Advertisement

Space-time noncommutativity, discreteness of time and unitarity

  • M. Chaichian
  • A. Demichev
  • P. Prešnajder
  • A. Tureanu
Technical physics

Abstract.

Violation of unitarity for noncommutative field theory on compact space-times is considered. Although such theories are free of ultraviolet divergences they still violate unitarity, while in a usual field theory such a violation occurs when the theory is nonrenormalizable. The compactness of space-like coordinates implies discreteness of the time variable which leads to the appearance of unphysical modes and violation of unitarity even in the absence of a star-product in the interaction terms. Thus, this conclusion holds also for other quantum field theories with discrete time. Violation of causality, among others, occurs also in the case of the nonvanishing of the commutation relations between observables at space-like distances with a typical scale of noncommutativity. While this feature allows for a possible violation of the spin-statistics theorem, such a violation does not rescue the situation but makes causality violation scale as the inverse of the mass appearing in the considered model, i.e., it becomes even more severe. We also stress the role of smearing over the noncommutative coordinates entering the field operator symbols.

Keywords

Field Theory Quantum Field Theory Time Variable Field Operator Discrete Time 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag Berlin Heidelberg / Società Italiana di Fisica 2001

Authors and Affiliations

  • M. Chaichian
    • 1
  • A. Demichev
    • 1
  • P. Prešnajder
    • 1
  • A. Tureanu
    • 1
  1. 1.High Energy Physics Division, Department of Physics, University of Helsinki, Helsinki, Finland FI

Personalised recommendations