6533b838fe1ef96bd12a484e

RESEARCH PRODUCT

Quantum moment maps and invariants for G-invariant star products

Kentaro Hamachi

subject

Pure mathematicsStatistical and Nonlinear Physics37Kxx22E7Mathematics - Quantum AlgebraFOS: MathematicsQuantum Algebra (math.QA)16S3022E46Invariant (mathematics)16S8916S89; 16S30; 37Kxx; 22E46; 22E7Moment mapQuantumMathematical PhysicsSymplectic manifoldMathematics

description

We study a quantum moment map and propose an invariant for $G$-invariant star products on a $G$-transitive symplectic manifold. We start by describing a new method to construct a quantum moment map for $G$-invariant star products of Fedosov type. We use it to obtain an invariant that is invariant under $G$-equivalence. In the last section we give two simple examples of such invariants, which involve non-classical terms and provide new insights into the classification of $G$-invariant star products.

yearjournalcountryeditionlanguage
2002-03-20
10.1142/s0129055x02001314http://arxiv.org/abs/math/0203209