Spectrum of the -Neumann Laplacian on the Fock space

The spectrum of the ∂ ¯ -Neumann Laplacian on the Fock space L 2 ( 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 ∂ ¯ -Neumann Laplacian on the Fock space is closely related to Schrödinger operators with magnetic fields and to the complex Witten Laplacian.