Self-adjointness of semi-relativistic Pauli-Fierz models
Self-adjointness of semi-relativistic Pauli-Fierz models
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半相对论泡利-菲尔兹模型的自伴性
DOI：
10.1142/s0129055x15500154
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发表时间：
2015
期刊：
影响因子：
--
通讯作者：
T. Hidaka and F. Hiroshima
中科院分区：
文献类型：
--
作者：
F. Hiroshima;T. Ichinose and J. Lorinczi;F.Hiroshima and S.Osawa;T. Hidaka and F. Hiroshima;F. Hiroshima and I.Sasaki;T. Hidaka and F. Hiroshima
考虑量子电动力学中无自旋半相对论Pauli-Fierz哈密顿量H = \sqrt{（p \otimes 1\kern-4pt 1- A）^2 + M^2} + V \otimes 1\kern-4pt 1\otimes {\rmH_f}，$$.其中p表示动量算符，A表示量子化辐射场，M ≥ 0，Hf表示玻色-福克空间的自由哈密顿量，V表示外部势。证明了H的自伴性和本质自伴性。需要强调的是，它包括M = 0的情况。进一步证明了具有固定总动量P ∈ φ d的半相对论Pauli-Fierz模型：$$H（P）= \sqrt{（P - {\rmP_f} - A（0））^2 + M^2} + {\rmH_f}，\quad M \geq 0，$$对任意P的自伴性和本质自伴性.
The spinless semi-relativistic Pauli–Fierz Hamiltonian $$H = \sqrt{(p \otimes 1\kern-4pt1 - A)^2 + M^2} + V \otimes 1\kern-4pt1 + 1\kern-4pt1 \otimes {\rm H_f},$$ in quantum electrodynamics is considered. Here p denotes a momentum operator, A a quantized radiation field, M ≥ 0, Hfthe free Hamiltonian of a Boson Fock space and V an external potential. The self-adjointness and essential self-adjointness of H are shown. It is emphasized that it includes the case of M = 0. Furthermore, the self-adjointness and the essential self-adjointness of the semi-relativistic Pauli–Fierz model with a fixed total momentum P ∈ ℝd: $$H(P) = \sqrt{(P - {\rm P_f} - A(0))^2 + M^2} + {\rm H_f}, \quad M \geq 0,$$is also proven for arbitrary P.