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 improve

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

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

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

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 $S$-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: reference adde