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The dynamics of symplectic gauge fields provides a consistent framework for fundamental interactions based on spin three gauge fields. One remarkable property is that symplectic gauge fields only have minimal couplings with gravitational fields and not with any other field of the Standard Model. Interactions with ordinary matter and radiation can only arise from radiative corrections. In spite of the gauge nature of symplectic fields they acquire a mass by the Coleman-Weinberg mechanism which generates Higgs-like mass terms where the gravitational field is playing the role of a Higgs field. Massive symplectic gauge fields weakly interacting with ordinary matter are natural candidates for the dark matter component of the Universe., Comment: 16 pages

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 $\theta$--term becomes $\theta=\pi$ (mod $2\pi$). The result follows from a non-perturbative analysis of the nodal structure of the vacuum functional $\psi_0(z)$. 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 $\theta=\pi$ (mod $2\pi$).

We show that the vacuum functional of 3+1 dimensional non abelian gauge theories vanishes for some classical field configurations {psi}{sub 0}({ital A})=0 when the coefficient of the CP violating {theta} term becomes {theta}={pi} (mod.2{pi}). Some of these classical configurations are explicitly identified and include sphalerons. The results shed new light into the nonperturbative behavior of nonabelian gauge theories and suggest a relevant role for these classical configurations in the confinement mechanism at {theta}=0. {copyright} {ital 1996 The American Physical Society.}

We compute by Monte Carlo numerical simulations the critical exponents of two-dimensional scalar field theories at the $\lambda\phi^6$ tricritical point. The results are in agreement with the Zamolodchikov conjecture based on conformal invariance., Comment: 13 pages, uuencode tar-compressed Postscript file, preprint numbers: IF/UFRJ/25/94, DFTUZ 94.06 and NYU--TH--94/10/01

The renormalized energy-momentum tensor of vacuum has been deeply explored many years ago. The main result of these studies was that such a tensor should satisfy the conservation laws which reflects the covariance of the theory in the presence of loop corrections. In view of this general result we address two important questions, namely how to implement the momentum cut-off in a covariant way and whether this general result holds in the theory with Spontaneous Symmetry Breaking. In the last case some new interesting details arise and although the calculations are more involved we show that the final result satisfies the conservation laws.

We analyze the antiferromagnetic $\mathit{SU}(3)$ Heisenberg chain by means of the density-matrix renormalization group. The results confirm that the model is critical and the computation of its central charge and the scaling dimensions of the first-excited states show that the underlying low-energy conformal field theory is the $\mathit{SU}{(3)}_{1}$ Wess-Zumino-Novikov-Witten model.

The tomographic probability distribution on the phase space (cylinder) related to a circle or an interval is introduced. The explicit relations of the tomographic probability densities and the probability densities on the phase space for the particle motion on a torus are obtained and the relation of the suggested map to the Radon transform on the plane is elucidated. The generalization to the case of a multidimensional torus is elaborated and the geometrical meaning of the tomographic probability densities as marginal distributions on the helix discussed., Comment: 9 pages, 3 figures

Quaternionic quantum mechanics has been revealed to be a very useful framework to describe quantum phenomena. In the case of two qubit compound systems we show that the complex projection of quaternionic pure states and quaternionic unitary maps permits the description of interesting phenomena such as decoherence and optimal entanglement generation. The approach, however, presents severe limitations for the case of multipartite or higher dimensional bipartite quantum systems as we point out.

We analyze the problem of the existing ambiguities in the conformal anomaly in theories with external scalar field in curved backgrounds. In particular, we consider the anomaly of self-interacting massive scalar field theory and of Yukawa model in the massless conformal limit. In all cases the ambiguities are related to finite renormalizations of a local non-minimal terms in the effective action. We point out the generic nature of this phenomenon and provide a general method to identify the theories where such an ambiguity can arise., RevTeX, 10 pages, no figures. Small comment and two references added. Accepted for publication in Physical Review D

The quantum planar rotor is chosen as a model to test different approximate techniques, emphasizing the analogies between this simple system and the non-Abelian quantum gauge field theories (instantons, $\ensuremath{\theta}$ vacuum, etc.). In particular, variational and perturbative methods, path-integral techniques, and Monte Carlo simulations are applied. It is pointed out that the maximal destructive interference between instantons takes place in the $\ensuremath{\theta}$-vacuum realization of the interacting rotor system with $\ensuremath{\theta}=\frac{1}{2}$, where the tunneling effects are shown to be severely diminished.