Abstract
We present a new theorem concerning a sufficient condition for a symmetric operator acting in a complex Hilbert space to be essentially self-adjoint. By applying the theorem, we prove that the Dirac–Maxwell Hamiltonian, which describes a quantum system of a Dirac particle and a radiation field minimally interacting with each other, is essentially self-adjoint. Our theorem covers the case where the Dirac particle is in the Coulomb-type potential.
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Futakuchi, S., Usui, K. New Criteria for Self-Adjointness and its Application to Dirac–Maxwell Hamiltonian. Lett Math Phys 104, 1107–1119 (2014). https://doi.org/10.1007/s11005-014-0708-z
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DOI: https://doi.org/10.1007/s11005-014-0708-z