0000000000132750
AUTHOR
Manuel Calixto
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…
Generalized Conformal Symmetry and Extended Objects from the Free Particle
The algebra of linear and quadratic functions of basic observables on the phase space of either the free particle or the harmonic oscillator possesses a finite-dimensional anomaly. The quantization of these systems outside the critical values of the anomaly leads to a new degree of freedom which shares its internal character with spin, but nevertheless features an infinite number of different states. Both are associated with the transformation properties of wave functions under the Weyl-symplectic group $WSp(6,\Re)$. The physical meaning of this new degree of freedom can be established, with a major scope, only by analysing the quantization of an infinite-dimensional algebra of diffeomorphi…
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…
The electromagnetic and Proca fields revisited: A unified quantization
Quantizing the electromagnetic field with a group formalism faces the difficulty of how to turn the traditional gauge transformation of the vector potential, Aμ(x) → Aμ(x) + ∂μφ(x), into a group law. In this paper, it is shown that the problem can be solved by looking at gauge transformations in a slightly different manner which, in addition, does not require introducing any BRST-like parameter. This gauge transformation does not appear explicitly in the group law of the symmetry but rather as the trajectories associated with generalized equations of motion generated by vector fields with null Noether invariants. In the new approach the parameters of the local group, U(1)(x, t), acquire dyn…