3,096 research outputs found
Quantum Mechanics of a Point Particle in 2+1 Dimensional Gravity
We study the phase space structure and the quantization of a pointlike
particle in 2+1 dimensional gravity. By adding boundary terms to the first
order Einstein Hilbert action, and removing all redundant gauge degrees of
freedom, we arrive at a reduced action for a gravitating particle in 2+1
dimensions, which is invariant under Lorentz transformations and a group of
generalized translations. The momentum space of the particle turns out to be
the group manifold SL(2). Its position coordinates have non-vanishing Poisson
brackets, resulting in a non-commutative quantum spacetime. We use the
representation theory of SL(2) to investigate its structure. We find a
discretization of time, and some semi-discrete structure of space. An
uncertainty relation forbids a fully localized particle. The quantum dynamics
is described by a discretized Klein Gordon equation.Comment: 58 pages, 3 eps figures, presentation of the classical theory
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A semiclassical realization of infrared renormalons
Perturbation series in quantum field theory are generally divergent
asymptotic series which are also typically not Borel resummable in the sense
that the resummed series is ambiguous. The ambiguity is associated with
singularities in the Borel plane on the positive real axis. In quantum
mechanics there are cases in which the ambiguity that arises in perturbation
theory cancels against a similarly ambiguous contribution from
instanton--anti-instanton events. In asymptotically free gauge theories this
mechanism does not suffice because perturbation theory develops ambiguities
associated with singularities in the Borel plane which are closer to the origin
by a factor of about N (the rank of the gauge group) compared to the
singularities realized by instanton events. These are called IR renormalon
poles, and on R**4 they do not possess any known semiclassical realization. By
using continuity on R**3 x S**1, and by generalizing the works of Bogomolny and
Zinn-Justin to QFT, we identify saddle point field configurations, e.g.,
bion--anti-bion events, corresponding to singularities in the Borel plane which
are of order N times closer to the origin than the 4d BPST
instanton--anti-instanton singularity. We conjecture that these are the leading
singularities in the Borel plane and that they are the incarnation of the
elusive renormalons in the weak coupling regime.Comment: 4 page
Two particle Quantummechanics in 2+1 Gravity using Non Commuting Coordinates
We find that the momentum conjugate to the relative distance between two
gravitating particles in their center of mass frame is a hyperbolic angle. This
fact strongly suggests that momentum space should be taken to be a hyperboloid.
We investigate the effect of quantization on this curved momentum space. The
coordinates are represented by non commuting, Hermitian operators on this
hyperboloid. We also find that there is a smallest distance between the two
particles of one half times the Planck length.Comment: 18 pages Latex, 2 eps figure
Dimensional Reduction via Noncommutative Spacetime: Bootstrap and Holography
Unlike noncommutative space, when space and time are noncommutative, it seems
necessary to modify the usual scheme of quantum mechanics. We propose in this
paper a simple generalization of the time evolution equation in quantum
mechanics to incorporate the feature of a noncommutative spacetime. This
equation is much more constraining than the usual Schr\"odinger equation in
that the spatial dimension noncommuting with time is effectively reduced to a
point in low energy. We thus call the new evolution equation the spacetime
bootstrap equation, the dimensional reduction called for by this evolution
seems close to what is required by the holographic principle. We will discuss
several examples to demonstrate this point.Comment: 15 pages, harvmac. v2: typos corrected and some changes mad
Gedanken Experiments involving Black Holes
Analysis of several gedanken experiments indicates that black hole
complementarity cannot be ruled out on the basis of known physical principles.
Experiments designed by outside observers to disprove the existence of a
quantum-mechanical stretched horizon require knowledge of Planck-scale effects
for their analysis. Observers who fall through the event horizon after sampling
the Hawking radiation cannot discover duplicate information inside the black
hole before hitting the singularity. Experiments by outside observers to detect
baryon number violation will yield significant effects well outside the
stretched horizon.Comment: 22 pages (including 7 figures), SU-ITP-93-1
Quark Confinement and Dual Representation in 2+1 Dimensional Pure Yang-Mills Theory
We study the quark confinement problem in 2+1 dimensional pure Yang-Mills
theory using euclidean instanton methods. The instantons are regularized and
dressed Wu-Yang monopoles. The dressing of a monopole is due to the mean field
of the rest of the monopoles. We argue that such configurations are stable to
small perturbations unlike the case of singular, undressed monopoles. Using
exact non-perturbative results for the 3-dim. Coulomb gas, where Debye
screening holds for arbitrarily low temperatures, we show in a self-consistent
way that a mass gap is dynamically generated in the gauge theory. The mass gap
also determines the size of the monopoles. In a sense the pure Yang-Mills
theory generates a dynamical Higgs effect. We also identify the disorder
operator of the model in terms of the Sine-Gordon field of the Coulomb gas.Comment: 26 pages, RevTex, Title changed, a new section added, the discussion
on stability of dressed monopole expanded. Version to appear in Physical
Review
Feynman Propagator for a Free Scalar Field on a Causal Set
The Feynman propagator for a free bosonic scalar field on the discrete
spacetime of a causal set is presented. The formalism includes scalar field
operators and a vacuum state which define a scalar quantum field theory on a
causal set. This work can be viewed as a novel regularisation of quantum field
theory based on a Lorentz invariant discretisation of spacetime.Comment: 4 pages, 2 plots. Minor updates to match published versio
Identification of indirect new physics effects at e^+e^- colliders: the large extra dimensions case
We discuss indirect manifestations of graviton exchange, predicted by large
extra dimensions, in fermion-pair production at a high-energy e^+e^- collider.
By means of specifically defined asymmetries among integrated angular
distributions, the graviton exchange signal can be cleanly distinguished from
the effects of either vector-vector contact interactions or heavy scalar
exchanges. The role of initial electron and positron beams polarization is also
discussed. The method is applied to a quantitative assessment of the
sensitivity to the mass cut-off parameter M_H of the KK graviton tower in the
ADD scenario, and of the potential identification reach of this mechanism
obtainable at the currently planned Linear Collider.Comment: 21 pages, 11 figure
Black Hole Evaporation without Information Loss
An approach to black hole quantization is proposed wherein it is assumed that
quantum coherence is preserved. A consequence of this is that the Penrose
diagram describing gravitational collapse will show the same topological
structure as flat Minkowski space. After giving our motivations for such a
quantization procedure we formulate the background field approximation, in
which particles are divided into "hard" particles and "soft" particles. The
background space-time metric depends both on the in-states and on the
out-states. We present some model calculations and extensive discussions. In
particular, we show, in the context of a toy model, that the -matrix
describing soft particles in the hard particle background of a collapsing star
is unitary, nevertheless, the spectrum of particles is shown to be
approximately thermal. We also conclude that there is an important topological
constraint on functional integrals.Comment: 35 pages (including Figures); TEX, 3 figures in postscrip
Global AdS Picture of 1/2 BPS Wilson Loops
We study the holographic dual string configuration of 1/2 BPS circular Wilson
loops in N=4 super Yang-Mills theory by using the global coordinate of AdS. The
dual string worldsheet is given by the Poincare disk AdS_2 sitting at a
constant global time slice of AdS_5. We also analyze the correlator of two
concentric circular Wilson loops from the global AdS perspective and study the
phase transition associated with the instability of annulus worldsheet
connecting the two Wilson loops.Comment: 14 pages, 3 figures, v2: discussion on two branches corrected, v3:
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