Quantization of the Laplacian operator on vector bundles, I.

Let ( E, h) be a holomorphic, Hermitian vector bundle over a polarized manifold. We provide a canonical quantization of the Laplacian operator acting on sections of the bundle of Hermitian endomorphisms of E. If E is simple we obtain an approximation of the eigenvalues and eigenspaces of the Laplacian. [ABSTRACT FROM AUTHOR]