Noncommutative hamiltonian formalism for noncommutative gravity

Abstract

We present a covariant canonical formalism for noncommutative gravity, and in general for noncommutative geometric theories defined via a twisted $\star$-wedge product between forms. Noether theorems are generalized to the noncommutative setting, and gauge generators are constructed in a twisted phase space with $\star$-deformed Poisson bracket. This formalism is applied to noncommutative $d=4$ vierbein gravity, and allows to find the canonical generators of the tangent space $\star$-gauge group.

20 pages, version to be published in Class. and Quantum Gravity. v3: title slightly changed, minor improvements, paragraph added in Conclusions. v2: improved discussion in Sect.3, completed the list of momenta variations in Sect. 5.2. In memoriam of Alessandro D'Adda

References in corpus (3)

• Noncommutative D=4 gravity coupled to fermions
• Noncommutative supergravity in D=3 and D=4
• Covariant hamiltonian for supergravity in $d=3$ and $d=4$