1,093 research outputs found
Generators of Local Supersymmetry Transformation from First Class Constraints
We show how the generator of local supersymmetry transformations can be found
from Fermionic first class constraints. This is done by adapting the approaches
of Henneaux, Teit- elboim and Zanelli and of Castellani that has been used to
find the generator of gauge trans- formations from Bosonic first class
constraints. We illustrate how a supersymmetric gauge generator can be found by
considering the spinning particle. The invariances that we find are not those
presented in the original discussion of the spinning particle.Comment: nine page
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
Gauge Dependence in Chern-Simons Theory
We compute the contribution to the modulus of the one-loop effective action
in pure non-Abelian Chern-Simons theory in an arbitrary covariant gauge. We
find that the results are dependent on both the gauge parameter () and
the metric required in the gauge fixing. A contribution arises that has not
been previously encountered; it is of the form . This is possible as in three dimensions
is dimensionful. A variant of proper time regularization is used to render
these integrals well behaved (although no divergences occur when the
regularization is turned off at the end of the calculation). Since the original
Lagrangian is unaltered in this approach, no symmetries of the classical theory
are explicitly broken and is handled unambiguously
since the system is three dimensional at all stages of the calculation. The
results are shown to be consistent with the so-called Nielsen identities which
predict the explicit gauge parameter dependence using an extension of BRS
symmetry. We demonstrate that this dependence may potentially
contribute to the vacuum expectation values of products of Wilson loops.Comment: 17 pp (including 3 figures). Uses REVTeX 3.0 and epsfig.sty
(available from LANL). Latex thric
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
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
Spinors in Weyl Geometry
We consider the wave equation for spinors in -dimensional Weyl
geometry. By appropriately coupling the Weyl vector as well as
the spin connection to the spinor field, conformal
invariance can be maintained. The one loop effective action generated by the
coupling of the spinor field to an external gravitational field is computed in
two dimensions. It is found to be identical to the effective action for the
case of a scalar field propagating in two dimensions.Comment: 13 pages, REVTEX, no figure
The Supersymmetric Stueckelberg Mass and Overcoming the Fayet-Iliopoulos Mechanism for Breaking Symmetry
Gauge invariant generation of mass for supersymmetric U(1) vector field
through use of a chiral Stueckelberg superfield is considered. When a
Fayet-Iliopoulos D term is also present, no breaking of supersymmetry ever
occurs so long as the Stueckelberg mass is not zero. A moduli space in which
gauge symmetry is spontaneously broken arises in this case
Vortical Gusts: Experimental Generation and Interaction with Wing
We describe the experimental generation of isolated vortical gusts and the interaction between these gusts and a downstream airfoil at a Reynolds number of 20,000. A standard method of generating a vortical gust has been to rapidly pitch an airfoil. A different approach is presented here: heaving a plate across a tunnel and changing direction rapidly to release a vortex. This method is motivated by the desire to limit a test article’s exposure to the wake of the gust generator by moving it to the side of the tunnel. Two suites of experiments were performed to characterize the performance of the gust generators and to measure the forces on and flow around the downstream airfoil. The novel mechanism allowed for measurement of the resumption of vortex shedding from the downstream airfoil, which was impossible with the pitching generator
- …