[en] In a very simplified, descriptive way, the main trends of phenomenological cosmology are reviewed. A sketchy view of the fashionable Standard Model(1,2) is considered preliminarly its most pretentious variant, the Symmetric Model, is then introduced

[en] A natural candidate model for a gauge theory for the Poincare group is discussed. It satisfies the usual electric-magnetic symmetry of gauge models and is a contraction of a gauge model for the De Sitter group. Its field equations are just the Yang-Mills equations for the Poincare group. It is shown that these equations do not follow from a Lagrangean. (Author)

[en] Identical impenetrable particles in a 2-dimensional configuration space obey braid statistics, intermediate between bosons and fermions. This statistics, based on braid groups, is introduced as a generalization of the usual statistics founded on the symmetric groups. The main properties of an ideal gas of such particles are presented. They do interpolate the properties of bosons and fermions but include classical particles as a special case. Restriction to 2 dimensions precludes lambda points but originates a peculiar symmetry, responsible in particular for the identity of boson and fermion specific heats. (author)

[en] A short review on theories for the gravitational interactions is presented with emphasis in the gauge-like models.(L.C.)

[en] Quantum phase space is given a description which entirely parallels the usual presentation of Classical Phase Space. A particular Schwinger unitary operator basis, in which the expansion of each operator is its own Weyl expression, is specially convenient for the purpose. The quantum Hamiltonian structure obtains from the classical structure by the conversion of the classical pointwise product of dynamical quantities into the noncommutative star product of Wigner functions. The main qualitative difference in the general structure is that, in the quantum case, the inverse symplectic matrix is not simply antisymmetric. This difference leads to the presence of braiding in the backstage of Quantum Mechanics. (author)

[en] A statistical analysis is made of the randon geometry of an early symmetric matter-antimatter universe model. Such a model is shown to determine the total number of the largest agglomerations in the universe, as well as of some special configurations. Constraints on the time development of the protoagglomerations are also obtained

[en] The space of labels characterizating the elements of Schwinger's basis for unitary quantum operators is endowed with a structure of symplectic type. This structure is embodied in a certain algebric cocycle, whose main features are inherited by the symplectic form of classical phase space. In consequence, the label space may be taken as the Quantum Phase Space Space: it plays, in the quantum case, the same role played by phase in classical mechanics, some differences coming inevitably from its non-linear character. (author)

[en] A gauge model based on the Yang-Mills equations for the Poincare group cannot be consistently quantized, at least in a perturbative approach. The problem is related to the absence of a Lagrangian. Adding the counterterms required by consistency and renormalizability turns the model into a gauge theory for a de Sitter group. (Author)

[en] Gauge theories for non-semisimple groups are examined. A theory for the Poincare group with all the essential characteristics of a Yang-Mills theory possesses necessarily extra equations. Inonu-Wigner contractions of gauge theories are introduced which provide a Lagrangian formalism, equivalent to a lagrangian de Sitter theory supplemented by weak constraints. (Author)

[en] The Weyl-Wigner correspondence prescription, which makes large use of Fourier duality, is reexamined from the point of view of Kac algebras, the most general background for non-commutative Fourier analysis allowing for that property. It is shown how the standard Kac structure has to be extended in order to accommodate the physical requirements. An Abelian and a symmetric projective Kac algebras are shown to provide, in close parallel to the standard case, a new dual framework and a well-defined notion of projective Fourier duality for the group of translations on the plane. The Weyl formula arises naturally as an irreducible component of the duality mapping between these projective algebras. (author). 29 refs