Fourier duality as a quantization principle

The Weyl-Wigner prescription for quantization on Euclidean phase spaces makes essential use of Fourier duality. The extension of this property to more general phase spaces requires the use of Kac algebras, which provide the necessary background for the implementation of Fourier duality on general locally compact groups. Kac algebras - and the duality they incorporate - are consequently examined as candidates for a general quantization framework extending the usual formalism. Using as a test case the simplest nontrivial phase space, the half-plane, it is shown how the structures present in the complete-plane case must be modified. Traces, for example, must be replaced by their noncommutative generalizations - weights - and the correspondence embodied in the Weyl-Wigner formalism is no longer complete. Provided the underlying algebraic structure is suitably adapted to each case, Fourier duality is shown to be indeed a very powerful guide to the quantization of general physical systems.

Projective Fourier duality and Weyl quantization

The Weyl-Wigner correspondence prescription, which makes great use of Fourier duality, is reexamined from the point of view of Kac algebras, the most general background for noncommutative 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. Both an Abelian and a symmetric projective Kac algebra 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.

Electric charge quantization in a chiral bilepton gauge model

In the context of the standard model the quantization of the electric charge occurs only family by family. When we consider the three families together with massless neutrinos the electric charge is not quantized any more. Here we show that a chiral bilepton gauge model based on the gauge group SU(3)C ⊗ SU(3)L ⊗ U(1)N explains the quantization of the electric charge when we take into account the three families of fermions. This result does not depend on the neutrino masses. Charge quantization occurs whether the neutrinos are massless or Dirac or Majorana massive fields.

Symmetry transform in Faddeev-Jackiw quantization of dual models

We study the presence of symmetry transformations in the Faddeev-Jackiw approach for constrained systems. Our analysis is based in the case of a particle submitted to a particular potential which depends on an arbitrary function. The method is implemented in a natural way and symmetry generators are identified. These symmetries permit us to obtain the absent elements of the sympletic matrix which complement the set of Dirac brackets of such a theory. The study developed here is applied in two different dual models. First, we discuss the case of a two-dimensional oscillator interacting with an electromagnetic potential described by a Chern-Simons term and second the Schwarz-Sen gauge theory, in order to obtain the complete set of non-null Dirac brackets and the correspondent Maxwell electromagnetic theory limit. ©1999 The American Physical Society.

Remark on the vectorlike nature of electromagnetism and electric charge quantization

In this work we study the structure of electromagnetic interactions and electric charge quantization in gauge theories of electroweak interactions based on semisimple groups. We show that in the standard model of electroweak interactions the structure of electromagnetic interactions is strongly correlated to the quantization pattern of electric charges. We examine these two questions also in all possible chiral bilepton gauge models of electroweak interactions. In all, we can explain the vectorlike nature of electromagnetic interactions and electric charge quantization together demanding nonvanishing fermion masses and anomaly cancellations. ©1999 The American Physical Society.

Quantization of the superstring with manifest U(5) super-Poincaré invariance

The superstring is quantized in a manner which manifestly preserves a U(5) subgroup of the (Wick-rotated) ten-dimensional super-Poincaré invariance. This description of the superstring contains critical N = 2 worldsheet superconformal invariance and is a natural covariantization of the U(4)-invariant light-cone Green-Schwarz description. © 1999 Published by Elsevier Science B.V. All rights reserved.

Quantization of the type II superstring in a curved six-dimensional background

A sigma model action with N = 2 D = 6 superspace variables is constructed for the Type II superstring compactified to six curved dimensions with Ramond - Ramond flux. The action can be quantized since the sigma model is linear when the six-dimensional space-time is flat. When the six-dimensional space-time is AdS 3 × S 3, the action reduces to one found earlier with Vafa and Witten. © 2000 Elsevier Science B.V. All rights reserved.

BFFT quantization and dynamical solutions of a fluid field theory

We study a field theory formulation of a fluid mechanical model. We implement the Hamiltonian formalism by using the BFFT conjecture in order to build a gauge invariant fluid field theory. We also generalize previous known classical dynamical field solutions for the fluid model. ©2000 The American Physical Society.

Low-energy sector quantization of a massless scalar field outside a Reissner-Nordström black hole and static sources

We quantize the low-energy sector of a massless scalar field in Reissner-Nordström spacetime. This allows the analysis of processes involving soft scalar particles occurring outside charged black holes. In particular, we compute the response of a static scalar source interacting with Hawking radiation using the Unruh (and the Hartle-Hawking) vacuum. This response is compared with the one obtained when the source is uniformly accelerated in the usual vacuum of Minkowski spacetime with the same proper acceleration. We show that both responses are in general different in opposition to the result obtained when the Reissner-Nordström black hole is replaced by a Schwarzschild one. The conceptual relevance of this result is commented on. ©2000 The American Physical Society.

Super-Poincaré covariant quantization of the superstring

Using pure spinors, the superstring is covariantly quantized. For the first time, massless vertex operators are constructed and scattering amplitudes are computed in a manifestly ten-dimensional super-Poincaré covariant manner. Quantizable non-linear sigma model actions are constructed for the superstring in curved backgrounds, including the AdS 5 × S 5 background with Ramond-Ramond flux.

Covariant quantization of the superstring

After reviewing the Green-Schwarz superstring using the approach of Siegel, the superstring is covariantly quantized by constructing a BRST operator from the fermionic constraints and a bosonic pure spinor ghost variable. Physical massless vertex operators are constructed and, for the first time, N-point tree amplitudes are computed in a manifestly ten-dimensional super-Poincaré covariant manner. Quantization can be generalized to curved supergravity backgrounds and the vertex operator for fluctuations around AdS 5 x S 5 is explicitly constructed.

Covariant quantization of the superparticle using pure spinors

The ten-dimensional superparticle is covariantly quantized by constructing a BRST operator from the fermionic Green-Schwarz constraints and a bosonic pure spinor variable. This same method was recently used for covariantly quantizing the superstring, and it is hoped that the simpler case of the superparticle will be useful for those who want to study this quantization method. It is interesting that quantization of the superparticle action closely resembles quantization of the worldline action for Chern-Simons theory.

Towards covariant quantization of the supermembrane

By replacing ten-dimensional pure spinors with eleven-dimensional pure spinors, the formalism recently developed for covariantly quantizing the d = 10 superparticle and superstring is extended to the d = 11 superparticle and supermembrane. In this formalism, kappa symmetry is replaced by a BRST-like invariance using the nilpotent operator Q = ∮ λ αdα where dα is the worldvolume variable corresponding to the d = 11 spacetime supersymmetric derivative and λα is an SO(10, 1) pure spinor variable satisfying λΓcλ = 0 for c = 1 to 11. Super-Poincaré covariant unintegrated and integrated supermembrane vertex operators are explicitly constructed which are in the cohomology of Q. After double-dimensional reduction of the eleventh dimension, these vertex operators are related to type-IIA superstring vertex operators where Q = QL + QR is the sum of the left and right-moving type-IIA BRST operators and the eleventh component of the pure spinor constraint, λΓ 11λ = 0, replaces the bL 0 - b R 0 constraint of the closed superstring. A conjecture is made for the computation of M-theory scattering amplitudes using these supermembrane vertex operators. © SISSA/ISAS 2002.

Sm-Nd system in total rock open versus closed isotopic composition in zones of high deformation

High strain shear zones of Brasiliano age, developed in Paleoproterozoic basement gneiss of the Caicó region, Borborema Province, NE Brazil, were associated with medium- to low-grade metamorphism and deformational processes that transformed porphyritic augen gneiss into muscovite quartzite, modifying their original mineralogy and chemical properties. During the last hydrothermal event mobility of major, minor and trace elements was great, whereas the pattern of Rare Earth Elements was not changed. We carried out a Sm-Nd isotopic study in these rocks in order to understand the behavior of Nd isotopes during mylonite generation. TDM model ages at around 2.6 Ga and εNd (t) values for both protolith and transformed rock suggest that the Nd isotopic system remained closed, recording the original source rock signature, despite undergoing two superposed metamorphic events. These new Sm-Nd results provide important information on the geologic evolution of basement rocks in the central Rio Grande do Norte Terrane of the Borborema Province, NE Brazil.

Covariant quantization of the superstring

After constructing a BRST operator from the fermionic Green-Schwarz constraints and a bosonic pure spinor ghost variable, the superstring is covariantly quantized and N-point tree amplitudes are computed in a manifestly ten-dimensional super-Poincaré covariant manner. © 2004 Published by Elsevier B.V.