arXiv subjects

F. Falceto

Publications and source records attributed to F. Falceto.

32 records · Page 2Linked to original sources

arXiv2010

Generalized Central Limit Theorem and Renormalization Group

We introduce a simple instance of the renormalization group transformation in the Banach space of probability densities. By changing the scaling of the renormalized variables we obtain, as fixed points of the transformation, the Lévy strictly stable laws. We also investigate the behavior of the transformation around these fixed points and the domain of attraction for different values of the scaling parameter. The physical interest of a renormalization group approach to the generalized central limit theorem is discussed.

math-ph↗

arXiv2009

Reduction of Dirac structures along isotropic subbundles

Given a Dirac subbundle and an isotropic subbundle of a Courant algebroid, we provide a canonical method to obtain a new Dirac subbundle. When the original Dirac subbundle is involutive (i.e., a Dirac structure) this construction has interesting applications, for instance to Dirac's theory of constraints and to the Marsden-Ratiu reduction in Poisson geometry.

math.DG↗

arXiv2009

Generalization of the Hellmann-Feynman theorem

The well known Hellmann-Feynman theorem of Quantum Mechanics connected with the derivative of the eigenvalues with respect to a parameter upon which the Hamiltonian depends, is generalized to include cases in which the domain of definition of the Hamiltonian of the system also depends on that parameter.

quant-ph↗

arXiv2005

Phase transition in the assignment problem for random matrices

We report an analytic and numerical study of a phase transition in a P problem (the assignment problem) that separates two phases whose representatives are the simple matching problem (an easy P problem) and the traveling salesman problem (a NP-complete problem). Like other phase transitions found in combinatoric problems (K-satisfiability, number partitioning) this can help to understand the nature of the difficulties in solving NP problems an to find more accurate algorithms for them.

cs.CC↗

arXiv2001

Universalty and Ultraviolet Regularizations of Chern-Simons Theory

The universality of radiative corrections to the gauge coupling constant $k$ of Chern-Simons theory is studied in a very general regularization scheme. We show that the effective coupling constant $k$ induced by radiative corrections depends crucially on the balance between the ultraviolet behavior of scalar and pseudoscalar terms in the regularized action. There are three different regimes. When the ultraviolet leading term is scalar the coupling $k$ is shifted to $k+h^{\vee}$.However, if the leading term is pseudoscalar the shift is $k+s h^{\vee}$ with $s=0$ or $s=2$ depending on the sign of such a term. In the borderline case when the scalar and pseudoscalar terms have the same ultraviolet behavior the shift of $k$ becomes arbitrary (even non-integer) and depends on the parameters of the regularization. We also show that the coefficient of the induced gravitational Chern-Simons term is different for the three regimes and has the same universality properties than the effective coupling constant $k$. The results open the possibility of a connection with non-rational two-dimensional conformal theories in the borderline regime.

hep-th↗

arXiv2001

Renormalization Ambiguities in Chern-Simons Theory

We introduce a new family of gauge invariant regularizations of Chern-Simons theories which generate one-loop renormalizations of the coupling constant of the form $k\to k+2 s c_v$ where $s$ can take any arbitrary integer value. In the particular case $s=0$ we get an explicit example of a gauge invariant regularization which does not generate radiative corrections to the bare coupling constant. This ambiguity in the radiative corrections to $k$ is reminiscent of the Coste-Lüscher results for the parity anomaly in (2+1) fermionic effective actions.

hep-th↗

arXiv1998

Unstable Bundles in Quantum Field Theory

The relation between connections on 2-dimensional manifolds and holomorphic bundles provides a new perspective on the role of classical gauge fields in quantum field theory in two, three and four dimensions. In particular we show that there is a close relation between unstable bundles and monopoles, sphalerons and instantons. Some of these classical configurations emerge as nodes of quantum vacuum states in non-confining phases of \qft which suggests a relevant role for those configurations in the mechanism of quark confinement in QCD.

hep-th↗

arXiv1997

Vacuum structure of CP^N sigma models at theta=pi

We show that parity symmetry is not spontaneously broken in the CP^N sigma model for any value of N when the coefficient of the $θ$--term becomes $θ=π$ (mod $2π$). The result follows from a non-perturbative analysis of the nodal structure of the vacuum functional $ψ_0(z)$. The dynamical role of sphalerons turns out to be very important for the argument. The result introduces severe constraints on the possible critical behavior of the models at $θ=π$ (mod $2π$).

hep-th↗

arXiv1997

Vacuum Nodes in QCD at $θ=π$: Exact Results

We show that the vacuum functional of 3+1 dimensional non-abelian gauge theories vanishes for some classical field configurations $ψ_0(A)=0$ when the coefficient of the CP violating $θ$--term becomes $θ=π$ (mod. $2π$). Some of these classical configurations are explicitly identified and include sphalerons. The results shed new light into the non-perturbative behavior of non-abelian gauge theories and suggest a relevant role for these classical configurations in the confinement mechanism at $θ=0$.

hep-th↗

arXiv1996

Consistency of the Regularization of Gauge Theories by High Covariant Derivatives

We show that regularization of gauge theories by higher covariant derivatives and gauge invariant Pauli-Villars regulators is a consistent method if the Pauli-Villars vector fields are considered in a covariant in the regulating Pauli-Villars fields is pathological and the original Slavnov proposal in covariant Landau gauge is not correct because of the appearance of massless modes in the regulators which do not decouple when the ultraviolet regulator is removed. In such a case the method does not correspond to the regularization of a pure gauge theory but that of a gauge theory in interaction with massless ghost fields. This explains the problems pointed out by Martin and Ruiz in covariant Landau gauge. However, a minor modification of Slavnov method provides a consistent regularization even for such a case. The regularization that we introduce also solves the problem of overlapping divergences in a way similar to geometric regularization and yields the standard values of the $β$ and $γ$ functions of the renormalization group equations.

hep-th↗

arXiv1995

Nodes, Monopoles and Confinement in 2+1-Dimensional Gauge Theories

In the presence of Chern-Simons interactions the wave functionals of physical states in 2+1-dimensional gauge theories vanish at anumber of nodal points. We show that those nodes are located at some classical configurations which carry a non-trivial magnetic charge. In abelian gauge theories this fact explains why magnetic monopoles are suppressed by Chern-Simons interactions. In non-abelian theories it suggests a relevant role for nodal gauge field configurations in the confinement mechanism of Yang-Mills theories. We show that the vacuum nodes correspond to the chiral gauge orbits of reducible gauge fields with non-trivial magnetic monopole components.

hep-th↗

arXiv1994

Tricritical Behavior of Two-Dimensional Scalar Field Theories

We compute by Monte Carlo numerical simulations the critical exponents of two-dimensional scalar field theories at the $λϕ^6$ tricritical point. The results are in agreement with the Zamolodchikov conjecture based on conformal invariance.

hep-lat↗

arXiv1993

Chern-Simons States and Topologically Massive Gauge Theories

In an abelian topologically massive gauge theory, any eigenstate of the Hamiltonian can be decomposed into a factor describing massive propagating gauge bosons and a Chern-Simons wave function describing a set of nonpropagating ``topological'' excitations. The energy depends only on the propagating modes, and energy eigenstates thus occur with a degeneracy that can be parametrized by the Hilbert space of the pure Chern-Simons theory. We show that for a {\em nonabelian} topologically massive gauge theory, this degeneracy is lifted: although the Gauss law constraint can be solved with a similar factorization, the Hamiltonian couples the propagating and nonpropagating (topological) modes.

hep-th↗

arXiv1992

Chern-Simons Theory on the Torus

We compute explicitly the Schrödinger picture space of states of SU(2) Chern-Simons theory on $T^2\times R$ in the presence of temporal Wilson lines. Relation with Friedan-Shenker bundle of conformal field theory and the existence of a projective flat connection on this bundle is discussed. Talk given by the first author at the XIX International Colloquium on Group Theoretical Methods in Physics, Salamanca (Spain), June 29-July 4, 1992

hep-th↗