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 $\Delta$ 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: SU(2)SU(2) gauge theory

We demonstrate that confinement in $SU(2)$ gauge theory is produced by dual superconductivity of the vacuum. We show that for $T < T_c$ (temperature of deconfining phase transition) the $U(1)$ symmetry related to monopole charge conservation is spontaneously broken; for $T > T_c$ 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 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 $S_2\times S_1$ topology yields a physically most interesting lattice within which first quantization of Dirac particles is possible. An $S_3$ topology also gives a lattice, but does not allow first quantized particles.Comment: 23 pages Plain TeX, 3 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

2+12+1 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 $2 \pi$. 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