4,842 research outputs found
Geometry of Scattering at Planckian Energies
We present an alternative derivation and geometrical formulation of Verlinde
topological field theory, which may describe scattering at center of mass
energies comparable or larger than the Planck energy. A consistent trunckation
of 3+1 dimensional Einstein action is performed using the standard geometrical
objects, like tetrads and spin connections. The resulting topological invariant
is given in terms of differential forms.Comment: 8
Pauli-Lubanski scalar in the Polygon Approach to 2+1-Dimensional Gravity
In this paper we derive an expression for the conserved Pauli-Lubanski scalar
in 't Hooft's polygon approach to 2+1-dimensional gravity coupled to point
particles. We find that it is represented by an extra spatial shift in
addition to the usual identification rule (being a rotation over the cut). For
two particles this invariant is expressed in terms of 't Hooft's phase-space
variables and we check its classical limit.Comment: Some errors are corrected and a new introduction and discussion are
added. 6 pages Latex, 4 eps-figure
Chiral determinant on the lattice -- Anomalies and Instantons
An expression for the lattice effective action induced by chiral fermions in
any even dimensions in terms of an overlap of two states is shown to have
promising properties in two and four dimensions: The correct abelian anomaly is
reproduced and gauge field configurations with non-zero topological charge are
completely suppressed.Comment: 3 pages, ps-fil
Holographic entropy bound from gravitational Fock space truncation
A simplified derivation of Yurtsever's result, which states that the entropy
of a truncated bosonic Fock space is given by a holographic bound when the
energy of the Fock states is constrained gravitationally, is given for
asymptotically flat spacetimes with arbitrary dimension d greater or equal to
four. For this purpose, a scalar field confined to a spherical volume in
d-dimensional spacetime is considered. Imposing an upper bound on the total
energy of the corresponding Fock states which ensures that the system is in a
stable configuration against gravitational collapse and imposing a cutoff on
the maximum energy of the field modes of the order of the Planck energy leads
to an entropy bound of holographic type. A simple derivation of the entropy
bound is also given for the fermionic case.Comment: 5 pages, Latex (incl. style file), minor typos correcte
Strong to weak coupling transitions of SU(N) gauge theories in 2+1 dimensions
We investigate strong-to-weak coupling transitions in D=2+1 SU(N->oo) gauge
theories, by simulating lattice theories with a Wilson plaquette action. We
find that there is a strong-to-weak coupling cross-over in the lattice theory
that appears to become a third-order phase transition at N=oo, in a manner that
is essentially identical to the Gross-Witten transition in the D=1+1 SU(oo)
lattice gauge theory. There is also evidence for a second order transition at
N=oo at approximately the same coupling, which is connected with centre
monopoles (instantons) and so analogues to the first order bulk transition that
occurs in D=3+1 lattice gauge theories for N>4. We show that as the lattice
spacing is reduced, the N=oo gauge theory on a finite 3-torus suffers a
sequence of (apparently) first-order ZN symmetry breaking transitions
associated with each of the tori (ordered by size). We discuss how these
transitions can be understood in terms of a sequence of deconfining transitions
on ever-more dimensionally reduced gauge theories.We investigate whether the
trace of the Wilson loop has a non-analyticity in the coupling at some critical
area, but find no evidence for this although, just as in D=1+1,the eigenvalue
density of a Wilson loop forms a gap at N=oo for a critical trace. The physical
implications of this are unclear.The gap formation is a special case of a
remarkable similarity between the eigenvalue spectra of Wilson loops in D=1+1
and D=2+1 (and indeed D=3+1): for the same value of the trace, the eigenvalue
spectra are nearly identical.This holds for finite as well as infinite N;
irrespective of the Wilson loop size in lattice units; and for Polyakov as well
as Wilson loops.Comment: 44 pages, 28 figures. Extensive changes and clarifications with new
results on non-analyticities and eigenvalue spectra of Wilson loops. This
version to be submitted for publicatio
Quantum Gravity as a Dissipative Deterministic System
It is argued that the so-called holographic principle will obstruct attempts
to produce physically realistic models for the unification of general
relativity with quantum mechanics, unless determinism in the latter is
restored. The notion of time in GR is so different from the usual one in
elementary particle physics that we believe that certain versions of hidden
variable theories can -- and must -- be revived. A completely natural procedure
is proposed, in which the dissipation of information plays an essential role.
Unlike earlier attempts, it allows us to use strictly continuous and
differentiable classical field theories as a starting point (although discrete
variables, leading to fermionic degrees of freedom, are also welcome), and we
show how an effective Hilbert space of quantum states naturally emerges when
one attempts to describe the solutions statistically. Our theory removes some
of the mysteries of the holographic principle; apparently non-local features
are to be expected when the quantum degrees of freedom of the world are
projected onto a lower-dimensional black hole horizon. Various examples and
models illustrate the points we wish to make, notably a model showing that
massless, non interacting neutrinos are deterministic.Comment: 20 pages plain TeX, 2 figures PostScript. Added some further
explanations, and the definitions of `beable' and `changeable'. A minor error
correcte
Groundstate with Zero Eigenvalue for Generalized Sombrero-shaped Potential in -dimensional Space
Based on an iterative method for solving the goundstate of Schroedinger
equation, it is found that a kind of generalized Sombrero-shaped potentials in
N-dimensional space has groundstates with zero eigenvalue. The restrictions on
the parameters in the potential are discussed.Comment: 8 pages, 3 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
Quantization of Point Particles in 2+1 Dimensional Gravity and Space-Time Discreteness
By investigating the canonical commutation rules for gravitating quantized
particles in a 2+1 dimensional world it is found that these particles live on a
space-time lattice. The space-time lattice points can be characterized by three
integers. Various representations are possible, the details depending on the
topology chosen for energy-momentum space. We find that an
topology yields a physically most interesting lattice within which first
quantization of Dirac particles is possible. An topology also gives a
lattice, but does not allow first quantized particles.Comment: 23 pages Plain TeX, 3 Figure
1+1 Dimensional NCOS and its U(N) Gauge Theory Dual
We study some aspects of open string theories on D-branes with critical
electric fields. We show that the massless open string modes that move in the
direction of the electric field decouple. In the 1+1 dimensional case the dual
theory is U(N) SYM with electric flux, and the decoupling of massless open
strings is dual to the decoupling of the U(1) degrees of freedom. We also show
that, if the direction along the electric field is compact, then there are
finite energy winding closed string modes. They are dual to Higgs branch
excitations of the SYM theory, and their energetics works accordingly. These
properties provide new non-trivial evidence for the duality.Comment: 14 pages, LaTeX, 1 figure. V2: references and remarks on Hagedorn
behavior added. V3: minor typos fixe
- …