TY - CHAP
T1 - Noncommutative symmetries and gravity
AU - Aschieri, Paolo
PY - 2009
Y1 - 2009
N2 - Spacetime geometry is twisted (deformed) into noncommutative spacetime geometry, where functions and tensors are now star multiplied. Consistently, spacetime diffeomorphisms are twisted into noncommutative diffeomorphisms. Their deformed Lie algebra structure and that of infinitesimal Poincaré transformations is defined and explicitly constructed. We can then define covariant derivatives (that implement the principle of general covariance on noncommutative spacetime) and torsion and curvature tensors. With these geometric tools we formulate a noncommutative theory of gravity.
AB - Spacetime geometry is twisted (deformed) into noncommutative spacetime geometry, where functions and tensors are now star multiplied. Consistently, spacetime diffeomorphisms are twisted into noncommutative diffeomorphisms. Their deformed Lie algebra structure and that of infinitesimal Poincaré transformations is defined and explicitly constructed. We can then define covariant derivatives (that implement the principle of general covariance on noncommutative spacetime) and torsion and curvature tensors. With these geometric tools we formulate a noncommutative theory of gravity.
UR - http://www.scopus.com/inward/record.url?scp=69349100110&partnerID=8YFLogxK
U2 - 10.1007/978-3-540-89793-4_8
DO - 10.1007/978-3-540-89793-4_8
M3 - Chapter
SN - 9783540897927
T3 - Lecture Notes in Physics
SP - 133
EP - 164
BT - Noncommutative Spacetimes
A2 - Aschieri, Paolo
A2 - Dimitrijevic, Marija
A2 - Dimitrijevic, Marija
A2 - Hajicek, Petr
A2 - Lizzi, Fedele
A2 - Wess, Julius
A2 - Wess, Julius
ER -