4,476 research outputs found
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
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
Colour confinement as dual Meissner effect: gauge theory
We demonstrate that confinement in gauge theory is produced by dual
superconductivity of the vacuum. We show that for (temperature of
deconfining phase transition) the symmetry related to monopole charge
conservation is spontaneously broken; for the symmetry is restored.Comment: 10 pages + 4 figures, uuencoded shell archiv
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
Magnetic Monopoles in Field Theory and Cosmology
The existence of magnetic monopoles is predicted by many theories of particle
physics beyond the Standard Model. However, in spite of extensive searches,
there is no experimental or observational sign of them. I review the role of
magnetic monopoles in quantum field theory and discuss their implications for
particle physics and cosmology. I also highlight their differences and
similarities with monopoles found in frustrated magnetic systems, and discuss
how experiments carried out in these systems could help us understand the
physics of fundamental monopoles.Comment: 15 pages, no figures. Based on a talk given at the discussion meeting
"Emergent magnetic monopoles in frustrated magnetic systems" at the Kavli
Royal Society International Centre, 17-18 October 2011. To be published in
Philosophical Transactions of the Royal Society
Gravitational Correction to Running of Gauge Couplings
We calculate the contribution of graviton exchange to the running of gauge
couplings at lowest non-trivial order in perturbation theory. Including this
contribution in a theory that features coupling constant unification does not
upset this unification, but rather shifts the unification scale. When
extrapolated formally, the gravitational correction renders all gauge couplings
asymptotically free.Comment: 4 pages, 2 figures; v2: Clarified awkward sentences and notations.
Corrected typos. Added references and discussion thereof in introduction.
Minor copy editting changes to agree with version to be published in Physical
Review Letter
Color Dynamics in External Fields
We investigate the vacuum dynamics of U(1), SU(2), and SU(3) lattice gauge
theories in presence of external (chromo)magnetic fields, both in (3+1) and
(2+1) dimensions. We find that the critical coupling for the phase transition
in compact U(1) gauge theory is independent of the strength of an external
magnetic field. On the other hand we find that, both in (3+1) and (2+1)
dimensions, the deconfinement temperature for SU(2) and SU(3) gauge systems in
a constant abelian chromomagnetic field decreases when the strength of the
applied field increases. We conclude that the dependence of the deconfinement
temperature on the strength of an external constant chromomagnetic field is a
peculiar feature of non abelian gauge theories and could be useful to get
insight into color confinement.Comment: 26 pages, 14 figure
Quantization, group contraction and zero point energy
We study algebraic structures underlying 't Hooft's construction relating
classical systems with the quantum harmonic oscillator. The role of group
contraction is discussed. We propose the use of SU(1,1) for two reasons:
because of the isomorphism between its representation Hilbert space and that of
the harmonic oscillator and because zero point energy is implied by the
representation structure. Finally, we also comment on the relation between
dissipation and quantization.Comment: 6 pages, 3 figure
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
Covariant Lattice Theory and t'Hooft's Formulation
We show that 't Hooft's representation of (2+1)-dimensional gravity in terms
of flat polygonal tiles is closely related to a gauge-fixed version of the
covariant Hamiltonian lattice theory. 't Hooft's gauge is remarkable in that it
leads to a Hamiltonian which is a linear sum of vertex Hamiltonians, each of
which is defined modulo . A cyclic Hamiltonian implies that ``time'' is
quantized. However, it turns out that this Hamiltonian is {\it constrained}. If
one chooses an internal time and solves this constraint for the ``physical
Hamiltonian'', the result is not a cyclic function. Even if one quantizes {\it
a la Dirac}, the ``internal time'' observable does not acquire a discrete
spectrum. We also show that in Euclidean 3-d lattice gravity, ``space'' can be
either discrete or continuous depending on the choice of quantization. Finally,
we propose a generalization of 't Hooft's gauge for Hamiltonian lattice
formulations of topological gravity dimension 4.Comment: 10 pages of text. One figure available from J.A. Zapata upon reques
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