Spectrum of the d-bar Neumann Laplacian on the Fock space

Abstract

The spectrum of the d-bar-Neumann Laplacian on the Fock space $L^2(\mathbb{C}^n, e^{-|z|^2})$ is explicitly computed. It turns out that it consists of positive integer eigenvalues each of which is of infinite multiplicity. Spectral analysis of the d-bar-Neumann Laplacian on the Fock space is closely related to Schr\"odinger operators with magnetic field and to the complex Witten-Laplacian.