44,476 research outputs found
Quantum Holonomies in (2+1)-Dimensional Gravity
We describe an approach to the quantization of (2+1)--dimensional gravity
with topology R x T^2 and negative cosmological constant, which uses two
quantum holonomy matrices satisfying a q--commutation relation. Solutions of
diagonal and upper--triangular form are constructed, which in the latter case
exhibit additional, non--trivial internal relations for each holonomy matrix.
This leads to the notion of quantum matrix pairs. These are pairs of matrices
with non-commuting entries, which have the same pattern of internal relations,
q-commute with each other under matrix multiplication, and are such that
products of powers of the matrices obey the same pattern of internal relations
as the original pair. This has implications for the classical moduli space,
described by ordered pairs of commuting SL(2,R) matrices modulo simultaneous
conjugation by SL(2,R) matrices.Comment: 5 pages, to appear in the proceedings of 10th Marcel Grossmann
Meeting on Recent Developments in Theoretical and Experimental General
Relativity, Gravitation and Relativistic Field Theories (MG X MMIII), Rio de
Janeiro, Brazil, 20-26 Jul 200
On the divine clockwork: the spectral gap for the correspondence limit of the Nelson diffusion generator for the atomic elliptic state
The correspondence limit of the atomic elliptic state in three dimensions is
discussed in terms of Nelson's stochastic mechanics. In previous work we have
shown that this approach leads to a limiting Nelson diffusion and here we
discuss in detail the invariant measure for this process and show that it is
concentrated on the Kepler ellipse in the plane z=0. We then show that the
limiting Nelson diffusion generator has a spectral gap; thereby proving that in
the infinite time limit the density for the limiting Nelson diffusion will
converge to its invariant measure. We also include a summary of the Cheeger and
Poincare inequalities both of which are used in our proof of the existence of
the spectral gap.Comment: 30 pages, 5 figures, submitted to J. Math. Phy
The generalized Fenyes-Nelson model for free scalar field theory
The generalized Fenyes--Nelson model of quantum mechanics is applied to the
free scalar field. The resulting Markov field is equivalent to the Euclidean
Markov field with the times scaled by a common factor which depends on the
diffusion parameter. This result is consistent between Guerra's earlier work on
stochastic quantization of scalar fields. It suggests a deep connection between
Euclidean field theory and the stochastic interpretation of quantum mechanics.
The question of Lorentz covariance is also discussed.Comment: 6 page
Study of growth parameters for refractory carbide single crystals quarterly status report no. 4, dec. 1, 1964 - mar. 1, 1965
Growth of single crystals of tantalum carbide and hafnium carbide, and their solid solution
Quantum geometry from 2+1 AdS quantum gravity on the torus
Wilson observables for 2+1 quantum gravity with negative cosmological
constant, when the spatial manifold is a torus, exhibit several novel features:
signed area phases relate the observables assigned to homotopic loops, and
their commutators describe loop intersections, with properties that are not yet
fully understood. We describe progress in our study of this bracket, which can
be interpreted as a q-deformed Goldman bracket, and provide a geometrical
interpretation in terms of a quantum version of Pick's formula for the area of
a polygon with integer vertices.Comment: 19 pages, 11 figures, revised with more explanations, improved
figures and extra figures. To appear GER
Nonlinear Phenomena in Canonical Stochastic Quantization
Stochastic quantization provides a connection between quantum field theory
and statistical mechanics, with applications especially in gauge field
theories. Euclidean quantum field theory is viewed as the equilibrium limit of
a statistical system coupled to a thermal reservoir. Nonlinear phenomena in
stochastic quantization arise when employing nonlinear Brownian motion as an
underlying stochastic process. We discuss a novel formulation of the Higgs
mechanism in QED.Comment: 8 pages, invited talk at the International Workshop ``Critical
Phenomena and Diffusion in Complex Systems'', Dec. 5-7, 2006, Nizhni
Novgorod, Russi
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