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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:  DiracMaxwell operator  Dirac operator  Dirac particle  Heisenberg operator  position operator  quantum radiation filed  velocity operator  Zitterbewegung 
Issue Date:  13Apr2010 
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 £ 4Hermitian matrixvalued potential V . Under the assumption that the total Hamiltonian HV is essentially selfadjoint (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 jth position operator of the Dirac particle at time t 2 R and its strong derivative dxj(t)/dt (the jth velocity operator), where xj is the multiplication operator by the jth coordinate variable xj (the jth 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

Submitter: 数学紀要登録作業用
