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Dirac operators on
noncommutative
curved spacetimes
Alexander Schenkel, Christoph F. Uhlemann
Description:
We study Dirac operators in the framework of
twist-deformed noncommutative geometry. The
definition of noncommutative Dirac operators is
not unique and we focus on three different ones,
each generalizing the commutative Dirac operator
in a natural way. We show that the three
definitions are mutually inequivalent, and that
demanding formal self-adjointness with respect to
a suitable inner product singles out a preferred
choice. A detailed analysis shows that, if the
Drinfeld twist contains sufficiently many Killing
vector fields, the three operators coincide, which
can simplify explicit calculations considerably. We
then turn to the construction of quantized Dirac
fields on noncommutative curved spacetimes. We
show that there exist unique retarded and
advanced Green’s operators and construct a
canonical anti-commutation relation algebra. In
the last part we study noncommutative Minkowski
and AdS spacetimes as explicit examples.
Cite as: arXiv:1308.1929 [hep-th] (or
arXiv:1308.1929v1 [hep-th] for this version)
Read full version at : Paper
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