36 research outputs found
Wheeler-DeWitt Quantization of Gravity Models of Unified Dark Energy and Dark Matter
First, we describe the construction of a new type of gravity-matter models
based on the formalism of non-Riemannian space-time volume forms - alternative
generally covariant integration measure densities (volume elements) defined in
terms of auxiliary antisymmetric tensor gauge fields. Here gravity couples in a
non-conventional way to two distinct scalar fields providing a unified
Lagrangian action principle description of: (i) the evolution of both "early"
and "late" Universe - by the "inflaton" scalar field; (ii) dark energy and dark
matter as a unified manifestation of a single material entity - the "darkon"
scalar field. A physically very interesting phenomenon occurs when including in
addition interactions with the electro-weak model bosonic sector - we obtain a
gravity-assisted dynamical generation of electro-weak spontaneous gauge
symmetry breaking in the post-inflationary "late" Universe, while the
Higgs-like scalar remains massless in the "early" Universe. Next, we proceed to
the Wheeler-DeWitt minisuperspace quantization of the above models. The
"darkon" field plays here the role of cosmological "time". In particular, we
show the absence of cosmological space-time singularities.Comment: 15 pages, to be published in the Proceedings of QTS10 - 10th
International Symposium "Quantum Theory and Symmetries" (Varna, 2017),
Springer Proceedings in Mathematics and Statistics, V. Dobrev (ed.). arXiv
admin note: text overlap with arXiv:1609.0691
An introduction to quantum gravity
After an overview of the physical motivations for studying quantum gravity,
we reprint THE FORMAL STRUCTURE OF QUANTUM GRAVITY, i.e. the 1978 Cargese
Lectures by Professor B.S. DeWitt, with kind permission of Springer. The reader
is therefore introduced, in a pedagogical way, to the functional integral
quantization of gravitation and Yang-Mills theory. It is hoped that such a
paper will remain useful for all lecturers or Ph.D. students who face the task
of introducing (resp. learning) some basic concepts in quantum gravity in a
relatively short time. In the second part, we outline selected topics such as
the braneworld picture with the same covariant formalism of the first part, and
spectral asymptotics of Euclidean quantum gravity with diffeomorphism-invariant
boundary conditions. The latter might have implications for singularity
avoidance in quantum cosmology.Comment: 68 pages, Latex file. Sections from 2 to 17 are published thanks to
kind permission of Springe
Green's function for gravitational waves in FRW spacetimes
A method for calculating the retarded Green's function for the gravitational
wave equation in Friedmann-Roberson-Walker spacetimes, within the formalism of
linearized Einstein gravity is developed. Hadamard's general solution to
Cauchy's problem for second-order, linear partial differential equations is
applied to the FRW gravitational wave equation. The retarded Green's function
may be calculated for any FRW spacetime, with curved or flat spatial sections,
for which the functional form of the Ricci scalar curvature is known. The
retarded Green's function for gravitational waves propagating through a
cosmological fluid composed of both radiation and dust is calculated
analytically for the first time. It is also shown that for all FRW spacetimes
in which the Ricci scalar curvatures does not vanish, , the Green's
function violates Huygens' principle; the Green's function has support inside
the light-cone due to the scatter of gravitational waves off the background
curvature.Comment: 9 pages, FERMILAB-Pub-93/189-
The Quantized Sigma Model Has No Continuum Limit in Four Dimensions. I. Theoretical Framework
The nonlinear sigma model for which the field takes its values in the coset
space is similar to quantum gravity in being
perturbatively nonrenormalizable and having a noncompact curved configuration
space. It is therefore a good model for testing nonperturbative methods that
may be useful in quantum gravity, especially methods based on lattice field
theory. In this paper we develop the theoretical framework necessary for
recognizing and studying a consistent nonperturbative quantum field theory of
the model. We describe the action, the geometry of the
configuration space, the conserved Noether currents, and the current algebra,
and we construct a version of the Ward-Slavnov identity that makes it easy to
switch from a given field to a nonlinearly related one. Renormalization of the
model is defined via the effective action and via current algebra. The two
definitions are shown to be equivalent. In a companion paper we develop a
lattice formulation of the theory that is particularly well suited to the sigma
model, and we report the results of Monte Carlo simulations of this lattice
model. These simulations indicate that as the lattice cutoff is removed the
theory becomes that of a pair of massless free fields. Because the geometry and
symmetries of these fields differ from those of the original model we conclude
that a continuum limit of the model which preserves
these properties does not exist.Comment: 25 pages, no figure
The EPR paradox, Bell's inequality, and the question of locality
Most physicists agree that the Einstein-Podolsky-Rosen-Bell paradox
exemplifies much of the strange behavior of quantum mechanics, but argument
persists about what assumptions underlie the paradox. To clarify what the
debate is about, we employ a simple and well-known thought experiment involving
two correlated photons to help us focus on the logical assumptions needed to
construct the EPR and Bell arguments. The view presented in this paper is that
the minimal assumptions behind Bell's inequality are locality and
counterfactual definiteness, but not scientific realism, determinism, or hidden
variables, as is often suggested. We further examine the resulting constraints
on physical theory with an illustration from the many-worlds interpretation of
quantum mechanics -- an interpretation that we argue is deterministic, local,
and realist, but that nonetheless violates the Bell inequality.Comment: 28 pages; change of title, minor wording changes, move to TeX forma
Feynman's interpretation of quantum theory
A historically important but little known debate regarding the necessity and
meaning of macroscopic superpositions, in particular those containing different
gravitational fields, is discussed from a modern perspective.Comment: Published version for Eur.Phys.J. H. 15 pages pdf. Final version
available at
http://www.springerlink.com/openurl.asp?genre=article&id=doi:10.1140/epjh/e2011-10035-
Perfect Fluid Quantum Anisotropic Universe: Merits and Challenges
The present paper deals with quantization of perfect fluid anisotropic
cosmological models. Bianchi type V and IX models are discussed following
Schutz's method of expressing fluid velocities in terms of six potentials. The
wave functions are found for several examples of equations of state. In one
case a complete wave packet could be formed analytically. The initial
singularity of a zero proper volume can be avoided in this case, but it is
plagued by the usual problem of non-unitarity of anisotropic quantum
cosmological models. It is seen that a particular operator ordering alleviates
this problem.Comment: 13 pages, 4 figures; Accepted for publication in Gen Relativ Gravi
The Quantized Sigma Model Has No Continuum Limit in Four Dimensions. II. Lattice Simulation
A lattice formulation of the sigma model is
developed, based on the continuum theory presented in the preceding paper.
Special attention is given to choosing a lattice action (the ``geodesic''
action) that is appropriate for fields having noncompact curved configuration
spaces. A consistent continuum limit of the model exists only if the
renormalized scale constant vanishes for some value of the bare scale
constant~. The geodesic action has a special form that allows direct
access to the small- limit. In this limit half of the degrees of freedom
can be integrated out exactly. The remaining degrees of freedom are those of a
compact model having a -independent action which is noteworthy in being
unbounded from below yet yielding integrable averages. Both the exact action
and the -independent action are used to obtain from Monte
Carlo computations of field-field averages (2-point functions) and
current-current averages. Many consistency cross-checks are performed. It is
found that there is no value of for which vanishes. This
means that as the lattice cutoff is removed the theory becomes that of a pair
of massless free fields. Because these fields have neither the geometry nor the
symmetries of the original model we conclude that the
model has no continuum limit.Comment: 32 pages, 7 postscript figures, UTREL 92-0
Harmonic BRST Quantization of Systems with Irreducible Holomorphic Boson and Fermion Constraints
We show that the harmonic Becchi-Rouet-Stora-Tyutin method of quantizing
bosonic systems with second-class constraints or first-class holomorphic
constraints extends to systems having both bosonic and fermionic second-class
or first-class holomorphic constraints. Using a limit argument, we show that
the harmonic BRST modified path integral reproduces the correct Senjanovic
measure.Comment: 11 pages, phyzz
Recommended from our members
Quantum mechanics
textLecture Notes by
Bryce S. De Witt,
Radiation Laboratory,
University of California. Cours professe a Ecole d'ete de physique theorique. Les Houches, Haute-Savoie, FranceEcole d'ete de physique theorique. Les Houches, Haute-Savoie, FrancePhysic