74 research outputs found
Semi-classical analysis of non self-adjoint transfer matrices in statistical mechanics. I
We propose a way to study one-dimensional statistical mechanics models with
complex-valued action using transfer operators. The argument consists of two
steps. First, the contour of integration is deformed so that the associated
transfer operator is a perturbation of a normal one. Then the transfer operator
is studied using methods of semi-classical analysis.
In this paper we concentrate on the second step, the main technical result
being a semi-classical estimate for powers of an integral operator which is
approximately normal.Comment: 28 pp, improved the presentatio
Inverting Ray-Knight identity
We provide a short proof of the Ray-Knight second generalized Theorem, using
a martingale which can be seen (on the positive quadrant) as the Radon-Nikodym
derivative of the reversed vertex-reinforced jump process measure with respect
to the Markov jump process with the same conductances. Next we show that a
variant of this process provides an inversion of that Ray-Knight identity. We
give a similar result for the Ray-Knight first generalized Theorem.Comment: 18 page
Topological Graph Polynomials in Colored Group Field Theory
In this paper we analyze the open Feynman graphs of the Colored Group Field
Theory introduced in [arXiv:0907.2582]. We define the boundary graph
\cG_{\partial} of an open graph \cG and prove it is a cellular complex.
Using this structure we generalize the topological (Bollobas-Riordan) Tutte
polynomials associated to (ribbon) graphs to topological polynomials adapted to
Colored Group Field Theory graphs in arbitrary dimension
On Batalin-Vilkovisky Formalism of Non-Commutative Field Theories
We apply the BV formalism to non-commutative field theories, introduce BRST
symmetry, and gauge-fix the models. Interestingly, we find that treating the
full gauge symmetry in non-commutative models can lead to reducible gauge
algebras. As one example we apply the formalism to the Connes-Lott two-point
model. Finally, we offer a derivation of a superversion of the
Harish-Chandra-Itzykson-Zuber integral.Comment: 20 pages, LaTeX. v2: minor corrections. v3: Added an Appendix about
Harish-Chandra-Itzykson-Zuber integrals. v4: Added Reference
Functional Integral Construction of the Thirring model: axioms verification and massless limit
We construct a QFT for the Thirring model for any value of the mass in a
functional integral approach, by proving that a set of Grassmann integrals
converges, as the cutoffs are removed and for a proper choice of the bare
parameters, to a set of Schwinger functions verifying the Osterwalder-Schrader
axioms. The corresponding Ward Identities have anomalies which are not linear
in the coupling and which violate the anomaly non-renormalization property.
Additional anomalies are present in the closed equation for the interacting
propagator, obtained by combining a Schwinger-Dyson equation with Ward
Identities.Comment: 55 pages, 9 figure
Constructive Field Theory and Applications: Perspectives and Open Problems
In this paper we review many interesting open problems in mathematical
physics which may be attacked with the help of tools from constructive field
theory. They could give work for future mathematical physicists trained with
the constructive methods well within the 21st century
Cluster and virial expansions for the multi-species tonks gas
We consider a mixture of non-overlapping rods of different lengths ℓk moving in R or Z. Our main result are necessary and sufficient convergence criteria for the expansion of the pressure in terms of the activities zk and the densities ρk. This provides an explicit example against which to test known cluster expansion criteria, and illustrates that for non-negative interactions, the virial expansion can converge in a domain much larger than the activity expansion. In addition, we give explicit formulas that generalize the well-known relation between non-overlapping rods and labelled rooted trees. We also prove that for certain choices of the activities, the system can undergo a condensation transition akin to that of the zero-range process. The key tool is a fixed point equation for the pressure
Quantum Gravity, Field Theory and Signatures of Noncommutative Spacetime
A pedagogical introduction to some of the main ideas and results of field
theories on quantized spacetimes is presented, with emphasis on what such field
theories may teach us about the problem of quantizing gravity. We examine to
what extent noncommutative gauge theories may be regarded as gauge theories of
gravity. UV/IR mixing is explained in detail and we describe its relations to
renormalization, to gravitational dynamics, and to deformed dispersion
relations in models of quantum spacetime of interest in string theory and in
doubly special relativity. We also discuss some potential experimental probes
of spacetime noncommutativity.Comment: 26 pages, 4 figures; v2: comments and references added; v3: typos
corrected, clarifying comments and references added; Based on Plenary Lecture
delivered at the XXIX Encontro Nacional de Fisica de Particulas e Campos, Sao
Lourenco, Brasil, September 22-26, 2008; Final version to be published in
General Relativity and Gravitatio
Effectiveness of cardiac resynchronization therapy in heart failure patients with valvular heart disease: comparison with patients affected by ischaemic heart disease or dilated cardiomyopathy. The InSync/InSync ICD Italian Registry
AimsTo analyse the effectiveness of cardiac resynchronization therapy (CRT) in patients with valvular heart disease (a subset not specifically investigated in randomized controlled trials) in comparison with ischaemic heart disease or dilated cardiomyopathy patients.Methods and resultsPatients enrolled in a national registry were evaluated during a median follow-up of 16 months after CRT implant. Patients with valvular heart disease treated with CRT (n = 108) in comparison with ischaemic heart disease (n = 737) and dilated cardiomyopathy (n = 635) patients presented: (i) a higher prevalence of chronic atrial fibrillation, with atrioventricular node ablation performed in around half of the cases; (ii) a similar clinical and echocardiographic profile at baseline; (iii) a similar improvement of LVEF and a similar reduction in ventricular volumes at 6-12 months; (iv) a favourable clinical response at 12 months with an improvement of the clinical composite score similar to that occurring in patients with dilated cardiomyopathy and more pronounced than that observed in patients with ischaemic heart disease; (v) a long-term outcome, in term of freedom from death or heart transplantation, similar to patients affected by ischaemic heart disease and basically more severe than that of patients affected by dilated cardiomyopathy.ConclusionIn 'real world' clinical practice, CRT appears to be effective also in patients with valvular heart disease. However, in this group of patients the outcome after CRT does not precisely overlap any of the two other groups of patients, for which much more data are currently available
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