3,260 research outputs found
Large-D Expansion from Variational Perturbation Theory
We derive recursively the perturbation series for the ground-state energy of
the D-dimensional anharmonic oscillator and resum it using variational
perturbation theory (VPT). From the exponentially fast converging approximants,
we extract the coefficients of the large-D expansion to higher orders. The
calculation effort is much smaller than in the standard field-theoretic
approach based on the Hubbard-Stratonovich transformation.Comment: Author Information under http://hbar.wustl.edu/~sbrandt and
http://www.theo-phys.uni-essen.de/tp/ags/pelster_di
Low-Energy Effective Action in Non-Perturbative Electrodynamics in Curved Spacetime
We study the heat kernel for the Laplace type partial differential operator
acting on smooth sections of a complex spin-tensor bundle over a generic
-dimensional Riemannian manifold. Assuming that the curvature of the U(1)
connection (that we call the electromagnetic field) is constant we compute the
first two coefficients of the non-perturbative asymptotic expansion of the heat
kernel which are of zero and the first order in Riemannian curvature and of
arbitrary order in the electromagnetic field. We apply these results to the
study of the effective action in non-perturbative electrodynamics in four
dimensions and derive a generalization of the Schwinger's result for the
creation of scalar and spinor particles in electromagnetic field induced by the
gravitational field. We discover a new infrared divergence in the imaginary
part of the effective action due to the gravitational corrections, which seems
to be a new physical effect.Comment: LaTeX, 42 page
The Existence of Einstein Static Universes and their Stability in Fourth order Theories of Gravity
We investigate whether or not an Einstein Static universe is a solution to
the cosmological equations in gravity. It is found that only one class
of theories admits an Einstein Static model, and that this class is
neutrally stable with respect to vector and tensor perturbations for all
equations of state on all scales. Scalar perturbations are only stable on all
scales if the matter fluid equation of state satisfies
. This result is remarkably similar to
the GR case, where it was found that the Einstein Static model is stable for
.Comment: Minor changes, To appear in PR
Common vacuum conservation amplitude in the theory of the radiation of mirrors in two-dimensional space-time and of charges in four-dimensional space-time
The action changes (and thus the vacuum conservation amplitudes) in the
proper-time representation are found for an accelerated mirror interacting with
scalar and spinor vacuum fields in 1+1 space. They are shown to coincide to
within the multiplier e^2 with the action changes of electric and scalar
charges accelerated in 3+1 space. This coincidence is attributed to the fact
that the Bose and Fermi pairs emitted by a mirror have the same spins 1 and 0
as do the photons and scalar quanta emitted by charges. It is shown that the
propagation of virtual pairs in 1+1 space can be described by the causal
Green's function \Delta_f(z,\mu) of the wave equation for 3+1 space. This is
because the pairs can have any positive mass and their propagation function is
represented by an integral of the causal propagation function of a massive
particle in 1+1 space over mass which coincides with \Delta_f(z,\mu). In this
integral the lower limit \mu is chosen small, but nonzero, to eliminate the
infrared divergence. It is shown that the real and imaginary parts of the
action change are related by dispersion relations, in which a mass parameter
serves as the dispersion variable. They are a consequence of the same relations
for \Delta_f(z,\mu). Therefore, the appearance of the real part of the action
change is a direct consequence of the causality, according to which real part
of \Delta_f(z,\mu) is nonzero only for timelike and zero intervals.Comment: 23 pages, Latex, revte
Homogeneous Solutions of Quadratic Gravity
It is believed that soon after the Planck time, Einstein's general relativity
theory should be corrected to an effective quadratic theory. In this work we
present the 3+1 decomposition for the zero vorticity case for arbitrary
spatially homogenous spaces. We specialize for the particular Bianchi
diagonal case. The 3- curvature can be understood as a generalized potential,
and the Bianchi case is a limiting case where this potential is negligible
to the dynamics. The spirit should be analogous, in some sense to the BKL
solution. In this sense, a better understanding of the Bianchi case could
shed some light into the general Bianchi case.Comment: talk presented in the 8th Friedmann Seminar, 30 May - 03 June 2011,
Rio de Janeiro, Brazi
On vacuum-vacuum amplitude and Bogoliubov coefficients
Even if the electromagnetic field does not create pairs, virtual pairs lead
to the appearance of a phase in vacuum-vacuum amplitude. This makes it
necessary to distinguish the in- and out-solutions even when it is commonly
assumed that there is only one complete set of solutions as, for example, in
the case of a constant magnetic field. Then in- and out-solutions differ only
by a phase factor which is in essence the Bogoliubov coefficient. The
propagator in terms of in- and out-states takes the same form as the one for
pair creating fields. The transition amplitude for an electron to go from an
initial in-state to out-state is equal to unity (in diagonal representation).
This is in agreement with Pauli principal: if in the field there is an electron
with given (conserved) set of quantum numbers, virtual pair cannot appear in
this state. So even the phase of transition amplitude remains unaffected by the
field. We show how one may redefine the phases of Bogoliubov coefficients in
order to express the vacuum-vacuum amplitude through them.Comment: 20pages, no figures, some typos corrected, minor improvement
Non-commutative Corrections in Spectral Matrix Gravity
We study a non-commutative deformation of general relativity based on
spectral invariants of a partial differential operator acting on sections of a
vector bundle over a smooth manifold. We compute the first non-commutative
corrections to Einstein equations in the weak deformation limit and analyze the
spectrum of the theory. Related topics are discussed as well.Comment: 32 Pages, LaTex. Some nonessential typos in intermediate calculations
in sect. 3 and 4 are corrected. The final results are the sam
Integral Equations for Heat Kernel in Compound Media
By making use of the potentials of the heat conduction equation the integral
equations are derived which determine the heat kernel for the Laplace operator
in the case of compound media. In each of the media the parameter
acquires a certain constant value. At the interface of the media the
conditions are imposed which demand the continuity of the `temperature' and the
`heat flows'. The integration in the equations is spread out only over the
interface of the media. As a result the dimension of the initial problem is
reduced by 1. The perturbation series for the integral equations derived are
nothing else as the multiple scattering expansions for the relevant heat
kernels. Thus a rigorous derivation of these expansions is given. In the one
dimensional case the integral equations at hand are solved explicitly (Abel
equations) and the exact expressions for the regarding heat kernels are
obtained for diverse matching conditions. Derivation of the asymptotic
expansion of the integrated heat kernel for a compound media is considered by
making use of the perturbation series for the integral equations obtained. The
method proposed is also applicable to the configurations when the same medium
is divided, by a smooth compact surface, into internal and external regions, or
when only the region inside (or outside) this surface is considered with
appropriate boundary conditions.Comment: 26 pages, no figures, no tables, REVTeX4; two items are added into
the Reference List; a new section is added, a version that will be published
in J. Math. Phy
Quantization of Two-Dimensional Gravity with Dynamical Torsion
We consider two-dimensional gravity with dynamical torsion in the Batalin -
Vilkovisky and Batalin - Lavrov - Tyutin formalisms of gauge theories
quantization as well as in the background field method.Comment: 12 pages, LaTe
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