103 research outputs found
Non-abelian self-duality from self-interaction
The non-abelian self-dual action in three dimensions is derived using the
self-interaction mechanism.Comment: Latex, 7 page
A normal coordinate expansion of the gauge potential
In this pedagogical note, I present a method for constructing a fully covariant normal coordinate expansion of the gauge potential on a curved space-time manifold. Although the content of this paper is elementary, the results may prove useful in some applications and have not, to the best of my knowledge, been discussed in the literature
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
Quantum discontinuity between zero and infinitesimal graviton mass with a Lambda term
We show that the recently demonstrated absence of the usual discontinuity for
massive spin 2 with a Lambda term is an artifact of the tree approximation, and
that the discontinuity reappears at one loop.Comment: 8 pages, revtex 3.1, title changed (version to appear in Phys. Rev.
Lett.
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
Effective Lagrangian from Higher Curvature Terms: Absence of vDVZ Discontinuity in AdS Space
We argue that the van Dam-Veltman-Zakharov discontinuity arising in the limit of the massive graviton through an explicit Pauli-Fierz mass term
could be absent in anti de Sitter space. This is possible if the graviton can
acquire mass spontaneously from the higher curvature terms or/and the massless
limit is attained faster than the cosmological constant . We discuss the effects of higher-curvature couplings and of an explicit
cosmological term () on stability of such continuity and of massive
excitations.Comment: 23 pages, Latex, the version to appear in Class. Quant. Gra
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
Accelerated Universe from Gravity Leaking to Extra Dimensions
We discuss the idea that the accelerated Universe could be the result of the
gravitational leakage into extra dimensions on Hubble distances rather than the
consequence of non-zero cosmological constant.Comment: 20 pages, 6 figure
Two-Loop Quantum Corrections of Scalar QED with Non-Minimal Chern-Simons Coupling
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 the 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.Comment: 29 pages, including 21 figures. One author added, some formulae
corrected and references adde
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