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Space/time non-commutative field theories and causality

  • Theoretical Physics
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The European Physical Journal C - Particles and Fields Aims and scope Submit manuscript

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.

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Received: 11 December 2002 / Revised version: 20 March 2003 / Published online: 23 May 2003

RID="a"

ID="a" Work supported by Fonds zur Förderung der Wissenschaften (FWF) under contract P15463

RID="b"

ID="b" e-mail: fischer@hep.itp.tuwien.ac.at; work supported by Fonds zur Förderung der Wissenschaften (FWF) under contract P15463

RID="c"

ID="c" e-mail: grosse@doppler.thp.univie.ac.at

RID="d"

ID="d" Work supported by Fonds zur Förderung der Wissenschaften (FWF) under contract P15463

RID="e"

ID="e" e-mail: vputz@mis.mpg.de; work supported by Fonds zur Förderung der Wissenschaften (FWF) under contract P15015-TPH

RID="f"

ID="f" e-mail: mschweda@tph.tuwien.ac.at

RID="g"

ID="g" e-mail: raimar.wulkenhaar@mis.mpg.de; Schloeßmann fellow

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Bozkaya, H., Fischer, P., Grosse, H. et al. Space/time non-commutative field theories and causality. Eur. Phys. J. C 29, 133–141 (2003). https://doi.org/10.1140/epjc/s2003-01210-9

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  • DOI: https://doi.org/10.1140/epjc/s2003-01210-9

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