A new approach to integrable theories in any dimension

The zero curvature representation for two-dimensional integrable models is generalized to spacetimes of dimension d + 1 by the introduction of a d-form connection. The new generalized zero curvature conditions can be used to represent the equations of motion of some relativistic invariant field theories of physical interest in 2 + 1 dimensions (BF theories, Chern-Simons, 2 + 1 gravity and the CP1 model) and 3 + 1 dimensions (self-dual Yang-Mills theory and the Bogomolny equations). Our approach leads to new methods of constructing conserved currents and solutions. In a submodel of the 2 + 1-dimensional CP1 model, we explicitly construct an infinite number of previously unknown non-trivial conserved currents. For each positive integer spin representation of sl(2) we construct 2j + 1 conserved currents leading to 2j + 1 Lorentz scalar charges. (C) 1998 Elsevier B.V. B.V.

Torsion and the gravitational interaction

By using a nonholonomous-frame formulation of the general covariance principle, seen as an active version of the strong equivalence principle, an analysis of the gravitational coupling prescription in the presence of curvature and torsion is made. The Coupling prescription implied by this principle is found to be always equivalent to that of general relativity, a result that reinforces the completeness of this theory, as well as the teleparallel point of view according to which torsion does not represent additional degrees of freedom for gravity, but simply an alternative way of representing the gravitational field.

Metric-scalar gravity with torsion and the measurability of the non-minimal coupling

The measurability of the non-minimal coupling is discussed by considering the correction to the Newtonian static potential in the semiclassical approach. The coefficient of the gravitational Darwin term (GDT) gets redefined by the non-minimal torsion scalar couplings. Based on a similar analysis of the GDT in the effective field theory approach to non-minimal scalar, we conclude that for reasonable values of the couplings the correction is very small.

Nonabelian Toda theories from parafermionic reductions of the WZW model

We investigate a class of conformal nonabelian-Toda models representing noncompact SL(2, R)/U(1) parafermions (PF) interacting with specific abelian Toda theories and having a global U(1) symmetry. A systematic derivation of the conserved currents, their algebras, and the exact solution of these models are presented. An important property of this class of models is the affine SL(2, R)(q) algebra spanned by charges of the chiral and antichiral nonlocal currents and the U(1) charge. The classical (Poisson brackets) algebras of symmetries VG(n), of these models appear to be of mixed PF-WG(n) type. They contain together with the local quadratic terms specific for the W-n-algebras the nonlocal terms similar to the ones of the classical PF-algebra. The renormalization of the spins of the nonlocal currents is the main new feature of the quantum VA(n)-algebras. The quantum VA(2)-algebra and its degenerate representations are studied in detail. (C) 1999 Academic Press.

Duffin-Kemmer-Petiau and Klein-Cordon-Fock equations for electromagnetic, Yang-Mills and external gravitational field interactions: proof of equivalence

Starting from the Generating functional for the Green Function (GF), constructed from the Lagrangian action in the Duffin-Kemmer-Petiau (DKP) theory (L-approach) we strictly prove that the physical matrix elements of the S-matrix in DKP and Klein-Gordon-Fock (KGF) theories coincide in cases of interacting spin O particles with external and quantized Maxwell and Yang-Mills fields and in case of external gravitational field (without or with torsion), For the proof we use the reduction formulas of Lehmann, Symanzik and Zimmermann (LSZ). We prove that many photons and Yang-Mills particles GF coincide in both theories too. (C) 2000 Elsevier B.V. B.V. All rights reserved.

Mass neutrino flavor evolution in spacetime with torsion

In the framework of the spacetime with torsion, we obtain the flavor evolution equation of the mass neutrino oscillation in vacuum. A comparison with the result of general relativity case shows that the flavor evolutionary equations in Riemann spacetime and Weitzenbock spacetimes are equivalent in the spherical symmetric Schwarzschild spacetime, but turn out to be different in the case of the axial symmetry.

Axial-vector torsion and the teleparallel Kerr spacetime

In the context of the teleparallel equivalent of general relativity, we obtain the tetrad and the torsion fields of the stationary axisymmetric Kerr spacetime. It is shown that, in the slow rotation and weak-field approximations, the axial-vector torsion plays the role of the gravitomagnetic component of the gravitational field, and is thus responsible for the Lense-Thirring effect.

Interacting spin 0 fields with torsion via Duffin-Kemmer-Petiau theory

Here we study the behaviour of the spin 0 sector of the DKP field in spaces with torsion. First we show that in a Riemann-Cartan manifold the DKP field presents an interaction with torsion when minimal coupling is performed, contrary to the behaviour of the KO field, a result that breaks the usual equivalence between the DKP and the KG fields.Next we analyse the case of the Teleparallel Equivalent of General Relativity (Weitzenbock manifold), showing that in this case there is a perfect agreement between KG and DKP fields. The origins of both results are also discussed.

Noncommutative integrable field theories in 2d

We study the noncommutative generalization of (Euclidean) integrable models in two dimensions, specifically the sine- and sinh-Gordon and the U(N) principal chiral models. By looking at tree-level amplitudes for the sinh-Gordon model we show that its naive noncommutative generalization is not integrable. on the other hand, the addition of extra constraints, obtained through the generalization of the zero-curvature method, renders the model integrable. We construct explicit nonlocal nontrivial conserved charges for the U(N) principal chiral model using the Brezin-Itzykson-Zinn-Justin-Zuber method. (C) 2003 Elsevier B.V. All rights reserved.

Vacuum energy as a c-function for theories with dynamically generated masses

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Chiral symmetry breaking in QCD-like gauge theories with a confining propagator and dynamical gauge boson mass generation

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Hamilton-Jacobi approach for first order actions and theories with higher derivatives

In this work, we analyze systems described by Lagrangians with higher order derivatives in the context of the Hamilton-Jacobi formalism for first order actions. Two different approaches are studied here: the first one is analogous to the description of theories with higher derivatives in the hamiltonian formalism according to [D.M. Gitman, S.L. Lyakhovich, I.V. Tyutin, Soviet Phys. J. 26 (1983) 730; D.M. Gitman, I.V. Tyutin, Quantization of Fields with Constraints, Springer-Verlag, New York, Berlin, 1990] the second treats the case where degenerate coordinate are present, in an analogy to reference [D.M. Gitman, I.V. Tyutin, Nucl. Phys. B 630 (2002) 509]. Several examples are analyzed where a comparison between both approaches is made. (C) 2007 Elsevier B.V. All rights reserved.

Extended 2D generalized dilaton gravity theories

We show that an anomaly-free description of matter in (1+1) dimensions requires a deformation of the 2D relativity principle, which introduces a non-trivial centre in the 2D Poincare algebra. Then we work out the reduced phase space of the anomaly-free 2D relativistic particle, in order to show that it lives in a noncommutative 2D Minkowski space. Moreover, we build a Gaussian wave packet to show that a Planck length is well defined in two dimensions. In order to provide a gravitational interpretation for this noncommutativity, we propose to extend the usual 2D generalized dilaton gravity models by a specific Maxwell component, which guages the extra symmetry associated with the centre of the 2D Poincare algebra. In addition, we show that this extension is a high energy correction to the unextended dilaton theories that can affect the topology of spacetime. Further, we couple a test particle to the general extended dilaton models with the purpose of showing that they predict a noncommutativity in curved spacetime, which is locally described by a Moyal star product in the low energy limit. We also conjecture a probable generalization of this result, which provides strong evidence that the noncommutativity is described by a certain star product which is not of the Moyal type at high energies. Finally, we prove that the extended dilaton theories can be formulated as Poisson-Sigma models based on a nonlinear deformation of the extended Poincare algebra.

The analytic torsion of a disc

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

STOCHASTIC QUANTIZATION OF FERMIONIC THEORIES - RENORMALIZATION OF THE MASSIVE THIRRING MODEL

Using the Langevin approach for stochastic processes, we study the renormalizability of the massive Thirring model. At finite fictitious time, we prove the absence of induced quadrilinear counterterms by verifying the cancellation of the divergencies of graphs with four external lines. This implies that the vanishing of the renormalization group beta function already occurs at finite times.