Group-Theoretic analysis of the mixing angle in the electroweak gauge group

In this paper the authors provide strong mathematical support for the idea that the experimentally measured magnitude 1 - M{sub W}{sup 2}/M{sub Z}{sup 2} associated with sin{sup 2}{theta}{sub w} in the standard model of electroweak interactions cannot be simultaneously identified with the squared quotient of the electric charge by the SU(2) charge, e{sup 2}/g{sup 2}. In fact, the natural, mathematical requirement that the Weinberg rotation between the gauge fields associated with the third component of the {open_quotes}weak isospin{close_quotes} (T{sub 3}) and the hypercharge (Y) proceeds from a global Lie-group homomorphism of the SU(2) {circle_times} U(1){sub y} gauge group in some locall…

Geometric quantization in the presence of an electromagnetic field

Some aspects of the formalism of geometric quantization are described emphasizing the role played by the symmetry group of the quantum system which, for the free particle, turns out to be a central extensionG(m) of the Galilei groupG. The resulting formalism is then applied to the case of a particle interacting with the electromagnetic field, which appears as a necessary modification of the connection 1-form of the quantum bundle when its invariance group is generalized to alocal extension ofG. Finally, the quantization of the electric charge in the presence of a Dirac monopole is also briefly considered.

Relativistic wave equations from supergroup quantization

A formalism of geometric quantization recently introduced which is based on the consideration of Lie groups which are central extensions by U(1) is applied to the relativistic case by using the N-2 super Poincare group with a central charge.

Quantization as a consequence of the group law

A method of gemetric quantization which solely makes use of the structure of the symmetry group of the dynamical system is proposed; the classical limit is discussed along similar lines. The method is applied to two examples, the free particle and the harmonic oscillator.

Three physical quantum manifolds from the conformal group

Algebraic Quantization, Good Operators and Fractional Quantum Numbers

The problems arising when quantizing systems with periodic boundary conditions are analysed, in an algebraic (group-) quantization scheme, and the ``failure" of the Ehrenfest theorem is clarified in terms of the already defined notion of {\it good} (and {\it bad}) operators. The analysis of ``constrained" Heisenberg-Weyl groups according to this quantization scheme reveals the possibility for new quantum (fractional) numbers extending those allowed for Chern classes in traditional Geometric Quantization. This study is illustrated with the examples of the free particle on the circumference and the charged particle in a homogeneous magnetic field on the torus, both examples featuring ``anomal…

Cohomology and contraction: The “non-relativistic” limit revisited

In this note we reconsider the transition from P⊗U(1) to the N extended Galilei group \(\tilde G\)(m),first discussed by Saletan. To this aim, we first analyse the relations between the groups G⊗U(1) and \(\tilde G\)c , where G is a Lie group of trivial H o 2 (G,U(1)) cohomology and \(\tilde G\)c is a central extension of Gc (obtained from G by contraction) by U(1).

The electromagnetic group: Bosonic BRST charge

Abstract We give an infinite-dimensional Lie group from which a group approach to quantization (GAQ) derives a Gupta-Bleuler-like quantization for the electromagnetic field. The incorporation into the group law of the gauge transformation properties of Aμ(x), Aμ(x) → Aμ(x) + ∂μφ, requires a non-conventional generator which is related to the BRST charge.

On the canonical structure of higher-derivative field theories. The gravitational WZW-model

Abstract A general expression for the symplectic structure of a higher-derivative lagrangian field theory is given. General relativity and the gravitational WZW-model are considered in this framework. In the second case we work out explicitly the Poisson bracket for both chiral solutions giving rise, in two different ways, to the classical exchange algebra of the SL q (2) group.

Cohomology, central extensions, and (dynamical) groups

We analyze in this paper the process of group contraction which allows the transition from the Einstenian quantum dynamics to the Galilean one in terms of the cohomology of the Poincare and Galilei groups. It is shown that the cohomological constructions on both groups do not commute with the contraction process. As a result, the extension coboundaries of the Poincare group which lead to extension cocycles of the Galilei group in the “nonrelativistic” limit are characterized geometrically. Finally, the above results are applied to a quantization procedure based on a group manifold.

Symmetry and quantization : higher-order polarizations and anomalies

Group Foundations of Quantum and Classical Dynamics : Towards a Globalization and Classification of Some of Their Structures

This paper is devoted to a constructiveand critical analysis of the structure of certain dynamical systems from a group manifold point of view recently developed. This approach is especially suitable for discussing the structure of the quantum theory, the classical limit, the Hamilton-Jacobi theory and other problems such as the definition and globalization of the Poincare-Cartan form which appears in the variational approach to higher order dynamical systems. At the same time, i t opens a way for the classification of all hamiltonian and lagrangian systems associated with suitably defined dynamical groups. Both classical and quantum dynamics are discussed, and examples of all the different…