Quantization of the Laplacian operator on vector bundles I

14 May 2015 · Keller Julien, Meyer Julien, Seyyedali Reza ·

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.