Relativistic field equations from higher-order polarizations of the Poincar\'e group

The theory of free relativistic fields is shown to arise in a unified manner from higher-order, configuration-space, irreducible representations of the Poincar\'e group. A de Sitter subalgebra, in the massive case, and a Poincar\'e subalgebra, in the massless case, of the enveloping algebra of the Poincar\'e group are the suitable higher-order polarizations. In particular, a simple group-theoretic derivation of the Dirac equation is given.Comment: The paper has been reordered. LaTeX file, 15 pp. To appear in Rep. Math. Phy

Group Approach to Quantization of Yang-Mills Theories: A Cohomological Origin of Mass

New clues for the best understanding of the nature of the symmetry-breaking mechanism are revealed in this paper. A revision of the standard gauge transformation properties of Yang-Mills fields, according to a group approach to quantization scheme, enables the gauge group coordinates to acquire dynamical content outside the null mass shell. The corresponding extra (internal) field degrees of freedom are transferred to the vector potentials to conform massive vector bosons.Comment: 21 pages, LaTeX, no figures; final for

Central extensions and quantum physics

The unitary implementation of a symmetry group G of a classical system in the corresponding quantum theory entails unavoidable deformations ˜G of G, namely, central extensions by the typical phase invariance group U(1). The appearance of central charges in the corresponding Lie-algebra quantum commutators, as a consequence of non-trivial responses of the phase of the wave function under symmetry transformations, lead to a quantum generation of extra degrees of freedom with regard to the classical counterpart. In particular, symmetries of the Hall effect, Yang-Mills and conformally invariant classical field theories are affected when passing to the quantum realm.M. Calixto thanks the University of Granada for a Post-doctoral grant and the Department of Physics of Swansea for its hospitality

Los Mantos apujárrides del tercio central de las Cordilleras Béticas. Ensayo de la correlación tectónica de los Alpujárrides

Los Mantos Alpujárrides se componen de una secuencia metapelítica constituída en general por tres formaciones esquistosas (Paleozoico-Triásico inferior), coronada por series carbonatadas triásicas; se detectan diferencias esiratigráficas de unos mantos a otros, sobre todo entre términos permetriásicos. Las superficies de corrimiento han cizallado la sucesión alpujárride y se hallan situadas a niveles diferentes según los mantos. El metamorfismo -y también varias fases de plegamiento- es anterior a la tectónica de corrimiento y ha afectado a los materiales con una intensidad variable, dependiente de las posiciones ocupadas por los mantos en el orógeno. Una vez discutido el valor de estas características como criterios para el agrupamiento de los Alpujárrides y considerando la posición de cada unidad en la pila de mantos, se ha realizado una subdivisión engrupos de mantos que poseen el carácter de subconjuntos con entidad tectónica significativa fundados esencialmente en datos y observaciones de los autores sobre el tercio central de las Cordilleras Béticas, se proponen los siguientes grupos: Lujar, Guadalfeo, Contraviesa y Almijara.Estos grupos tienen validez para el resto de la Zona Bética y se han usado en la correlación de elementos tectónicos de distintas áreas

Group Quantization on Configuration Space: Gauge Symmetries and Linear Fields

A new, configuration-space picture of a formalism of group quantization, the GAQ formalism, is presented in the context of a previous, algebraic generalization. This presentation serves to make a comprehensive discussion in which other extensions of the formalism, principally to incorporate gauge symmetries, are developed as well. Both images are combined in order to analyse, in a systematic manner and with complete generality, the case of linear fields (abelian current groups). To ilustrate these developments we particularize them for several fields and, in particular, we carry out the quantization the abelian Chern-Simons models over an arbitrary closed surface in detail.M.N. is grateful to the Imperial College, where this paper has mainly been written, for its hospitality. M.N. is also grateful to the Spanish MEC, CSIC and IMAFF (Madrid) for a research contract. M.C. is grateful to the Spanish MEC for a FPI fellowship

Group-Theoretical Determination of the Mixing Angle in the Electroweak Gauge Group

The assumption that the Weinberg rotation between the gauge fields associated with the third component of the “weak isospin” (T3) and the hypercharge (Y ) proceeds in a natural way from a global homomorphism of the SU(2) U(1) gauge group in some locally isomorphic group (which proves to be U(2)), imposes strong restrictions so as to fix the single value sin2 W = 1/2. This result can be thought of only as being an asymptotic limit corresponding to an earlier stage of the Universe. It also lends support to the idea that e2/g2 and 1−M2W /M2Z are in principle unrelated quantities.V.A. is grateful to M. Asorey, J. Julve and A. Tiemblo, and all of us to J.M. Cerveró, J. Navarro-Salas, M. Navarro and A. Romero for valuable discussions

Group Quantization on Configuration Space

New features of a previously introduced Group Approach to Quantization are presented. We show that the construction of the symmetry group associated with the system to be quantized (the “quantizing group”) does not require, in general, the explicit construction of the phase space of the system, i.e., does not require the actual knowledgement of the general solution of the classical equations of motion: in many relevant cases an implicit construction of the group can be given, directly, on configuration space. As an application we construct the symmetry group for the conformally invariant massless scalar and electromagnetic fields and the scalar and Dirac fields evolving in a symmetric curved spacetime or interacting with symmetric classical electromagnetic fields. Further generalizations of the present procedure are also discussed and in particular the conditions under which non-abelian (mainly Kac-Moody) groups can be included.M. Navarro is grateful to the Spanish MEC for a postdoctoral FPU grant. M. Calixto thanks the Spanish MEC for a FPU grant

Global restrictions to the Mixing Angle W

In spite of its firm hold in particle physics, the gauge group SU(2)⊗U(1)Y proves not to be the most appropriate to describe the unification of weak and electromagnetic interactions. In fact, a look at the structure of SU(2)⊗U(1)Y tells us that both, the electric charge generator Q and its corresponding electromagnetic gauge field Aμ(x),are not basic constituents of this gauge group.This work was partially supported by the DGICYT. M. Calixto thanks the Spanish MEC for a FPI grant

Algebraic versus Topologic Anomalies

Within the frame of a Group Approach to Quantization anomalies arise in a quite natural way. We present in this talk an analysis of the basic obstructions that can be found when we try to translate symmetries of the Newton equations to the Quantum Theory. They fall into two classes: algebraic and topologic according to the local or global character of the obstruction. We present here one explicit example of each

Quantization on the Torus and modular invariance

The implementation of modular invariance on the torus as a phase space at the quantum level is discussed in a group-theoretical framework. Unlike the classical case, at the quantum level some restrictions on the parameters of the theory should be imposed to ensure modular invariance. Two cases must be considered, depending on the cohomology class of the symplectic form on the torus. If it is of integer cohomology class n, then full modular invariance is achieved at the quantum level only for those wave functions on the torus which are periodic if n is even, or antiperiodic if n is odd. If the symplectic form is of rational cohomology class n/r , a similar result holds –the wave functions must be either periodic or antiperiodic on a torus r times larger in both direccions, depending on the parity of nr. Application of these results to the Abelian Chern-Simons is discussed.J. Guerrero thanks the Spanish MEC for a Postdoctoral grant and the Department of Physics of Naples-INFN for its hospitality and financial support, and M. Calixto thanks the Spanish MEC for a FPI grant. Work partially supported by the DGICYT