Non-relativistic Limit of a Dirac Polaron in Relativistic Quantum Electrodynamics |
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Authors: | Asao Arai |
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Affiliation: | (1) Department of Mathematics, Hokkaido University, Sapporo 060-0810, Japan |
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Abstract: | A quantum system of a Dirac particle interacting with the quantum radiation field is considered in the case where no external potentials exist. Then the total momentum of the system is conserved and the total Hamiltonian is unitarily equivalent to the direct integral of a family of self-adjoint operators acting in the Hilbert space, where is the Hilbert space of the quantum radiation field. The fiber operator is called the Hamiltonian of the Dirac polaron with total momentum. The main result of this paper is concerned with the non-relativistic (scaling) limit of. It is proven that the non-relativistic limit of yields a self-adjoint extension of a Hamiltonian of a polaron with spin 1/2 in non-relativistic quantum electrodynamics. |
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Keywords: | 81V10 81Q10 47N50 |
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