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Aschieri P., Dimitrijević M., Meyer F., Wess J., Noncommutative geometry and gravity,
1911
Earlier work this paper cites.
Breitenlohner P., Freedman D.Z., Stability in gauged extended supergravity,
1982
Earlier work this paper cites.
Zuckerman G.J., Action principles and global geometry, in Mathematical Aspects of String Theory (San Diego, Calif., 1986),
Original
1987
Earlier work this paper cites.
Connes A., Noncommutative geometry, Academic Press Inc., San Diego, CA, 1994
1994
Earlier work this paper cites.
Doplicher S., Fredenhagen K., Roberts J.E., Spacetime quantization induced by classical gravity,
1994
Earlier work this paper cites.
Doplicher S., Fredenhagen K., Roberts J.E., The quantum structure of spacetime at the Planck scale and quantum fields,
1995
Earlier work this paper cites.
Taylor M.E., Partial differential equations. I. Basic theory,
1996
Earlier work this paper cites.
Connes A., Landi G., Noncommutative manifolds, the instanton algebra and isospectral deformations,
2001
Earlier work this paper cites.
D’Andrea F., Spectral geometry of
2006
Earlier work this paper cites.
Zahn J., Remarks on twisted noncommutative quantum field theory,
2006
Earlier work this paper cites.
Fiore G., Wess J., Full twisted Poincaré symmetry and quantum field theory on Moyal–Weyl spaces,
2007
Earlier work this paper cites.

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2013

Schenkel, Alexander, Uhlemann, Christoph F.

We study the notion of a Dirac operator in the framework of twist-deformed noncommutative geometry.

We provide a number of well-motivated candidate constructions and propose a minimal set of axioms that a noncommutative Dirac operator should satisfy.
These criteria turn out to be restrictive, but they do not fix a unique construction: two of our operators generally satisfy the axioms, and we provide an explicit example where they are inequivalent.
For highly symmetric spacetimes with Drinfeld twists constructed from sufficiently many Killing vector fields, all of our operators coincide.

Aschieri P., Dimitrijević M., Meyer F., Wess J., Noncommutative geometry and gravity,
1911
Earlier work this paper cites.
Breitenlohner P., Freedman D.Z., Stability in gauged extended supergravity,
1982
Earlier work this paper cites.
Zuckerman G.J., Action principles and global geometry, in Mathematical Aspects of String Theory (San Diego, Calif., 1986),
Original
1987
Earlier work this paper cites.
Connes A., Noncommutative geometry, Academic Press Inc., San Diego, CA, 1994
1994
Earlier work this paper cites.
Doplicher S., Fredenhagen K., Roberts J.E., Spacetime quantization induced by classical gravity,
1994
Earlier work this paper cites.
Doplicher S., Fredenhagen K., Roberts J.E., The quantum structure of spacetime at the Planck scale and quantum fields,
1995
Earlier work this paper cites.
Taylor M.E., Partial differential equations. I. Basic theory,
1996
Earlier work this paper cites.
Connes A., Landi G., Noncommutative manifolds, the instanton algebra and isospectral deformations,
2001
Earlier work this paper cites.
D’Andrea F., Spectral geometry of
2006
Earlier work this paper cites.
Zahn J., Remarks on twisted noncommutative quantum field theory,
2006
Earlier work this paper cites.
Fiore G., Wess J., Full twisted Poincaré symmetry and quantum field theory on Moyal–Weyl spaces,
2007
Earlier work this paper cites.