288 research outputs found
On Special Re-quantization of a Black Hole
Quantized expressions for the gravitational energy and momentum are derived
from a linearized theory of teleparallel gravity. The derivation relies on a
second-quantization procedure that constructs annihilation and creation
operators for the graviton. The resulting gravitational field is a collection
of gravitons, each of which has precise energy and momentum. On the basis of
the weak-field approximation of Schwarzschild's solution, a new form for the
quantization of the mass of a black hole is derived.Comment: 4 page
DeWitt-Virasoro construction
We study a particular approach for analyzing worldsheet conformal invariance
for bosonic string propagating in a curved background using hamiltonian
formalism. We work in the Schrodinger picture of a single particle description
of the problem where the particle moves in an infinite-dimensional space.
Background independence is maintained in this approach by adopting DeWitt's
(Phys.Rev.85:653-661,1952) coordinate independent formulation of quantum
mechanics. This enables us to construct certain background independent notion
of Virasoro generators, called DeWitt-Virasoro (DWV) generators, and invariant
matrix elements of an arbitrary operator constructed out of them in spin-zero
representation. We show that the DWV algebra is given by the Witt algebra with
additional anomalous terms that vanish for Ricci-flat backgrounds. The actual
quantum Virasoro generators should be obtained by first introducing the vacuum
state and then normal ordering the DWV generators with respect to that. We
demonstrate the procedure in the simple cases of flat and pp-wave backgrounds.
This is a shorter version of arXiv:0912.3987 [hep-th] with many technical
derivations omitted.Comment: 18 pages, shorter version of arXiv:0912.3987 [hep-th] accepted for
publication in Pramana - Journal of Physic
Asymptotic Implied Volatility at the Second Order with Application to the SABR Model
We provide a general method to compute a Taylor expansion in time of implied
volatility for stochastic volatility models, using a heat kernel expansion.
Beyond the order 0 implied volatility which is already known, we compute the
first order correction exactly at all strikes from the scalar coefficient of
the heat kernel expansion. Furthermore, the first correction in the heat kernel
expansion gives the second order correction for implied volatility, which we
also give exactly at all strikes. As an application, we compute this asymptotic
expansion at order 2 for the SABR model.Comment: 27 pages; v2: typos fixed and a few notation changes; v3: published
version, typos fixed and comments added. in Large Deviations and Asymptotic
Methods in Finance, Springer (2015) 37-6
Heat Kernel Expansion and Extremal Kerr-Newmann Black Hole Entropy in Einstein-Maxwell Theory
We compute the second Seely-DeWitt coefficient of the kinetic operator of the
metric and gauge fields in Einstein-Maxwell theory in an arbitrary background
field configuration. We then use this result to compute the logarithmic
correction to the entropy of an extremal Kerr-Newmann black hole.Comment: 12 page
Gauge invariance and radiative corrections in an extra dimensional theory
The gauge structure of the four dimensional effective theory originated in a
pure five dimensional Yang-Mills theory compactified on the orbifold ,
is discussed on the basis of the BRST symmetry. If gauge parameters propagate
in the bulk, the excited Kaluza-Klein (KK) modes are gauge fields and the four
dimensional theory is gauge invariant only if the compactification is carried
out by using curvatures as fundamental objects. The four dimensional theory is
governed by two types of gauge transformations, one determined by the KK zero
modes of the gauge parameters and the other by the excited ones. Within this
context, a gauge-fixing procedure to quantize the KK modes that is covariant
under the first type of gauge transformations is shown and the ghost sector
induced by the gauge-fixing functions is presented. If the gauge parameters are
confined to the usual four dimensional space-time, the known result in the
literature is reproduced with some minor variants, although it is emphasized
that the excited KK modes are not gauge fields, but matter fields transforming
under the adjoint representation of . A calculation of the one-loop
contributions of the excited KK modes of the electroweak gauge group on the
off-shell WWV, with V a photon or a Z boson, is exhibited. Such contributions
are free of ultraviolet divergences and well-behaved at high energies.Comment: 7 pages, conference proceedings, a new reference was added, the title
has been change
Quantum gravitational contributions to quantum electrodynamics
Quantum electrodynamics describes the interactions of electrons and photons.
Electric charge (the gauge coupling constant) is energy dependent, and there is
a previous claim that charge is affected by gravity (described by general
relativity) with the implication that the charge is reduced at high energies.
But that claim has been very controversial with the situation inconclusive.
Here I report an analysis (free from earlier controversies) demonstrating that
that quantum gravity corrections to quantum electrodynamics have a quadratic
energy dependence that result in the reduction of the electric charge at high
energies, a result known as asymptotic freedom.Comment: To be published in Nature. 19 pages LaTeX, no figure
Remarks on the method of comparison equations (generalized WKB method) and the generalized Ermakov-Pinney equation
The connection between the method of comparison equations (generalized WKB
method) and the Ermakov-Pinney equation is established. A perturbative scheme
of solution of the generalized Ermakov-Pinney equation is developed and is
applied to the construction of perturbative series for second-order
differential equations with and without turning points.Comment: The collective of the authors is enlarged and the calculations in
Sec. 3 are correcte
Quantum Gravity in Everyday Life: General Relativity as an Effective Field Theory
This article is meant as a summary and introduction to the ideas of effective
field theory as applied to gravitational systems.
Contents:
1. Introduction
2. Effective Field Theories
3. Low-Energy Quantum Gravity
4. Explicit Quantum Calculations
5. ConclusionsComment: 56 pages, 2 figures, JHEP style, Invited review to appear in Living
Reviews of Relativit
Renormalization of the Yang-Mills theory in the ambiguity-free gauge
The renormalization procedure for the Yang-Mills theory in the gauge free of
the Gribov ambiguity is constructed. It is shown that all the ultraviolet
infinities may be removed by renormalization of the parameters entering the
classical Lagrangian and the local redefinition of the fields.Comment: 20 pages. Some explanations extended, one reference added. Final
version published in the journa
An inhomogeneous toy-model of the quantum gravity with explicitly evolvable observables
An inhomogeneous (1+1)-dimensional model of the quantum gravity is
considered. It is found, that this model corresponds to a string propagating
against some curved background space. The quantization scheme including the
Wheeler-DeWitt equation and the "particle on a sphere" type of the gauge
condition is suggested. In the quantization scheme considered, the "problem of
time" is solved by building of the quasi-Heisenberg operators acting in a space
of solutions of the Wheeler-DeWitt equation and the normalization of the wave
function corresponds to the Klein-Gordon type. To analyze the physical
consequences of the scheme, a (1+1)-dimensional background space is considered
for which a classical solution is found and quantized. The obtained estimations
show the way to solution of the cosmological constant problem, which consists
in compensation of the zero-point oscillations of the matter fields by the
quantum oscillations of the scale factor. Along with such a compensation, a
slow global evolution of a background corresponding to an universe expansion
exists.Comment: 18 page
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