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MiS Preprint
12/1997

Harmonic symplectic spinors on Riemann surfaces

Katharina Habermann

Abstract

Symplectic spinor fields were introduced 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 symplectic spinor fields and started a systematical investigation. In this paper, we motivate the notion of harmonic symplectic spinor fields. We describe how many linearly independent harmonic symplectic spinors each Riemann surface admits. Furthermore, we calculate the spectrum of the symplectic spinor Laplacian on the complex projective space of complex dimension 1.

Received:
Apr 28, 1997
Published:
Apr 28, 1997

Related publications

inJournal
1997 Repository Open Access
Katharina Habermann

Harmonic symplectic spinors on Riemann surfaces

In: Manuscripta mathematica, 94 (1997) 4, pp. 465-484