Built on

K. S. Stelle and P. C. West, Spontaneously broken de Sitter symmetry and the gravitational holonomy group
1977
Earlier work this paper cites.
F. Wilczek, Riemann-Einstein structure from volume and gauge symmetry
1998
Earlier work this paper cites.
B. Jurčo, L. Möller, S. Schraml, P. Schupp and J. Wess, Construction of non-Abelian gauge theories on noncommutative spaces
1999
Earlier work this paper cites.
M. M. Sheikh-Jabbari, C , P C,P and T T Invariance of Noncommutative Gauge Theories
2000
Earlier work this paper cites.
A. H. Chamseeddine, Deforming Einstein’s gravity
2003
Earlier work this paper cites.
P. Aschieri, B. Jurčo, P. Schupp and J. Wess, Noncommutative GUTs, Standard Model and C , P , T C,P,T
2003
Earlier work this paper cites.
M. Chaichian, P.P. Kulish, K. Nishijima, A. Tureanu, On a Lorentz-invariant interpretation of noncommutative space-time and its implications on noncommutative QFT
2005
Earlier work this paper cites.
P.Aschieri, C. Blohmann, M. Dimitrijević, F. Meyer, P. Schupp and J. Wess, A Gravity Theory on Noncommutative Spaces
2006
Earlier work this paper cites.

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2017

Dirac field and gravity in NC $SO(2,3)_\star$ model

Gočanin, Dragoljub, Radovanović, Voja

Understand

Action for the Dirac spinor field coupled to gravity on noncommutative (NC) Moyal-Weyl space-time is obtained without prior knowledge of the metric tensor.

We emphasise gauge origins of gravity (i.e.
metric structure) and its interaction with fermions by demonstrating that a classical action invariant under $SO(2,3)$ gauge transformations can be exactly reduced to the Dirac action in curved space-time after breaking the original symmetry down to the local Lorentz $SO(1,3)$ symmetry.
The commutative, $SO(2,3)$ invariant action can be straightforwardly deformed via Moyal-Weyl $\star$-product to its NC $SO(2,3)_\star$ invariant version which can be expanded perturbatively in the powers of the deformation parameter using the Seiberg-Witten map.

Built on

K. S. Stelle and P. C. West, Spontaneously broken de Sitter symmetry and the gravitational holonomy group
1977
Earlier work this paper cites.
F. Wilczek, Riemann-Einstein structure from volume and gauge symmetry
1998
Earlier work this paper cites.
B. Jurčo, L. Möller, S. Schraml, P. Schupp and J. Wess, Construction of non-Abelian gauge theories on noncommutative spaces
1999
Earlier work this paper cites.
M. M. Sheikh-Jabbari, C , P C,P and T T Invariance of Noncommutative Gauge Theories
2000
Earlier work this paper cites.
A. H. Chamseeddine, Deforming Einstein’s gravity
2003
Earlier work this paper cites.
P. Aschieri, B. Jurčo, P. Schupp and J. Wess, Noncommutative GUTs, Standard Model and C , P , T C,P,T
2003
Earlier work this paper cites.
M. Chaichian, P.P. Kulish, K. Nishijima, A. Tureanu, On a Lorentz-invariant interpretation of noncommutative space-time and its implications on noncommutative QFT
2005
Earlier work this paper cites.
P.Aschieri, C. Blohmann, M. Dimitrijević, F. Meyer, P. Schupp and J. Wess, A Gravity Theory on Noncommutative Spaces
2006
Earlier work this paper cites.

Similar

A. Kobakhidze, C. Lagger and A. Manning, Constraining noncommutative spacetime from GW150914
Original
2006
Cited alongside, same era.
M. Burić and V. Radovanović, The One loop effective action for quantum electrodynamics on noncommutative space
2006
Cited alongside, same era.
M. Burić, T. Grammatikopoulos, J. Madore, G. Zoupanos, Gravity and the Structure of Noncommutative Algebras
Original
2008
Cited alongside, same era.
T. Ohl and A. Schenckel, Cosmological and Black Hole Spacetimes in Twisted Noncommutative Gravity
Original
2010
Cited alongside, same era.
H. S. Yang, Emergent gravity from noncommutative spacetime
Original
2010

Then

P. Aschieri and L. Castellani, Noncommutative D = 4 D=4 gravity coupled to fermions
Original
2012
Later among the works it cites.
Mir Faizal, Noncommutative Quantum Gravity
Original
2013
Later among the works it cites.
P. Aschieri and L. Castellani, Noncommutative supergravity in D = 3 D=3 and D = 4 D=4
Original
2013
Later among the works it cites.
P. Aschieri, L. Castellani and M. Dimitrijević, Noncommutative gravity at second order via Seiberg-Witten map
Original
2013
Later among the works it cites.
M. Burić and J. Madore, Spherically Symmetric Noncommutative Space: d = 4 d=4
Original

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

Cited alongside, same era.

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M. Dobrski, Background independent noncommutative gravity from Fedosov quantization of endomorphism bundle

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2011

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M. Dimitrijević, V. Radovanović and H. Štefančić, AdS-inspired noncommutative gravity on the Moyal plane

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2012

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I. Bars, M.M. Sheikh-Jabbari and M.A. Vasiliev, Noncommutative o ⋆ ( N ) o_{\star}(N) and u s p ⋆ ( 2 N ) usp_{\star}(2N) algebras and the corresponding gauge field theories

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M. Dimitrijević and V. Radovanović, Noncommutative S O ( 2 , 3 ) SO(2,3) gauge theory and noncommutative gravity

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Later among the works it cites.

M. Dimitrijević Ćirić, B. Nikolić and V. Radovanović, Noncommutative gravity and the relevance of the θ \theta -constant deformation

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2017

Closest in time.

M. Dimitrijević Ćirić, B. Nikolić and V. Radovanović, NC S O ( 2 , 3 ) ⋆ SO(2,3)_{\star} gravity: noncommutativity as a source of curvature and torsion

Original

2017

Closest in time.