8 research outputs found
A Massive Renormalizable Abelian Gauge Theory in 2+1 Dimensions
The standard formulation of a massive Abelian vector field in
dimensions involves a Maxwell kinetic term plus a Chern-Simons mass term; in
its place we consider a Chern-Simons kinetic term plus a Stuekelberg mass term.
In this latter model, we still have a massive vector field, but now the
interaction with a charged spinor field is renormalizable (as opposed to super
renormalizable). By choosing an appropriate gauge fixing term, the Stuekelberg
auxiliary scalar field decouples from the vector field. The one-loop spinor
self energy is computed using operator regularization, a technique which
respects the three dimensional character of the antisymmetric tensor
. This method is used to evaluate the vector self
energy to two-loop order; it is found to vanish showing that the beta function
is zero to two-loop order. The canonical structure of the model is examined
using the Dirac constraint formalism.Comment: LaTeX, 17 pages, expanded reference list and discussion of
relationship to previous wor
Off-Diagonal Elements of the DeWitt Expansion from the Quantum Mechanical Path Integral
The DeWitt expansion of the matrix element M_{xy} = \left\langle x \right|
\exp -[\case{1}{2} (p-A)^2 + V]t \left| y \right\rangle, in
powers of can be made in a number of ways. For (the case of interest
when doing one-loop calculations) numerous approaches have been employed to
determine this expansion to very high order; when (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 by a quantum mechanical path
integral. We also generalize our method to the case of curved space, allowing
us to determine the DeWitt expansion of \tilde M_{xy} = \langle x| \exp
\case{1}{2} [\case{1}{\sqrt {g}} (\partial_\mu - i
A_\mu)g^{\mu\nu}{\sqrt{g}}(\partial_\nu - i A_\nu) ] t| y \rangle 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 as a quantum mechanical path integral can be assessed. Furthermore, the
exact dependence of 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.Comment: 16pp, REVTeX. One additional appendix concerning end-point effects
for finite proper-time intervals; inclusion of these effects seem to make our
results consistent with those from explicit heat-kernel method
Structure of the Effective Potential in Nonrelativistic Chern-Simons Field Theory
We present the scalar field effective potential for nonrelativistic
self-interacting scalar and fermion fields coupled to an Abelian Chern-Simons
gauge field. Fermions are non-minimally coupled to the gauge field via a Pauli
interaction. Gauss's law linearly relates the magnetic field to the matter
field densities; hence, we also include radiative effects from the background
gauge field. However, the scalar field effective potential is transparent to
the presence of the background gauge field to leading order in the perturbative
expansion. We compute the scalar field effective potential in two gauge
families. We perform the calculation in a gauge reminiscent of the
-gauge in the limit and in the Coulomb family gauges.
The scalar field effective potential is the same in both gauge-fixings and is
independent of the gauge-fixing parameter in the Coulomb family gauge. The
conformal symmetry is spontaneously broken except for two values of the
coupling constant, one of which is the self-dual value. To leading order in the
perturbative expansion, the structure of the classical potential is deeply
distorted by radiative corrections and shows a stable minimum around the
origin, which could be of interest when searching for vortex solutions. We
regularize the theory with operator regularization and a cutoff to demonstrate
that the results are independent of the regularization scheme.Comment: 24 pages, UdeM-LPN-TH-93-185, CRM-192