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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
1

Weyl quantization, reduction, and star products

Bowes, David January 1993 (has links)
No description available.
2

Aspects différentiels et métriques de la géométrie non commutative : application à la physique / Aspects of the metric and differential noncommutative geometry : application to physics

Cagnache, Eric 25 June 2012 (has links)
La géométrie non commutative, du fait qu'elle permet de généraliser des objets géométriques sous forme algébrique, offre des perspectives intéressantes pour réunir la théorie quantique des champs et la relativité générale dans un seul cadre. Elle peut être abordée selon différents points de vue et deux d'entre eux sont présentés dans cette thèse. Le premier, le calcul différentiel basé sur les dérivations, nous a permis de construire une action de Yang-Mills-Higgs dans laquelle apparait des champs pouvant être interprétés comme des champs de Higgs. Avec le second, les triplets spectraux, on peut généraliser la notion de distance entre état et calculer des formules de distance. C'est ce que nous avons fait dans le cas de l'espace de Moyal et du tore non commutatif. / Noncommutative geometry offers interesting prospects to gather the quantum field theory and relativity in one general framework because it allows one to generalize geometric objects algebraically. It can be approached from different points of view and two of them are presented in this PhD. The first, calculus based on derivations, allowed us to construct a Yang-Mills-Higgs action which appears in fields that can be interpreted as Higgs fields. With the second, spectral triples, we can generalize the notion of distance between states. We calculated the distance formulas in the case of the Moyal space and the noncommutative torus.
3

Smooth $*$--Algebras

Peter.Michor@esi.ac.at 19 June 2001 (has links)
No description available.
4

Quantum Field Theory on Non-commutative Spacetimes

Borris, Markus 27 April 2011 (has links) (PDF)
The time coordinate is a common obstacle in the theory of non-commutative (nc.) spacetimes. Despite that, this work shows how the interplay between quantum fields and an underlying nc. spacetime can still be analyzed, even for the case of nc. time. This is done for the example of a general Moyal-type external potential scattering of the Dirac field in Moyal-Minkowski spacetime. The spacetime is a rare example of a Lorentzian non-compact nc. geometry. Elements of the associated spectral function algebra are shown to be operationally involved at the level of quantum field operators by Bogoliubovs formula. Furthermore, a similar task is attacked in the case of locally nc. spacetimes. An explicit star-product is constructed by a method of Kontsevich. It implements a decay of non-commutativity with increasing distance. This behavior should benefit the technical side - diverse interesting formal attempts are discussed. It is striven for unification of several toy models of nc. spacetimes and a general strategy to define quantum field operators. Within the latter one has to implement the usual quantum behavior as well as a new kind of spacetime behavior. It is shown how this two-fold character causes key difficulties in understanding.
5

Quantum Field Theory on Non-commutative Spacetimes

Borris, Markus 06 April 2011 (has links)
The time coordinate is a common obstacle in the theory of non-commutative (nc.) spacetimes. Despite that, this work shows how the interplay between quantum fields and an underlying nc. spacetime can still be analyzed, even for the case of nc. time. This is done for the example of a general Moyal-type external potential scattering of the Dirac field in Moyal-Minkowski spacetime. The spacetime is a rare example of a Lorentzian non-compact nc. geometry. Elements of the associated spectral function algebra are shown to be operationally involved at the level of quantum field operators by Bogoliubovs formula. Furthermore, a similar task is attacked in the case of locally nc. spacetimes. An explicit star-product is constructed by a method of Kontsevich. It implements a decay of non-commutativity with increasing distance. This behavior should benefit the technical side - diverse interesting formal attempts are discussed. It is striven for unification of several toy models of nc. spacetimes and a general strategy to define quantum field operators. Within the latter one has to implement the usual quantum behavior as well as a new kind of spacetime behavior. It is shown how this two-fold character causes key difficulties in understanding.
6

Bi-fractional transforms in phase space

Agyo, Sanfo David January 2016 (has links)
The displacement operator is related to the displaced parity operator through a two dimensional Fourier transform. Both operators are important operators in phase space and the trace of both with respect to the density operator gives the Wigner functions (displaced parity operator) and Weyl functions (displacement operator). The generalisation of the parity-displacement operator relationship considered here is called the bi-fractional displacement operator, O(α, β; θα, θβ). Additionally, the bi-fractional displacement operators lead to the novel concept of bi-fractional coherent states. The generalisation from Fourier transform to fractional Fourier transform can be applied to other phase space functions. The case of the Wigner-Weyl function is considered and a generalisation is given, which is called the bi-fractional Wigner functions, H(α, β; θα, θβ). Furthermore, the Q−function and P−function are also generalised to give the bi-fractional Q−functions and bi-fractional P−functions respectively. The generalisation is likewise applied to the Moyal star product and Berezin formalism for products of non-commutating operators. These are called the bi-fractional Moyal star product and bi-fractional Berezin formalism. Finally, analysis, applications and implications of these bi-fractional transforms to the Heisenberg uncertainty principle, photon statistics and future applications are discussed.
7

Bi-fractional transforms in phase space

Agyo, Sanfo D. January 2016 (has links)
The displacement operator is related to the displaced parity operator through a two dimensional Fourier transform. Both operators are important operators in phase space and the trace of both with respect to the density operator gives the Wigner functions (displaced parity operator) and Weyl functions (displacement operator). The generalisation of the parity-displacement operator relationship considered here is called the bi-fractional displacement operator, O(α, β; θα, θβ). Additionally, the bi-fractional displacement operators lead to the novel concept of bi-fractional coherent states. The generalisation from Fourier transform to fractional Fourier transform can be applied to other phase space functions. The case of the Wigner-Weyl function is considered and a generalisation is given, which is called the bi-fractional Wigner functions, H(α, β; θα, θβ). Furthermore, the Q−function and P−function are also generalised to give the bi-fractional Q−functions and bi-fractional P−functions respectively. The generalisation is likewise applied to the Moyal star product and Berezin formalism for products of non-commutating operators. These are called the bi-fractional Moyal star product and bi-fractional Berezin formalism. Finally, analysis, applications and implications of these bi-fractional transforms to the Heisenberg uncertainty principle, photon statistics and future applications are discussed.
8

Entropic Motors / Directed Motion without Energy Flow

Blaschke, Johannes Paul 24 February 2014 (has links)
No description available.

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