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Eliminating unphysical photon components from Dirac–Maxwell Hamiltonian quantized in the Lorenz gauge

Kouta Usui
(Hokkaido University)
Math/Phys Seminar
Tuesday, 3 October, 2017, at 14:00-14:45, in Aud. D4 (1531-219)
Note the time 14:00 sharp (or as soon as possible thereafter).

We study the Dirac–Maxwell model quantized in the Lorenz gauge. In  this gauge, the space of quantum mechanical state vectors inevitably adopt  an indefinite metric so that the canonical commutation relation (CCR) is  realized in a Lorentz covariant manner. In order to obtain a physical  subspace, in which no negative norm state exists, the method first proposed  by Gupta and Bleuler is applied with mathematical rigor. It is proved that  a suitably defined physical subspace has a positive semidefinite metric,  and naturally induces a physical Hilbert space with a positive definite  metric. Then, the original Dirac–Maxwell Hamiltonian defines an induced  Hamiltonian on the physical Hilbert space which is essentially  self-adjoint.

Contact person: Jacob Schach Møller