arXiv subjects

M. Calixto

Publications and source records attributed to M. Calixto.

49 records · Page 3Linked to original sources

arXiv1999

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 $\TG$ 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.

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arXiv1999

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.

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arXiv1998

Vacuum Radiation in Conformally Invariant Quantum Field Theory

Although the whole conformal group $SO(4,2)$ can be considered as a symmetry in a classical massless field theory, the subgroup of special conformal transformations (SCT), usually related to transitions to uniformly accelerated frames, causes vacuum radiation in the corresponding quantum field theory, in analogy to the Fulling-Unruh effect. The spectrum of the outgoing particles can be calculated exactly and proves to be a generalization of the Planckian one.

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arXiv1998

Vacuum Radiation and Symmetry Breaking in Conformally Invariant Quantum Field Theory

The underlying reasons for the difficulty of unitarily implementing the whole conformal group $SO(4,2)$ in a massless Quantum Field Theory (QFT) are investigated in this paper. Firstly, we demonstrate that the singular action of the subgroup of special conformal transformations (SCT), on the standard Minkowski space $M$, cannot be primarily associated with the vacuum radiation problems, the reason being more profound and related to the dynamical breakdown of part of the conformal symmetry (the SCT subgroup, to be more precise) when representations of null mass are selected inside the representations of the whole conformal group. Then we show how the vacuum of the massless QFT radiates under the action of SCT (usually interpreted as transitions to a uniformly accelerated frame) and we calculate exactly the spectrum of the outgoing particles, which proves to be a generalization of the Planckian one, this recovered as a given limit.

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arXiv1997

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 diffeomorphisms generalizing string symmetry and leading to more general extended objects.

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arXiv1997

Global restrictions to the Mixing Angle $θ_W$

We provide the theoretic value 1/2 for the quantity $\sin**2θ_W=e**2/g**2$, as opposite to the experimental value of $\sin**2θ_W=1-M_W**2/M_Z**2 \sim 0.23$, in the electro-weak gauge group $SU(2)\otimes U(1)_Y$. The arguments we use are of topological nature and have to do with natural requirements of globality in the transformations of the gauge algebra. This results supports the idea that the two definitions of $\sin**2θ_W$ cannot be simultaneously identified except, maybe, in an asymptotic limit corresponding to an earlier stage of the Universe, before the spontaneous symmetry breaking had taken place.

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arXiv1997

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.

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arXiv1997

Algebraic Quantization on the Torus and Modular Invariance

New features of systems with non-trivial topology such as fractional quantum numbers, inequivalent quantizations, good operators, topological anomalies, etc. are described in the framework of an algebraic quantization procedure on a group. Modular invariance naturally appears as a subgroup of good operators in the particular case of the torus.

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arXiv1996

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, particularly 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 of the abelian Chern-Simons models over an arbitrary closed surface in detail.

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arXiv1996

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, $A_μ(x)\rightarrow A_μ(x)+\partial_μφ(x)$, 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, $U(1)(\vec{x},t)$, acquire dynamical content outside the photon mass shell, a fact which also allows a unified quantization of both the electromagnetic and Proca fields.

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arXiv1995

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 ``anomalous" operators, non-equivalent quantization and the latter, fractional quantum numbers. These provide the rationale behind flux quantization in superconducting rings and Fractional Quantum Hall Effect, respectively.

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arXiv1995

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 space- time 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.

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arXiv1994

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" ($T_3$) and the hypercharge ($Y$) proceeds in a natural way from a global homomorphism of the $SU(2)\otimes U(1)$ gauge group in some locally isomorphic group (which proves to be $U(2)$), imposes strong restrictions so as to fix the single value $\sin^2θ_W=1/2$. 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 $e^2/g^2$ and $1-M_W^2/M_Z^2$ are in principle unrelated quantities.

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