988 research outputs found
Non-Quadratic Gauge Fixing and Global Gauge Invariance in the Effective Action
The possibility of having a gauge fixing term in the effective Lagrangian
that is not a quadratic expression has been explored in spin-two theories so as
to have a propagator that is both traceless and transverse. We first show how
this same approach can be used in spontaneously broken gauge theories as an
alternate to the 't Hooft gauge fixing which avoids terms quadratic in the
scalar fields. This "non-quadratic" gauge fixing in the effective action
results in there being two complex Fermionic and one real Bosonic ghost fields.
A global gauge invariance involving a Fermionic gauge parameter, analogous to
the usual BRST invariance, is present in this effective action.Comment: 4 pages, revtex4 (submitted to Phys. Rev. D
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
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".
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
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
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