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Space/time non-commutative field theories and causality

  • H. Bozkaya
  • P. Fischer
  • H. Grosse
  • M. Pitschmann
  • V. Putz
  • M. Schweda
  • R. Wulkenhaar
Theoretical Physics

Abstract.

As argued previously, amplitudes of quantum field theories on non-commutative space and time cannot be computed using naïve path integral Feynman rules. One of the proposals is to use the Gell-Mann-Low formula with time-ordering applied before performing the integrations. We point out that the previously given prescription should rather be regarded as an interaction-point time-ordering. Causality is explicitly violated inside the region of interaction. It is nevertheless a consistent procedure, which seems to be related to the interaction picture of quantum mechanics. In this framework we compute the one-loop self-energy for a space/time non-commutative \(\phi^4\) theory. Although in all intermediate steps only three-momenta play a rôle, the final result is manifestly Lorentz covariant and agrees with the naïve calculation. Deriving the Feynman rules for general graphs, we show, however, that such a picture holds for tadpole lines only.

Keywords

Field Theory Quantum Field Theory Quantum Mechanic Intermediate Step General Graph 
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.

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Copyright information

© Springer-Verlag Berlin Heidelberg / Società Italiana di Fisica 2003

Authors and Affiliations

  • H. Bozkaya
    • 1
  • P. Fischer
    • 1
  • H. Grosse
    • 2
  • M. Pitschmann
    • 1
  • V. Putz
    • 1
  • M. Schweda
    • 1
  • R. Wulkenhaar
    • 3
  1. 1.Institut für Theoretische Physik, Technische Universität Wien, Wiedner Hauptstraße 8-10, 1040 Wien, Austria AT
  2. 2. Institut für Theoretische Physik, Universität Wien, Boltzmanngasse 5, 1090 Wien, Austria AT
  3. 3. Max-Planck-Institut für Mathematik in den Naturwissenschaften, Inselstraße 22-26, 04103 Leipzig, Germany DE

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