arXiv subjects

G. Grignani

Publications and source records attributed to G. Grignani.

33 records · Page 2Linked to original sources

arXiv1999

Mean Field Theory of Josephson Junction Arrays with Charge Frustration

Using the path integral approach, we provide an explicit derivation of the equation for the phase boundary for quantum Josephson junction arrays with offset charges and non-diagonal capacitance matrix. For the model with nearest neighbor capacitance matrix and uniform offset charge $q/2e=1/2$, we determine, in the low critical temperature expansion, the most relevant contributions to the equation for the phase boundary. We explicitly construct the charge distributions on the lattice corresponding to the lowest energies. We find a reentrant behavior even with a short ranged interaction. A merit of the path integral approach is that it allows to provide an elegant derivation of the Ginzburg-Landau free energy for a general model with charge frustration and non-diagonal capacitance matrix. The partition function factorizes as a product of a topological term, depending only on a set of integers, and a non-topological one, which is explicitly evaluated.

cond-mat.supr-con↗

arXiv1998

Spectrum of the 2-Flavor Schwinger Model from the Heisenberg Spin Chain

We study the strong coupling limit of the 2-flavor lattice Schwinger model in the Hamiltonian formalism using staggered fermions. We show that the problem of finding the low-lying states is equivalent to solving the Heisenberg antiferromagnetic spin chain. We find good agreement with the continuum theory.

hep-th↗

arXiv1997

Chiral Symmetry Breaking on the Lattice: a Study of the Strongly Coupled Lattice Schwinger Model

We revisit the strong coupling limit of the Schwinger model on the lattice using staggered fermions and the hamiltonian approach to lattice gauge theories. Although staggered fermions have no continuous chiral symmetry, they posses a discrete axial invari ance which forbids fermion mass and which must be broken in order for the lattice Schwinger model to exhibit the features of the spectrum of the continuum theory. We show that this discrete symmetry is indeed broken spontaneously in the strong coupling li mit. Expanding around a gauge invariant ground state and carefully considering the normal ordering of the charge operator, we derive an improved strong coupling expansion and compute the masses of the low lying bosonic excitations as well as the chiral co ndensate of the model. We find very good agreement between our lattice calculations and known continuum values for these quantities already in the fourth order of strong coupling perturbation theory. We also find the exact ground state of the antiferromag netic Ising spin chain with long range Coulomb interaction, which determines the nature of the ground state in the strong coupling limit.

hep-lat↗

arXiv1997

Loop Correlators and Theta States in 2D Yang-Mills Theory

Explicit computations of the partition function and correlation functions of Wilson and Polyakov loop operators in theta-sectors of two dimensional Yang-Mills theory on the line cylinder and torus are presented. Several observations about the correspondence of two dimensional Yang-Mills theory with unitary matrix quantum mechanics are presented. The incorporation of the theta-angle which characterizes the states of two dimensional adjoint QCD is discussed.

hep-th↗

arXiv1996

G/G models as the strong coupling limit of topologically massive gauge theory

We show that the problem of computing the vacuum expectation values of gauge invariant operators in the strong coupling limit of topologically massive gauge theory is equivalent to the problem of computing similar operators in the $G_k/G$ model where $k$ is the integer coefficient of the Chern-Simons term. The $G_k/G$ model is a topological field theory and many correlators can be computed analytically. We also show that the effective action for the Polyakov loop operator and static modes of the gauge fields of the strongly coupled theory at finite temperature is a perturbed, non-topological $G_k/G$ model. In this model, we compute the one loop effective potential for the Polyakov loop operators and explicitly construct the low-lying excited states. In the strong coupling limit the theory is in a deconfined phase.

hep-th↗

arXiv1996

Charge Screening and Confinement in Hot 3-D QED

We examine the possibility of a confinement-deconfinement phase transition at finite temperature in both parity invariant and topologically massive three-dimensional quantum electrodynamics. We review an argument showing that the Abelian version of the Polyakov loop operator is an order parameter for confinement, even in the presence of dynamical electrons. We show that, in the parity invariant case, where the tree-level Coulomb potential is logarithmic, there is a Berezinskii-Kosterlitz-Thouless transition at a critical temperature ($T_c=e^2/8π+{\cal O}(e^4/m)$, when the ratio of the electromagnetic coupling and the temperature to the electron mass is small). Above $T_c$ the electric charge is not confined and the system is in a Debye plasma phase, whereas below $T_c$ the electric charges are confined by a logarithmic Coulomb potential, qualitatively described by the tree-level interaction. When there is a topological mass, no matter how small, in a strict sense the theory is not confining at any temperature; the model exhibits a screening phase, analogous to that found in the Schwinger model and two-dimensional QCD with massless adjoint matter. However, if the topological mass is much smaller than the other dimensional parameters, there is a temperature for which the range of the Coulomb interaction changes from the inverse topological mass to the inverse electron mass. We speculate that this is a vestige of the BKT transition of the parity-invariant system, separating regions with screening and deconfining behavior.

hep-th↗

arXiv1996

A Pseudoclassical Model for $P,T-$Invariant Planar Fermions

A pseudoclassical model is proposed for the description of planar $P,T-$invariant massive fermions. The quantization of the model leads to the (2+1)-dimensional $P,T-$invariant fermion model used recently in $P,T-$conserving theories of high-T${}_c$ superconductors. The rich symmetry of the quantum model is elucidated through the analysis of the canonical structure of its pseudoclassical counterpart. We show that both the quantum $P,T-$invariant planar massive fermion model and the proposed pseudoclassical model --- for a particular choice of the parameter appearing in the Lagrangian --- have a U(1,1) dynamical symmetry as well as an $N=3$ supersymmetry. The hidden supersymmetry leads to a non-standard superextension of the (2+1)-dimensional Poincaré group. In the quantum theory the one particle states provide an irreducible representation of the extended supergroup labelled by the zero eigenvalue of the superspin. We discuss the gauge modification of the pseudoclassical model and compare our results with those obtained from the standard pseudoclassical model for massive planar fermions.

hep-th↗

arXiv1996

Quantum States of Topologically Massive Electrodynamics and Gravity

The free quantum states of topologically massive electrodynamics and gravity in 2+1 dimensions, are explicitly found. It is shown that in both theories the states are described by infrared-regular polarization tensors containing a regularization phase which depends on the spin. This is done by explicitly realizing the quantum algebra on a functional Hilbert space and by finding the Wightman function to define the scalar product on such a Hilbert space. The physical properties of the states are analyzed defining creation and annihilation operators. For both theories, a canonical and covariant quantization procedure is developed. The higher order derivatives in the gravitational lagrangian are treated by means of a preliminary Dirac procedure. The closure of the Poincaré algebra is guaranteed by the infrared-finiteness of the states which is related to the spin of the excitations through the regularization phase. Such a phase may have interesting physical consequences.

hep-th↗

arXiv1995

Charge Screening in the Finite Temperature Schwinger Model

We compute the effective action and correlators of the Polyakov loop operator in the Schwinger model at finite temperature and discuss the realization of the discrete symmetries that occur there. We show that, due to nonlocal effects of massless fermions in two spacetime dimensions, the discrete symmetry which governs the screening of charges is spontaneously broken even in an effective one-dimensional model, when the volume is infinite. In this limit, the thermal state of the Schwinger model screens an arbitrary external charge; consequently the model is in the deconfined phase, with the charge of the deconfined fermions completely screened. In a finite volume we show that the Schwinger model is always confining.

hep-th↗

arXiv1995

Confinement-Deconfinement Transition in 3-Dimensional QED

We argue that, at finite temperature, parity invariant non-compact electrodynamics with massive electrons in 2+1 dimensions can exist in both confined and deconfined phases. We show that an order parameter for the confinement-deconfinement phase transition is the Polyakov loop operator whose average measures the free energy of a test charge that is not an integral multiple of the electron charge. The effective field theory for the Polyakov loop operator is a 2-dimensional Euclidean scalar field theory with a global discrete symmetry $Z$, the additive group of the integers. We argue that the realization of this symmetry governs confinement and that the confinement-deconfinement phase transition is of Berezinskii-Kosterlitz-Thouless type. We compute the effective action to one-loop order and argue that when the electron mass $m$ is much greater than the temperature $T$ and dimensional coupling $e^2$, the effective field theory is the Sine-Gordon model. In this limit, we estimate the critical temperature, $T_{\rm crit.}=e^2/8π(1-e^2/12πm+\ldots)$.

hep-th↗

arXiv1995

Polyakov Loops in 2D QCD

We discuss SU(N) gluo-dynamics at finite temperature and on a spatial circle. We show that the effective action for the Polyakov Loop operator is a one dimensional gauged SU(N) principle chiral model with variables in the loop space and loop algebra of the gauge group. We find that the quantum states can be characterized by a discrete $θ$-angle which appears with a particular 1-dimensional topological term in the effective action. We present an explicit computation of the partition function and obtain the spectrum of the model, together with its dependence on the discrete theta angle. We also present explicit formulae for 2-point correlators of Polyakov loop operators and an algorithm for computing all N-point correlators.

hep-th↗

arXiv1993

Canonical Analysis of Poincare' Gauge Theories for Two Dimansional Gravity

Following the general method discussed in Refs.[1,2], Liouville gravity and the 2 dimensional model of non-Einstenian gravity ${\cal L} \sim curv^2 + torsion^2 + cosm. const.$ can be formulated as ISO(1,1) gauge theories. In the first order formalism the models present, besides the Poincaré gauge symmetry, additional local symmetries. We show that in both models one can fix these additional symmetries preserving the ISO(1,1) gauge symmetry and the diffeomorphism invariance, so that, after a preliminary Dirac procedure, the remaining constraints uniquely satisfy the ISO(1,1) algebra. After the additional symmetry is fixed, the equations of motion are unaltered. One thus remarkably simplifies the canonical structure, especially of the second model. Moreover, one shows that the Poincaré group can always be used consistently as a gauge group for gravitational theories in two dimensions.

hep-th↗

arXiv1993

Reply to `Comment on Gravity and the Poincare' Group'

In the first order form, the model considered by Strobl presents, besides local Lorentz and diffeomorphism invariances, an additional local non-linear symmetry. When the model is realized as a Poincaré gauge theory according to the procedure outlined in Refs.[1,2], the generators of the non-linear symmetry are responsible for the ``nasty constraint algebra''. We show that not only the Poincaré gauge theoretic formulation of the model is not the cause of the emerging of the undesirable constraint algebra, but actually allows to overcome the problem. In fact one can fix the additional symmetry without breaking the Poincaré gauge symmetry and the diffeomorphisms, so that, after a preliminary Dirac procedure, the remaining constraints uniquely satisfy the Poincaré algebra. After the additional symmetry is fixed, the equations of motion are unaltered. The objections to our method raised by Strobl in Ref.[3] are then immaterial. Some minor points put forward in Ref.[3] are also discussed.

hep-th↗

arXiv1992

Chern--Simons Gravity from 3+1 Dimensional Gravity

In the context of a Poincaré gauge theoretical formulation, pure gravity in 3+1-dimensions is dimensionally reduced to gravity in 2+1-dimensions with or without cosmological constant $Λ$. The dimensional reductions are consistent with the gauge symmetries, mapping ISO(3, 1) gauge transformations into ISO(2,1) ones. One of the reductions leads to Chern-Simons-Witten gravity. The solutions of 2+1-gravity with $Λ\le 0$ (in particular the black-hole solution recently found by Banados, Teitelboim and Zanelli) and those of 1+1-dimensional Liouville gravity, are thus mapped into 3+1-dimensional vacuum solutions.

gr-qc↗

arXiv1992

Poincaré Gauge Theories for Lineal Garvity

We have shown that two of the most studied models of lineal gravities - Liouville gravity and a ``string-inspired'' model exhibiting the main characteristic features of a black-hole solution - can be formulated as gauge invariant theories of the Poincaré group. The gauge invariant couplings to matter (particles, scalar and spinor fields) and explicit solutions for some matter field configurations, are provided. It is shown that both the models, as well as the couplings to matter, can be obtained as suitable dimensional reductions of a 2+1-dimensional ISO(2,1) gauge invariant theory.

gr-qc↗