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.

Quantization on abelian varieties

SPERA, Mauro
1986

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.
geometric quantizazion; abelian varieties; von Neumann uniqueness theorem; Riemann-Roch theorem
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11562/393118
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