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Doctoral Thesis
DOI
https://doi.org/10.11606/T.45.2016.tde-20230727-113239
Document
Author
Full name
Daniel Vasques Paulino
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2016
Supervisor
Title in Portuguese
Completamentos C e a álgebra DFR
Keywords in Portuguese
Álgebras De Operadores
Análise Funcional
C Álgebras
Abstract in Portuguese
O objetivo do presente trabalho é apresentar a construçao de uma familia geral de C - algebras que inclui, como um caso especial, a algebra do espaço-tempo quantico, introduzida por Doplicher, Fredenhagen e Roberts. Esta construçao e baseada em uma extensao da noçao de completamento C - , de algebras para fibrados de algebras, compativel com o completamento usual no nivel de seçoes, combinada com uma nova definiçao para a algebra das relaçoes canonicas de comutaçao utilizando a teoria da quantizaçao estrita de Rieffel. Considerando a algebra C - das seçoes continuas, obtemos um funtor que associa a cada fibrado de Poisson uma algebra C - e produz a algebra DFR original como um exemplo particular.
Title in English
not available
Abstract in English
The aim of this work is to present the construction of a general family of C - algebras which includes, as a special case, the quantum spacetime algebra introduced by Doplicher, Fredenhagen and Roberts. It is based on an extension of the notion of C -completion, from algebras to bundles of algebras, compatible with the usual C - completion of the appropriate algebras of sections, combined with a novel definition for the algebra of the canonical commutation relations using Rieffel theory of strict deformation quantization. Taking the C - algebra of continuous sections vanishing at infinity, we arrive at a functor associating a C - algebra to any Poisson vector bundle and recover the original DFR-algebra as a particular example.
 
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PaulinoDanielVasques.pdf (579.90 Kbytes)
Publishing Date
2023-07-27
 
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