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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 →KAKEN DB |
| Keywords: | Dirac-Maxwell operator | | Dirac operator | | Dirac particle | | Heisenberg operator | | Position operator | | Quantum radiation field | | Velocity operator | | Zitterbewegung |
| Issue Date: | 15-Oct-2011 |
| Publisher: | Elsevier |
| Journal Title: | Journal of Mathematical Analysis and Applications |
| Volume: | 382 |
| Issue: | 2 |
| Start Page: | 714 |
| End Page: | 730 |
| Publisher DOI: | 10.1016/j.jmaa.2011.04.081 |
| Abstract: | We consider a quantum system of a Dirac particle interacting with the quantum radiation field, where the Dirac particle is in a 4 x 4-Hermitian matrix-valued potential V. Under the assumption that the total Hamiltonian HV is essentially self-adjoint (we denote its closure by H￣V), we investigate properties of the Heisenberg operator xj(t):=e^[itH￣V] x_[j]e^[-itH￣V] (j = 1,2,3) of the j-th position operator of the Dirac particle at time t ∊ ℝ and its strong derivative dx_[j](t)/dt (the j-th velocity operator), where x_[j] is the multiplication operator by the j-th coordinate variable x_[j] (the j-th position operator at time t = 0). We prove that D(x_[j]), the domain of the position operator x_[j], is invariant under the action of the unitary operator e^[-itH￣V) for all t ∊ ℝ and establish a mathematically rigorous formula for x_[j](t). Moreover, we derive asymptotic expansions of Heisenberg operators in the coupling constant q ∊ ℝ (the electric charge of the Dirac particle). |
| Type: | article (author version) |
| URI: | http://hdl.handle.net/2115/47270 |
| Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)
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Submitter: 新井 朝雄
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