Yi Liao, Klaus Sibold
Spectral Representation and Dispersion Relations in Field Theory on Noncommutative Space
Preprint series: ESI preprints

MSC:

58B30 Noncommutative differential geometry and topology, See also {46L30, 46L87, 46L89}

81R50 Quantum groups and related algebraic methods, See Also {16W30, 17B37}

81T99 None of the above but in this section

PACS: 02.40.Gh,11.55.Fv,11.10.-z
Abstract: We study the spectral representation and dispersion relations that follow from
some basic assumptions and the reduced spacetime symmetries on noncommutative
(NC) space. Kinematic variables involving the NC parameter appear naturally as
parametric variables in this analysis. When subtractions are necessary to
remove ultraviolet divergences, they are always made at the fixed values of
these NC variables. This point is also illustrated by a perturbative analysis
of self-energies. Our analysis of the reduced spacetime symmetries suggests a
weaker microcausality requirement. Starting from it, we make a first attempt at
dispersion relations for forward scattering. It turns out that the attempt is
hampered by a new unphysical region specified by a given motion in the NC
plane which does not seem to be surmountable using the usual tricks.
Implications for a possible subtraction and renormalization scheme for NC
field theory in which the ultraviolet-infrared (UV/IR) mixing is removed
are also briefly commented on.

Keywords: noncommutative spacetime, spectral representation, dispersion relations, causality