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Heisenberg Operators of a Dirac Particle Interacting with the Quantum Radiation Field

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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
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

Submitter: 数学紀要登録作業用

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