Second quantization for the Kepler problem

John Baez (UC Riverside)

Tuesday 22nd September 16:00-17:00
Maths 311B

Abstract

The Kepler problem concerns a point particle in an attractive inverse square force. After a brief review of the classical and quantum versions of this problem, focused on their hidden symmetries, we turn to the quantum Kepler problem for a spin-1/2 particle. We show that the Hilbert space H of bound states for this problem is unitarily equivalent to the Hilbert space of solutions of a massless chiral spin-1/2 particle on the spacetime R x S^3. The fermionic Fock space on H is thus equivalent to the Hilbert space of a massless chiral spin-1/2 free quantum field on R x S^3. By modifying the Hamiltonian on this Fock space, we obtain one that gives the well-known "Madelung rules", which describe the rough overall structure of the periodic table.

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