The characteristic classes of Morita equivalent star products on symplectic manifolds

Details The characteristic classes of Morita equivalent star products on symplectic manifolds The characteristic classes of Morita equivalent star products on symplectic manifolds

2001-06-20

arxiv.org/abs/math/0106178v2

Mathematics

Quantum Algebra

22 pages. A few corrections made to Sections 3.2 and 3.3

Scientific paper

10.1007/s002200200657

In this paper we give a complete characterization of Morita equivalent star products on symplectic manifolds in terms of their characteristic classes: two star products $\star$ and $\star'$ on $(M,\omega)$ are Morita equivalent if and only if there exists a symplectomorphism $\psi:M\longrightarrow M$ such that the relative class $t(\star,\psi^*(\star'))$ is $2 \pi \im$-integral. For star products on cotangent bundles, we show that this integrality condition is related to Dirac's quantization condition for magnetic charges.

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