90 research outputs found
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.
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
Spherically symmetric spacetimes in massive gravity
We explore spherically symmetric stationary solutions, generated by ``stars''
with regular interiors, in purely massive gravity. We reexamine the claim that
the resummation of non-linear effects can cure, in a domain near the source,
the discontinuity exhibited by the linearized theory as the mass m of the
graviton tends to zero. First, we find analytical difficulties with this claim,
which appears not to be robust under slight changes in the form of the mass
term. Second, by numerically exploring the inward continuation of the class of
asymptotically flat solutions, we find that, when m is ``small'', they all end
up in a singularity at a finite radius, well outside the source, instead of
joining some conjectured ``continuous'' solution near the source. We reopen,
however, the possibility of reconciling massive gravity with phenomenology by
exhibiting a special class of solutions, with ``spontaneous symmetry breaking''
features, which are close, near the source, to general relativistic solutions
and asymptote, for large radii, a de Sitter solution of curvature ~m^2.Comment: 57 pages, references addde
Mass and Gauge Invariance IV (Holography for the Karch-Randall Model)
We argue that the Karch-Randall compactification is holographically dual to a
4-d conformal field theory coupled to gravity on Anti de Sitter space. Using
this interpretation we recover the mass spectrum of the model. In particular,
we find no massless spin-2 states. By giving a purely 4-d interpretation to the
compactification we make clear that it represents the first example of a local
4-d field theory in which general covariance does not imply the existence of a
massless graviton. We also discuss some variations of the Karch-Randall model
discussed in the literature, and we examine whether its properties are generic
to all conformal field theory.Comment: 26 pages, uses package latexsym. Note added in proo
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