HARMONIC SYMPLECTIC SPINORS ON RIEMANN SURFACES

Symplectic spinor fields were considered already in the 70th in order to give the construction of half-densities in the context of geometric quantization. We introduced symplectic Dirac operators acting on symp lectic spinor fields and started a systematical investigation. In this paper, we motivate the notion of harmonic symplectic spinor fields. W e describe how many linearly independent harmonic symplectic spinors e ach Riemann surface admits. Furthermore, we calculate the spectrum of the symplectic spinor Laplacian on the complex projective space of com plex dimension 1.