984 research outputs found
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
The Canonical Structure of the Superstring Action
We consider the canonical structure of the Green-Schwarz superstring in dimensions using the Dirac constraint formalism; it is shown that its
structure is similar to that of the superparticle in and
dimensions. A key feature of this structure is that the primary Fermionic
constraints can be divided into two groups using field-independent projection
operators; if one of these groups is eliminated through use of a Dirac Bracket
(DB) then the second group of primary Fermionic constraints becomes first
class. (This is what also happens with the superparticle action.) These primary
Fermionic first class constraints can be used to find the generator of a local
Fermionic gauge symmetry of the action. We also consider the superstring action
in other dimensions of space-time to see if the Fermionic gauge symmetry can be
made simpler than it is in , and dimensions. With a dimensional target space, we find that such a simplification occurs. We
finally show how in five dimensions there is no first class Fermionic
constraint.Comment: 24 pages, Latex2e; further comments and clarifications adde
A New Approach to Axial Vector Model Calculations II
We further develop the new approach, proposed in part I (hep-th/9807072), to
computing the heat kernel associated with a Fermion coupled to vector and axial
vector fields. We first use the path integral representation obtained for the
heat kernel trace in a vector-axialvector background to derive a Bern-Kosower
type master formula for the one-loop amplitude with vectors and
axialvectors, valid in any even spacetime dimension. For the massless case we
then generalize this approach to the full off-diagonal heat kernel. In the D=4
case the SO(4) structure of the theory can be broken down to by use of the 't Hooft symbols. Various techniques for explicitly
evaluating the spin part of the path integral are developed and compared. We
also extend the method to external fermions, and to the inclusion of isospin.
On the field theory side, we obtain an extension of the second order formalism
for fermion QED to an abelian vector-axialvector theory.Comment: Sequel to hep-th/9807072, references added, some clarifications and
corrections, 29 pages, RevTex, 8 diagrams using epsfig.st
The effect of small-amplitude time-dependent changes to the surface morphology of a sphere
Typical approaches to manipulation of flow separation employ passive means or active techniques such as blowing and suction or plasma acceleration. Here it is
demonstrated that the flow can be significantly altered by making small changes to the shape of the surface. A proof of concept experiment is performed using a very simple time-dependent perturbation to the surface of a sphere: a roughness element of 1% of the sphere diameter is moved azimuthally around a sphere surface upstream of the uncontrolled laminar separation point, with a rotational frequency as large as the vortex shedding frequency. A key finding is that the non-dimensional time to observe
a large effect on the lateral force due to the perturbation produced in the sphere boundary layers as the roughness moves along the surface is ˆt =tU_(∞)/D ≈4. This slow
development allows the moving element to produce a tripped boundary layer over an extended region. It is shown that a lateral force can be produced that is as large as the
drag. In addition, simultaneous particle image velocimetry and force measurements reveal that a pair of counter-rotating helical vortices are produced in the wake, which
have a significant effect on the forces and greatly increase the Reynolds stresses in the wake. The relatively large perturbation to the flow-field produced by the small
surface disturbance permits the construction of a phase-averaged, three-dimensional (two-velocity component) wake structure from measurements in the streamwise/radial
plane. The vortical structure arising due to the roughness element has implications for flow over a sphere with a nominally smooth surface or distributed roughness. In
addition, it is shown that oscillating the roughness element, or shaping its trajectory, can produce a mean lateral force
Treatment of a System with Explicitly Broken Gauge Symmetries
A system in which the free part of the action possesses a gauge symmetry that
is not respected by the interacting part presents problems when quantized. We
illustrate how the Dirac constraint formalism can be used to address this
difficulty by considering an antisymmetric tensor field interacting with a
spinor field.Comment: 10 pages, LaTeX2e, typos correcte
The Effective Potential in Non-Conformal Gauge Theories
By using the renormalization group (RG) equation it has proved possible to
sum logarithmic corrections to quantities that arise due to quantum effects in
field theories. In particular, the effective potential V in the Standard Model
in the limit that there are no massive parameters in the classical action (the
"conformal limit") has been subject to this analysis, as has the effective
potential in a scalar theory with a quartic self coupling and in massless
scalar electrodynamics. Having multiple coupling constants and/or mass
parameters in the initial action complicates this analysis, as then several
mass scales arise. We show how to address this problem by considering the
effective potential in scalar electrodynamics when the scalar field has a tree
level mass term. In addition to summing logarithmic corrections by using the RG
equation, we also consider the consequences of the condition V'(v)=0 where v is
the vacuum expectation value of the scalar. If V is expanded in powers of the
logarithms that arise, then it proves possible to show that either v is zero or
that V is independent of the scalar. (That is, either there is no spontaneous
symmetry breaking or the vacuum expectation value is not determined by
minimizing V as V is "flat".
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