26,186 research outputs found
Invariant measure in hot gauge theories
We investigate properties of the invariant measure for the gauge field
in finite temperature gauge theories both on the lattice and in the continuum
theory. We have found the cancellation of the naive measure in both cases. The
result is quite general and holds at any finite temperature. We demonstrate,
however, that there is no cancellation at any temperature for the invariant
measure contribution understood as Z(N) symmetrical distribution of gauge field
configurations. The spontaneous breakdown of Z(N) global symmetry is entirely
due to the potential energy term of the gluonic interaction in the effective
potential. The effects of this measure on the effective action, mechanism of
confinement and condensation are discussed.Comment: Latex file, 65.5kB, no figure
Singular measures in circle dynamics
Critical circle homeomorphisms have an invariant measure totally singular
with respect to the Lebesgue measure. We prove that singularities of the
invariant measure are of Holder type. The Hausdorff dimension of the invariant
measure is less than 1 but greater than 0
Subexponential instability implies infinite invariant measure
We study subexponential instability to characterize a dynamical instability
of weak chaos. We show that a dynamical system with subexponential instability
has an infinite invariant measure, and then we present the generalized Lyapunov
exponent to characterize subexponential instability.Comment: 7 pages, 5 figure
Mixmaster Chaos via the Invariant Measure
The chaoticity of the Mixmaster is discussed in the framework of Statistical
Mechanics by using Misner--Chitre-like variables and an ADM reduction of its
dynamics. We show that such a system is well described by a microcanonical
ensemble whose invariant measure is induced by the corresponding Liouville one
and is uniform. The covariance with respect to the choice of the temporal gauge
of the obtained invariant measure is outlined.Comment: 3 pages, 1 figure, proceedings of the X Marcel Grossmann Meeting
22-26 July, 2003, Rio de Janeir
The invariant measure of homogeneous Markov processes in the quarter-plane: Representation in geometric terms
We consider the invariant measure of a homogeneous continuous-time Markov process in the quarter-plane. The basic solutions of the global balance equation are the geometric distributions. We first show that the invariant measure can not be a finite linear combination of basic geometric distributions, unless it consists of a single basic geometric distribution. Second, we show that a countable linear combination of geometric terms can be an invariant measure only if it consists of pairwise-coupled terms. As a consequence, we obtain a complete characterization of all countable linear combinations of geometric distributions that may yield an invariant measure for a homogeneous continuous-time Markov process in the quarter-plane
Diffeomorphism invariant measure for finite dimensional geometries
We consider families of geometries of D--dimensional space, described by a
finite number of parameters. Starting from the De Witt metric we extract a
unique integration measure which turns out to be a geometric invariant, i.e.
independent of the gauge fixed metric used for describing the geometries. The
measure is also invariant in form under an arbitrary change of parameters
describing the geometries. We prove the existence of geometries for which there
are no related gauge fixing surfaces orthogonal to the gauge fibers. The
additional functional integration on the conformal factor makes the measure
independent of the free parameter intervening in the De Witt metric. The
determinants appearing in the measure are mathematically well defined even
though technically difficult to compute.Comment: 18 pages, no figures, plain LaTeX fil
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