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Heisenberg Operators of a Dirac Particle Interacting with the Quantum Radiation Field
| Title: | Heisenberg Operators of a Dirac Particle Interacting with the Quantum Radiation Field |
| Authors: | Arai, Asao Browse this author |
| Keywords: | Dirac-Maxwell operator | | Dirac operator | | Dirac particle | | Heisenberg operator | | position operator | | quantum radiation filed | | velocity operator | | Zitterbewegung |
| Issue Date: | 13-Apr-2010 |
| Publisher: | Department of Mathematics, Hokkaido University |
| Journal Title: | Hokkaido University Preprint Series in Mathematics |
| Volume: | 957 |
| Start Page: | 1 |
| End Page: | 23 |
| Abstract: | We consider a quantum system of a Dirac particle interacting with the quantum radiation field, where the Dirac particle is in a 4 £ 4-Hermitian matrix-valued potential V . Under the assumption that the total Hamiltonian HV is essentially self-adjoint (we denote its closure by ¯HV ), we investigate properties of the Heisenberg operator xj(t) := eit ¯HV xje−it ¯HV (j = 1, 2, 3) of the j-th position operator of the Dirac particle at time t 2 R and its strong derivative dxj(t)/dt (the j-th velocity operator), where xj is the multiplication operator by the j-th coordinate variable xj (the j-th position operator at time t = 0). We prove that D(xj ), the domain of the position operator xj , is invariant under the action of the unitary operator e−it ¯HV for all t 2 R and establish a mathematically rigorous formula for xj(t). Moreover, we derive asymptotic expansions of Heisenberg operators in the coupling constant q 2 R (the electric charge of the Dirac particle). |
| Type: | bulletin (article) |
| URI: | http://hdl.handle.net/2115/69764 |
| Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics
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Submitter: 数学紀要登録作業用
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