arXiv subjects
Publications and source records attributed to Enore Guadagnini.
We consider topological gauge theories in three dimensions which are defined by metric independent lagrangians. It has been claimed that the functional integration necessarily depends nontrivially on the gauge-fixing metric. We demonstrate that the partition function and the mean values of the gauge invariant observables do not really depend on the gauge-fixing metric.
We consider the perturbative renormalization of the Schwinger-Dyson functional, which is the generating functional of the expectation values of the products of the composite operator given by the field derivative of the action. It is argued that this functional plays an important role in the topological Chern-Simons and BF quantum field theories. It is shown that, by means of the renormalized perturbation theory, a canonical renormalization procedure for the Schwinger-Dyson functional is obtained. The combinatoric structure of the Feynman diagrams is illustrated in the case of scalar models. For the Chern-Simons and the BF gauge theories, the relationship between the renormalized Schwinger-Dyson functional and the generating functional of the correlation functions of the gauge fields is produced.
We consider a superrenomalizable gauge theory of topological type, in which the structure group is equal to the inhomogeneous group ISU(2). The generating functional of the correlation functions of the gauge fields is derived and its connection with the generating functional of the Chern-Simons theory is discussed. The complete renomalization of this model defined in R^3 is presented. The structure of the ISU(2) conjugacy classes is determined. Gauge invariant observables are defined by means of appropriately normalized traces of ISU(2) holonomies associated with oriented, framed and coloured knots. The perturbative evaluation of the Wilson lines expectation values is investigated and the up-to-third-order contributions to the perturbative expansion of the observables, which correspond to knot invariants, are produced. The general dependence of the knot observables on the framing is worked out.
We analyze the structure of the surface states and Fermi arcs of Weyl semimetals as a function of the boundary conditions parameterizing the Hamiltonian self-adjoint extensions of a minimal model with two Weyl points. These boundary conditions determine both the pseudospin polarization of the system on the surface and the shape of the associated Fermi arcs. We analytically derive the expectation values of the density profile of the surface current, we evaluate the anomalous Hall conductivity as a function of temperature and chemical potential and we discuss the surface current correlation functions and their contribution to the thermal noise. Based on a lattice variant of the model, we numerically study the surface states at zero temperature and we show that their polarization and, consequently, their transport properties, can be varied by suitable Zeeman terms localized on the surface. We also provide an estimate of the bulk conductance of the system based on the Landauer-Büttiker approach. Finally, we analyze the surface anomalous thermal Hall conductivity and we show that the boundary properties lead to a correction of the expected universal thermal Hall conductivity, thus violating the Wiedemann-Franz law.
We derive the expression of the abelian axial anomaly in the so-called multi-Weyl and triple-point crossing semimetals. No simplifying restrictions are assumed on the symmetry of the spectrum. Three different computation methods are considered: the perturbative quantum field theory procedure which is based on the evaluation of the one-loop Feynman diagrams, the Nielsen-Ninomiya method, and the Atiyah-Singer index argument. It is shown that the functional form of the axial anomaly does not depend on the Lorentz symmetry, but it is determined by the gauge structure group. We discuss the stability of the anomaly - stemming from the quantisation of the anomaly coefficient - under smooth modifications of the lagrangian parameters.
A general method for the construction of smooth flat connections on 3-manifolds is introduced. The procedure is strictly connected with the deduction of the fundamental group of a manifold M by means of a Heegaard splitting presentation of M. For any given matrix representation of the fundamental group of M, a corresponding flat connection A on M is specified. It is shown that the associated classical Chern-Simons invariant assumes then a canonical form which is given by the sum of two contributions: the first term is determined by the intersections of the curves in the Heegaard diagram, and the second term is the volume of a region in the representation group which is determined by the representation of pi_1(M) and by the Heegaard gluing homeomorphism. Examples of flat connections in topologically nontrivial manifolds are presented and the computations of the associated classical Chern-Simons invariants are illustrated.
For helium II inside a rotating cylinder, it is proposed that the formation of vortex lines of the frictionless superfluid component of the liquid is caused by the presence of the rotating quasi-particles gas. By minimising the free energy of the system, the critical value Omega_0 of the angular velocity for the formation of the first vortex line is determined. This value nontrivially depends on the temperature, and numerical estimations of its temperature behaviour are produced. It is shown that the latent heat for a vortex formation and the associated discontinuous change in the angular momentum of the quasi-particles gas determine the slope of Omega_0 (T) via some kind of Clapeyron equation.
The thermodynamic properties of superconducting electrons are usually studied by means of the quasi-particles distribution; but in this approach, the ground state energy and the dependence of the chemical potential on the electron density cannot be determined. In order to solve these problems, the thermodynamic potentials are derived by means of the Bogoliubov-Valatin formalism. The thermodynamic potentials can be obtained by computing the free energy of a gas of quasi-particles, whose energy spectrum is conditional on the gap function. However, the nontrivial dependence of the gap on the temperature jeopardises the validity of the standard thermodynamic relations. In this article it is shown how the thermodynamic consistency (i.e. the validity of the Maxwell relations) is recovered, and the correction terms to the quasi-particles potentials are computed. It is shown that the Bogoliubov-Valatin transformation avoids the problem of the thermodynamic consistency of the quasi-particle approach; in facts, the correct identification of the variables, which are associated with the quasi-particles, leads to a precise calculation of the quasi-particles vacuum energy and of the dependence of the chemical potential on the electron density. The stationarity condition for the grand potential coincides with the gap equation, which guarantees the thermodynamic consistency. The expressions of various thermodynamic potentials, as functions of the (T,V,N) variables, are produced in the low temperature limit; as a final check, a rederivation of the condensation energy is presented.
In perturbative SU(N) Chern-Simons gauge theory, it is shown that the Schwinger-Dyson equations assume a quite simplified form. The generating functional of the correlation functions of the curvature is considered; it is demonstrated that the renormalized Schwinger-Dyson functional is related with the generating functional of the correlation functions of the gauge connections by some kind of duality transformation.
We consider the $U(1)$ Chern-Simons gauge theory defined in a general closed oriented 3-manifold $M$; the functional integration is used to compute the normalized partition function and the expectation values of the link holonomies. The nonperturbative path-integral is defined in the space of the gauge orbits of the connections which belong to the various inequivalent $U(1)$ principal bundles over $M$; the different sectors of the configuration space are labelled by the elements of the first homology group of $M$ and are characterized by appropriate background connections. The gauge orbits of flat connections, whose classification is also based on the homology group, control the extent of the nonperturbative contributions to the mean values. The functional integration is achieved in any 3-manifold $M$, and the corresponding path-integral invariants turn out to be strictly related with the abelian Reshetikhin-Turaev surgery invariants.
We implement the metric-independent Fock-Schwinger gauge in the abelian quantum Chern-Simons field theory defined in ${\mathbb R}^3$. The expressions of the various components of the propagator are determined. Although the gauge field propagator differs from the Gauss linking density, we prove that its integral along two oriented knots is equal to the linking number.
A new representation -which is similar to the Bargmann representation- of the creation and annihilation operators is introduced, in which the operators act like "multiplication with" and like "derivation with respect to" a single real variable. The Hilbert space structure of the corresponding states space is produced and the relations with the Schroedinger representation are derived. Possible connections of this new representation with the asymptotic wave functions of the gauge-fixed quantum Chern-Simons field theory and (2+1) gravity are pointed out. It is shown that the representation of the fields operator algebra of the Chern-Simons theory in the Landau gauge is not a *-representation; the consequences on the evolution of the states in the semiclassical approximation are discussed.
The perturbative approach to the topological quantum field theories of the Chern-Simons type formulated in R^3 is considered. By means of the canonical quantization of the euclidean Chern-Simons lagrangian in the Landau gauge, a Fock space representation of the free field operators is produced. The perturbative equivalence of the path-integral formalism and the field operator approach is exhibited. The expression of the one-loop effective action in background gauge is derived.
We consider a class of random, weighted networks, obtained through a redefinition of patterns in an Hopfield-like model and, by performing percolation processes, we get information about topology and resilience properties of the networks themselves. Given the weighted nature of the graphs, different kinds of bond percolation can be studied: stochastic (deleting links randomly) and deterministic (deleting links based on rank weights), each mimicking a different physical process. The evolution of the network is accordingly different, as evidenced by the behavior of the largest component size and of the distribution of cluster sizes. In particular, we can derive that weak ties are crucial in order to maintain the graph connected and that, when they are the most prone to failure, the giant component typically shrinks without abruptly breaking apart; these results have been recently evidenced in several kinds of social networks.
We consider the link invariants defined by the quantum Chern-Simons field theory with compact gauge group U(1) in a closed oriented 3-manifold M. The relation of the abelian link invariants with the homology group of the complement of the links is discussed. We prove that, when M is a homology sphere or when a link -in a generic manifold M- is homologically trivial, the associated observables coincide with the observables of the sphere S^3. Finally we show that the U(1) Reshetikhin-Turaev surgery invariant of the manifold M is not a function of the homology group only, nor a function of the homotopy type of M alone.
The functional integral computation of the various topological invariants, which are associated with the Chern-Simons field theory, is considered. The standard perturbative setting in quantum field theory is rewieved and new developments in the path-integral approach, based on the Deligne-Beilinson cohomology, are described in the case of the abelian U(1) Chern-Simons field theory formulated in S^1 x S^2.
For the abelian Chern-Simons field theory, we consider the quantum functional integration over the Deligne-Beilinson cohomology classes and we derive the main properties of the observables in a generic closed orientable 3-manifold. We present an explicit path-integral non-perturbative computation of the Chern-Simons links invariants in the case of the torsion-free 3-manifolds $S^3$, $S^1 \times S^2$ and $S^1 \times Σ_g$.
The helicity modification of light polarization which is induced by the gravitational deflection from a classical heavy rotating body, like a star or a planet, is considered. The expression of the helicity asymmetry is derived; this asymmetry signals the gravitationally induced spin transfer from the rotating body to the scattered photons.