Freiburg 2008 – wissenschaftliches Programm
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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik
MP 7: Nichtkommutative Geometrie
MP 7.4: Vortrag
Donnerstag, 6. März 2008, 15:00–15:20, KGI-HS 1023
On positivity and normalization for a quantum field theory on non–commutative spacetime — •Christoph Dehne — ITP, Universität Leipzig, Vor dem Hospitaltore 1, D - 04103 Leipzig
It is well–known that for non–commutative theories with time/space non–commutativity different perturbation schemes (for vacuum expectation values of quantum fields) are no longer equivalent. Therefore, we would like to find out which ones respect the criteria necessary for a probability interpretation, namely positivity and normalization. To this end, we derive - under special assumptions - spectral representations and sum rules that correspond to the different perturbation schemes. Then, in each case, we make a perturbative analysis of the spectral density for a theory with φ∗3–interaction. It turns out that the conditions are fulfilled by those Feynman rules that are considered as unitary. However, as for those Feynman rules that are “usually known to violate unitarity“, we argue that they can be understood as positivity and normalization preserving distributions, too.