• Citer

Deformation quantization of Hermitian vector bundles

par Bursztyn, Henrique ;Waldmann, Stefan
Référence letters in mathematical physics, 53, 4, page (349-365)
Publication Publié, 2000-09

Article révisé par les pairs

• Détails
• Contenu

Résumé :

Motivated by deformation quantization, we consider in this paper *-algebras A over rings C = R(i), where R is an ordered ring and i2 = -1, and study the deformation theory of projective modules over these algebras carrying the additional structure of a (positive) A-valued inner product. For A = C∞(M), M a manifold, these modules can be identified with Hermitian vector bundles E over M. We show that for a fixed Hermitian star product on M, these modules can always be deformed in a unique way, up to (isometric) equivalence. We observe that there is a natural bijection between the sets of equivalence classes of local Hermitian deformations of C∞(M) and Γ∞(End(E)) and that the corresponding deformed algebras are formally Morita equivalent, an algebraic generalization of strong Morita equivalence of C*-algebras. We also discuss the semi-classical geometry arising from these deformations.