- AutorIn
- Markus Borris
- Titel
- Quantum Field Theory on Non-commutative Spacetimes
- Zitierfähige Url:
- https://nbn-resolving.org/urn:nbn:de:bsz:15-qucosa-67788
- Datum der Einreichung
- 08.11.2010
- Datum der Verteidigung
- 06.04.2011
- Abstract (EN)
- 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.
- Freie Schlagwörter (DE)
- nichtkommutative Raumzeit, Quantenfeldtheorie, Moyal, Bogoliubovs Formel, nichtkommutative Zeit, Dirac-Feld, externe Potentialstreuung
- Freie Schlagwörter (EN)
- non-commutative spacetime, quantum field theory, Moyal, Bogoliubovs formula, non-commutative time, Dirac field, external potential, scattering
- Klassifikation (DDC)
- 530
- GutachterIn
- Prof. Dr. Rainer Verch
- Prof. Dr. Raimar Wulkenhaar
- Den akademischen Grad verleihende / prüfende Institution
- Universität Leipzig, Leipzig
- URN Qucosa
- urn:nbn:de:bsz:15-qucosa-67788
- Veröffentlichungsdatum Qucosa
- 27.04.2011
- Dokumenttyp
- Dissertation
- Sprache des Dokumentes
- Englisch