1997
DOI: 10.1007/bf02435738
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Fourier duality as a quantization principle

Abstract: The Weyi-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 non… Show more

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Cited by 4 publications
(14 citation statements)
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“…Remarkably, although rarely mentioned in standard textbooks, it is known that flat geometries with their well-defined notion of parallelism, provide alternative and fully equivalent representations of GR. On one hand, Weitzenböck spaces can host a Teleparallel Equivalent of GR (TEGR) [1] where gravity is identified with torsion. On the other hand, flat and torsion-free spacetimes only containing a non-trivial non-metricity can also accommodate a Symmetric Teleparallel Equivalent of GR (STEGR) [2,3].…”
Section: Introductionmentioning
confidence: 99%
“…Remarkably, although rarely mentioned in standard textbooks, it is known that flat geometries with their well-defined notion of parallelism, provide alternative and fully equivalent representations of GR. On one hand, Weitzenböck spaces can host a Teleparallel Equivalent of GR (TEGR) [1] where gravity is identified with torsion. On the other hand, flat and torsion-free spacetimes only containing a non-trivial non-metricity can also accommodate a Symmetric Teleparallel Equivalent of GR (STEGR) [2,3].…”
Section: Introductionmentioning
confidence: 99%
“…We can go further and ask whether it is possible to generalize this duality principle to quantization on any other phase space. This question is partially answered in Aldrovandi and Saeger (1996), where the authors showed how far it is possible to extend this principle to the half-plane, whose canonical group, though requiring no central extension, has the awkward properties of being neither Abelian nor unimodular.…”
Section: Final Remarksmentioning
confidence: 96%
“…Since the operators (73) come from the representations of the Heisenberg group, which is a group of type I, the algebra dlLn(R 2) is also of type I. In the following we will proceed along the lines of the symmetric Kac algebra decomposition exposed in Aldrovandi and Saeger (1996). The task here will be simpler than in that work, since the Haar weight involved is a trace.…”
Section: Irreducible Decomposition According To the Projective Dualmentioning
confidence: 97%
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“…Teleparallel theory is an alternative theory of gravity which is equivalent to GR at the level of the field equations for particular choices of the Lagrangian. For a comprehensive review, we refer to the monographs by Aldrovandi and Pereira [11], Cai, Capozziello, De-Laurentis and Saridakis [12]. The fundamental difference is that while GR is characterized by expressing gravitation through curvature by means of a Levi-Civita connection, Teleparallel gravity uses the Weitzenbock connection to replace curvature with torsion T or a generalized function f (T ).…”
Section: Introductionmentioning
confidence: 99%