects in the one-dimensional quantum mechanical path integral, and the curved space generalization of the Fock-Schwinger gauge.

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Massive renormalizable Abelian gauge theory in 2+1 dimensions

Cited by 7 publications

References 43 publications

Two-loop quantum corrections of scalar QED with nonminimal Chern-Simons coupling

Two-loop quantum corrections of scalar QED with nonminimal Chern-Simons coupling

Vortex solutions in the Chern-Simons Stuekelberg model

Off-diagonal elements of the DeWitt expansion from the quantum-mechanical path integral

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