DOI: 10.1140/epjc/s2003-01210
Space/time non-commutative field theories and causality
H. Bozkaya1, P. Fischer1, H. Grosse2, M. Pitschmann1, V. Putz1, 3, M. Schweda1 and R. Wulkenhaar31 Institut für Theoretische Physik, Technische Universität Wien, Wiedner Hauptstraße 8-10, 1040 Wien, Austria
2 Institut für Theoretische Physik, Universität Wien, Boltzmanngasse 5, 1090 Wien, Austria
3 Max-Planck-Institut für Mathematik in den Naturwissenschaften, Inselstraße 22-26, 04103 Leipzig, Germany
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(Received: 11 December 2002 / Revised version: 20 March 2003 / Published online: 23 May 2003 )
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
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.
© Società Italiana di Fisica, Springer-Verlag 2003
