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.
Spera, M., Quantization on abelian varieties, <<RENDICONTI DEL SEMINARIO MATEMATICO>>, 1986; 44 (3): 383-392 [http://hdl.handle.net/10807/35986]
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.
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