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Noncommutative symmetries and gravity

Paolo Aschieri
(
- Schrodinger Inst., Vienna and
- Piemonte Orientale U., Alessandria
)

Aug, 2006

28 pages

Part of Elementary particle physics. Proceedings, Corfu Summer Institute, CORFU2005, Corfu, Greece, September 4-26, 2005

Published in:

J.Phys.Conf.Ser. 53 (2006) 799-819

Contribution to:

e-Print:

hep-th/0608172 [hep-th]

DOI:

10.1088/1742-6596/53/1/052

View in:

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Abstract:

Spacetime geometry is twisted (deformed) into noncommutative spacetime geometry, where functions and tensors are now star-multiplied. Consistently, spacetime diffeomorhisms are twisted into noncommutative diffeomorphisms. Their deformed Lie algebra structure and that of infinitesimal Poincare' transformations is defined and explicitly constructed. This allows to construct a noncommutative theory of gravity.

Note:

26 pages. Lectures given at the workshop `Noncommutative Geometry in Field and String Theories', Corfu Summer Institute on EPP, September 2005, Corfu, Greece. Version 2: Marie Curie European Reintegration Grant MERG-CT-2004-006374 acknowledged

04.20.-q
02.40.Gh
02.20.Uw
04.60.-m
11.10.Nx
talk
gravitation
differential geometry: noncommutative
space-time: deformation
diffeomorphism: transformation

References(36)

Figures(0)

The Fuzzy sphere

J. Madore
(
- Orsay, LPT
)

- Class.Quant.Grav. 9 (1992) 69-88,
- In *Li, M. (ed.) et al.: Physics in non-commutative world* 74-89
•
DOI:
- 10.1088/0264-9381/9/1/008

Differential calculus on ISO-q(N), quantum Poincare algebra and q gravity

Leonardo Castellani
(
- INFN, Turin and
- Turin U.
)

- Commun.Math.Phys. 171 (1995) 383-404
•
e-Print:
- hep-th/9312179
•
DOI:
- 10.1007/BF02099276

The Lagrangian of q Poincare gravity

Leonardo Castellani
(
- INFN, Turin and
- Turin U.
)

- Phys.Lett.B 327 (1994) 22-28
•
e-Print:
- hep-th/9402033
•
DOI:
- 10.1016/0370-2693(94)91522-9

The Quantum structure of space-time at the Planck scale and quantum fields

- Commun.Math.Phys. 172 (1995) 187-220
•
e-Print:
- hep-th/0303037
•
DOI:
- 10.1007/BF02104515

Space-time quantization induced by classical gravity

- Phys.Lett.B 331 (1994) 39-44
•
DOI:
- 10.1016/0370-2693(94)90940-7

Gravity coupled with matter and foundation of noncommutative geometry

Alain Connes
(
- IHES, Bures-sur-Yvette
)

- Commun.Math.Phys. 182 (1996) 155-176
•
e-Print:
- hep-th/9603053
•
DOI:
- 10.1007/BF02506388

Quantum space-time and classical gravity

J. Madore
(
- Orsay, LPT
)
,
J. Mourad
(
- Cergy-Pontoise U.
)

- J.Math.Phys. 39 (1998) 423-442
•
e-Print:
- gr-qc/9607060
•
DOI:
- 10.1063/1.532328

Noncommutative quantum gravity

J.W. Moffat
(
- Toronto U.
)

- Phys.Lett.B 491 (2000) 345-352
•
e-Print:
- hep-th/0007181
•
DOI:
- 10.1016/S0370-2693(00)01064-9

Deforming Einstein's gravity

Ali H. Chamseddine
(
- American U. of Beirut, CAMS and
- American U. of Beirut
)

- Phys.Lett.B 504 (2001) 33-37
•
e-Print:
- hep-th/0009153
•
DOI:
- 10.1016/S0370-2693(01)00272-6

Gauge and Einstein gravity from nonAbelian gauge models on noncommutative spaces

Sergiu I. Vacaru
(
- IAP, Chisinau
)

- Phys.Lett.B 498 (2001) 74-86
•
e-Print:
- hep-th/0009163
•
DOI:
- 10.1016/S0370-2693(00)01369-1

Noncommutative deformation of four-dimensional Einstein gravity

Matteo A. Cardella
(
- Milan U. and
- INFN, Milan
)
,
Daniela Zanon
(
- Milan U. and
- INFN, Milan
)

- Class.Quant.Grav. 20 (2003) L95-L104
•
e-Print:
- hep-th/0212071
•
DOI:
- 10.1088/0264-9381/20/8/101

A Gravity theory on noncommutative spaces

Paolo Aschieri
(
- Piemonte Orientale U., Alessandria and
- INFN, Turin
)
,
Christian Blohmann
(
- Jacobs U., Bremen and
- UC, Berkeley, Math. Dept.
)
,
Marija Dimitrijevic
(
- Munich U. and
- Munich, Max Planck Inst. and
- Belgrade U.
)
,
Frank Meyer
(
- Munich U. and
- Munich, Max Planck Inst.
)
,
Peter Schupp
(
- Jacobs U., Bremen
)

et al.

- Class.Quant.Grav. 22 (2005) 3511-3532
•
e-Print:
- hep-th/0504183
•
DOI:
- 10.1088/0264-9381/22/17/011

Noncommutative geometry and gravity

Paolo Aschieri
(
- Piemonte Orientale U., Alessandria and
- INFN, Turin
)
,
Marija Dimitrijevic
(
- Munich U. and
- Munich, Max Planck Inst. and
- Belgrade U.
)
,
Frank Meyer
(
- Munich U. and
- Munich, Max Planck Inst.
)
,
Julius Wess
(
- Munich U. and
- Munich, Max Planck Inst.
)

- Class.Quant.Grav. 23 (2006) 1883-1912
•
e-Print:
- hep-th/0510059
•
DOI:
- 10.1088/0264-9381/23/6/005

Symmetry, gravity and noncommutativity

Richard J. Szabo
(
- Heriot-Watt U.
)

- Class.Quant.Grav. 23 (2006) R199-R242
•
e-Print:
- hep-th/0606233
•
DOI:
- 10.1088/0264-9381/23/22/R01

- Sov.Math.Dokl. 28 667

- Alg.Anal. 1 114

Multiparameter quantum groups and twisted quasitriangular Hopf algebras

N. Reshetikhin
(
- Harvard U.
)

- Lett.Math.Phys. 20 (1990) 331-335
•
DOI:
- 10.1007/BF00626530

Bicovariant calculus on twisted ISO(N), quantum Poincare group and quantum Minkowski space

Paolo Aschieri
(
- Pisa, Scuola Normale Superiore and
- INFN, Pisa
)
,
Leonardo Castellani
(
- Turin U., Alessandria and
- Turin U. and
- INFN, Turin
)

- Int.J.Mod.Phys.A 11 (1996) 4513-4550
•
e-Print:
- q-alg/9601006
•
DOI:
- 10.1142/S0217751X96002091

R matrix formulation of the quantum inhomogeneous group ISO-q,r(N) and ISp-q,r(N)

Paolo Aschieri
(
- Pisa, Scuola Normale Superiore and
- INFN, Pisa
)
,
Leonardo Castellani
(
- Turin U., Alessandria and
- INFN, Turin
)

- Lett.Math.Phys. 36 (1996) 197-211
•
e-Print:
- hep-th/9411039
•
DOI:
- 10.1007/BF00714382

Quantum orthogonal planes: ISO (q,r) (n+1, n-1) and SO (q,r) (n+1, n-1) bicovariant calculi

Paolo Aschieri
(
- LBL, Berkeley
)
,
Leonardo Castellani
(
- Turin U., Alessandria and
- INFN, Turin
)
,
Antonio Maria Scarfone
(
- Turin U.
)

- Eur.Phys.J.C 7 (1999) 159-175
•
e-Print:
- q-alg/9709032
•
DOI:
- 10.1007/s100529800968

Twist-related geometries on q-Minkowski space

- Proc.Steklov Inst.Math. 226 (1999) 97-111
•
e-Print:
- math/9901019

New Lie-algebraic and quadratic deformations of Minkowski space from twisted Poincare symmetries

Jerzy Lukierski
(
- Wroclaw U.
)
,
Mariusz Woronowicz
(
- Wroclaw U.
)

- Phys.Lett.B 633 (2006) 116-124
•
e-Print:
- hep-th/0508083
•
DOI:
- 10.1016/j.physletb.2005.11.052

Untwisting noncommutative R**d and the equivalence of quantum field theories

Robert Oeckl
(
- Cambridge U., DAMTP
)

- Nucl.Phys.B 581 (2000) 559-574
•
e-Print:
- hep-th/0003018
•
DOI:
- 10.1016/S0550-3213(00)00281-9

Deformed coordinate spaces: Derivatives

Julius Wess
(
- Munich U. and
- Munich, Max Planck Inst.
)

On a Lorentz-invariant interpretation of noncommutative space-time and its implications on noncommutative QFT

M. Chaichian
(
- Helsinki U. and
- Helsinki Inst. of Phys.
)
,
P.P. Kulish
(
- Steklov Math. Inst., St. Petersburg
)
,
K. Nishijima
(
)
,
A. Tureanu
(
- Helsinki U. and
- Helsinki Inst. of Phys.
)

- Phys.Lett.B 604 (2004) 98-102
•
e-Print:
- hep-th/0408069
•
DOI:
- 10.1016/j.physletb.2004.10.045

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