Quantization on abelian varieties

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Abstract

To a n-dimensional principally polarized abelian variety (M, [\Omega]) of period matrix (I, il) is naturally associated a family of irreducible representations of the Weyl Communication Relations. The Riemann theta function appears as the ground state space of a quantum harmonic oscillator hamiltonian. A geometric explanation for the zero point energy is provided.
Original languageEnglish
Pages (from-to)383-392
Number of pages10
JournalRendiconti del Seminario Matematico
Volume44
Publication statusPublished - 1986

Keywords

  • geometric quantizazion, abelian varieties, von Neumann uniqueness theorem, Riemann-Roch theorem

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