A characterisation of the Hoffman-Wohlgemuth surfaces in terms of their symmetries

For an embedded singly periodic minimal surface (M) over tilde with genus rho >= 4 and annular ends, some weak symmetry hypotheses imply its congruence with one of the Hoffman-Wohlgemuth examples. We give a very geometrical proof of this fact, along which they come out many valuable clues for the understanding of these surfaces.

Atividade óptica de um meio dielétrico diluído: Pasteur e as simetrias moleculares

Em 1848 Pasteur conjeturou que a rotação do plano de polarização da luz em um meio diluído é gerada pelas propriedades de simetria das moléculas do meio no qual a luz se propaga. O objetivo do nosso artigo é de mostrar que Pasteur estava correto usando conhecimentos de eletromagnetismo e mecânica quântica de um curso de graduação em física. Faremos um breve retrospecto das ideias básicas da teoria eletromagnética necessárias para o estudo da atividade óptica. A seguir, usando a teoria de perturbações em mecânica quântica e levando em conta as simetrias das moléculas calcularemos a atividade óptica do meio. Mostraremos que as previsões teóricas, que estão plenamente de acordo com os resultados experimentais, comprovam a hipótese de Pasteur.

Probability currents and entropy production in nonequilibrium lattice systems

The structure of probability currents is studied for the dynamical network after consecutive contraction on two-state, nonequilibrium lattice systems. This procedure allows us to investigate the transition rates between configurations on small clusters and highlights some relevant effects of lattice symmetries on the elementary transitions that are responsible for entropy production. A method is suggested to estimate the entropy production for different levels of approximations (cluster sizes) as demonstrated in the two-dimensional contact process with mutation.

Aetherlike Lorentz-breaking actions

We show that CPT-even aetherlike Lorentz-breaking actions, for the scalar and electromagnetic fields, are generated via their appropriate Lorentz-breaking coupling to spinor fields, in three, four, and five space-time dimensions. Besides, we also show that aetherlike terms for the spinor field can be generated as a consequence of the same couplings. We discuss the dispersion relations in the theories with aetherlike Lorentz-breaking terms and find the tree-level effective (Breit) potential for fermion scattering and the one-loop effective potential corresponding to the action of the scalar field.

Spontaneous long and short-range ferroelectric ordering in Pb(0.55)La(0.30)TiO(3) ceramics

In this work, we investigated the temperature dependence of short and long-range ferroelectric ordering in Pb(0.55)La(0.30)TiO(3) relaxor composition. High-resolution x-ray powder diffraction measurements revealed a clear spontaneous macroscopic cubic-to-tetragonal phase transition in the PLT relaxor sample at similar to 60 K below the maximum of the dielectric constant peak (T(m)). Indeed, the x-ray diffraction (XRD) data showed that at 300 K (above T(m) but below the Burns temperature, T(B)) the long-range order structure corresponds to a macroscopic cubic symmetry, space group number 221 (Pm-3m), whereas the data collected at 20 K revealed a macroscopic tetragonal symmetry, space group number 99 (P4mm) with c/a=1.0078, that is comparable to that of a normal ferroelectric. These results show that for samples with tetragonal composition, the long-range ferroelectric order may be recovered spontaneously at cryogenics temperatures, in contrast to ferroelectric samples with rhombohedral symmetry. On the other hand, x-ray absorption spectroscopy investigations intriguingly revealed the existence of local tetragonal disorder around Ti atoms for temperatures far below T(m) and above T(B), for which the sample presents macroscopic tetragonal and cubic symmetries, respectively. (C) 2010 American Institute of Physics. [doi: 10.1063/1.3431024]

A new oxovanadium(IV)-cucurbit[6]uril complex: Properties and potential for confined heterogeneous catalytic oxidation reactions

This work presents a new oxovanadium(IV)-cucurbit[6]uril complex, which combines the catalytic properties of the metal ion with the size-excluding properties of the macrocycle cavity. In this coordination compound, the VO(2-) ions are coordinated to the oxygen atoms located at the rim of the macrocycle in slightly distorted square-pyramidal configurations, which are in fact C(2v) symmetries. This combination results in a size-selective heterogeneous catalyst, which is able to oxidize linear alkanes like n-pentane at room temperature, but not styrene, cyclohexane or z-cyclooctene, which are too big to enter the cucurbit[6]uril cavity. The results presented here contribute to understanding the mechanism of alkane catalytic oxidation by oxovanadium(IV) complexes. (C) 2010 Elsevier Ltd. All rights reserved.

Invariant theory and reversible-equivariant vector fields

In this paper we present results for the systematic study of reversible-equivariant vector fields - namely, in the simultaneous presence of symmetries and reversing symmetries - by employing algebraic techniques from invariant theory for compact Lie groups. The Hilbert-Poincare series and their associated Molien formulae are introduced,and we prove the character formulae for the computation of dimensions of spaces of homogeneous anti-invariant polynomial functions and reversible-equivariant polynomial mappings. A symbolic algorithm is obtained for the computation of generators for the module of reversible-equivariant polynomial mappings over the ring of invariant polynomials. We show that this computation can be obtained directly from a well-known situation, namely from the generators of the ring of invariants and the module of the equivariants. (C) 2008 Elsevier B.V, All rights reserved.

Formulation of the standard model in terms of spinor fields

We propose an alternative formulation of the Standard Model which reduces the number of free parameters. In our framework, fermionic fields are assigned to fundamental representations of the Lorentz and the internal symmetry groups, whereas bosonic field variables transform as direct products of fundamental representations of all symmetry groups. This allows us to reduce the number of fundamental symmetries. We formulate the Standard Model by considering the SU(3) and SU(2) symmetry groups as the underlying symmetries of the fundamental interactions. This allows us to suggest a model, for the description of the interactions of the intermediate bosons among themselves and interactions of fermions, that makes use of just two parameters. One parameter characterizes the symmetric phase, whereas the other parameter (the asymmetry parameter) gives the breakdown strength of the symmetries. All coupling strengths of the Standard Model are then derived in terms of these two parameters. In particular, we show that all fermionic electric charges result from symmetry breakdown.

Perturbation treatment of symmetry breaking within random matrix theory

We discuss the applicability, within the random matrix theory, of perturbative treatment of symmetry breaking to the experimental data on the flip symmetry breaking in quartz crystal. We found that the values of the parameter that measures this breaking are different for the spacing distribution as compared to those for the spectral rigidity. We consider both two-fold and three-fold symmetries. The latter was found to account better for the spectral rigidity than the former. Both cases, however, underestimate the experimental spectral rigidity at large L. This discrepancy can be resolved if an appropriate number of eigenfrequencies is considered to be missing in the sample. Our findings are relevant for symmetry violation studies in general. (C) 2008 Elsevier B.V. All rights reserved.

Lorentz violation and the proper-time method

In this Letter, we apply the proper-time method to generate the Lorentz-violating Chern-Simons terms in the four-dimensional Yang-Mills and non-linearized gravity theories. It is shown that the coefficient of the induced Chern-Simons term is finite but regularization dependent. (C) 2008 Elsevier B.V. All rights reserved.

Spacetime noncommutativity with a bifermionic parameter

We consider a Moyal plane and propose to make the noncommutativity parameter Theta(mu nu) bifermionic, i.e. composed of two fermionic (Grassmann odd) parameters. The Moyal product then contains a finite number of derivatives, which avoid the difficulties of the standard approach. As an example, we construct a two-dimensional noncommutative field theory model based on the Moyal product with a bifermionic parameter and show that it has a locally conserved energy-momentum tensor. The model has no problem with the canonical quantization and appears to be renormalizable.

Classification of quantum relativistic orientable objects

Extending our previous work `Fields on the Poincare group and quantum description of orientable objects` (Gitman and Shelepin 2009 Eur. Phys. J. C 61 111-39), we consider here a classification of orientable relativistic quantum objects in 3 + 1 dimensions. In such a classification, one uses a maximal set of ten commuting operators (generators of left and right transformations) in the space of functions on the Poincare group. In addition to the usual six quantum numbers related to external symmetries (given by left generators), there appear additional quantum numbers related to internal symmetries (given by right generators). Spectra of internal and external symmetry operators are interrelated, which, however, does not contradict the Coleman-Mandula no-go theorem. We believe that the proposed approach can be useful for the description of elementary spinning particles considered as orientable objects. In particular, it gives a group-theoretical interpretation of some facts of the existing phenomenological classification of spinning particles.

Field on Poincare Group and Quantum Description of Orientable Objects

We propose an approach to the quantum-mechanical description of relativistic orientable objects. It generalizes Wigner`s ideas concerning the treatment of nonrelativistic orientable objects (in particular, a nonrelativistic rotator) with the help of two reference frames (space-fixed and body-fixed). A technical realization of this generalization (for instance, in 3+1 dimensions) amounts to introducing wave functions that depend on elements of the Poincar, group G. A complete set of transformations that test the symmetries of an orientable object and of the embedding space belongs to the group I =GxG. All such transformations can be studied by considering a generalized regular representation of G in the space of scalar functions on the group, f(x,z), that depend on the Minkowski space points xaG/Spin(3,1) as well as on the orientation variables given by the elements z of a matrix ZaSpin(3,1). In particular, the field f(x,z) is a generating function of the usual spin-tensor multi-component fields. In the theory under consideration, there are four different types of spinors, and an orientable object is characterized by ten quantum numbers. We study the corresponding relativistic wave equations and their symmetry properties.

Self-dual hopfions

We construct static and time-dependent exact soliton solutions with nontrivial Hopf topological charge for a field theory in 3 + 1 dimensions with the target space being the two dimensional sphere S(2). The model considered is a reduction of the so-called extended Skyrme-Faddeev theory by the removal of the quadratic term in derivatives of the fields. The solutions are constructed using an ansatz based on the conformal and target space symmetries. The solutions are said self-dual because they solve first order differential equations which together with some conditions on the coupling constants, imply the second order equations of motion. The solutions belong to a sub-sector of the theory with an infinite number of local conserved currents. The equation for the profile function of the ansatz corresponds to the Bogomolny equation for the sine-Gordon model.

Static Hopfions in the extended Skyrme-Faddeev model

We construct static soliton solutions with non-zero Hopf topological charges to a theory which is an extension of the Skyrme-Faddeev model by the addition of a further quartic term in derivatives. We use an axially symmetric ansatz based on toroidal coordinates, and solve the resulting two coupled non-linear partial differential equations in two variables by a successive over-relaxation (SOR) method. We construct numerical solutions with Hopf charge up to four, and calculate their analytical behavior in some limiting cases. The solutions present an interesting behavior under the changes of a special combination of the coupling constants of the quartic terms. Their energies and sizes tend to zero as that combination approaches a particular special value. We calculate the equivalent of the Vakulenko and Kapitanskii energy bound for the theory and find that it vanishes at that same special value of the coupling constants. In addition, the model presents an integrable sector with an in finite number of local conserved currents which apparently are not related to symmetries of the action. In the intersection of those two special sectors the theory possesses exact vortex solutions (static and time dependent) which were constructed in a previous paper by one of the authors. It is believed that such model describes some aspects of the low energy limit of the pure SU(2) Yang-Mills theory, and our results may be important in identifying important structures in that strong coupling regime.