Preprint 12/1997

Harmonic symplectic spinors on Riemann surfaces

Katharina Habermann

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Submission date: 28. Apr. 1997
Pages: 20
published in: Manuscripta mathematica, 94 (1997) 4, p. 465-484 

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.

24.11.2021, 02:10