Spectrum of semi-relativistic Pauli-Fierz Hamiltonian I
Spectrum of semi-relativistic Pauli-Fierz Hamiltonian I
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半相对论泡利-菲尔兹哈密顿量 I 的谱
DOI：
10.1016/j.jmaa.2015.11.081
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发表时间：
2016
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
研究了量子电动力学中半相对论性Pauli-Fierz哈密顿量H=（p <$1 − A）2+ M2 <$1 + V <$1 + 1 <$Hf，M≥ 0的HVZ型定理.这里H是Hilbert空间L2（Rd）<$F <$$> Rd <$F dx中的自伴算子，A=<$Rd <$A（x）dx是量子化辐射场，Hf是由色散关系ω：Rd → R的二次量子化定义的自由场哈密顿量.强调了无质量的情况，M= 0，包括在内。设E= inf <$σ（H）是H的谱底.假设ω的下确界为m> 0。证明了σ ess（H）=[E+ m，∞）.特别是可以证明H的基态的存在。
A HVZ type theorem for the semi-relativistic Pauli–Fierz Hamiltonian, H=(p⊗ 1− A) 2+ M 2⊗ 1+ V⊗ 1+ 1⊗ H f, M≥ 0, in quantum electrodynamics is studied. Here H is a self-adjoint operator in Hilbert space L 2 (R d)⊗ F≅∫ R d⊕ F d x, A=∫ R d⊕ A (x) d x is a quantized radiation field and H f is the free field Hamiltonian defined by the second quantization of a dispersion relation ω: R d→ R. It is emphasized that massless case, M= 0, is included. Let E= inf σ (H) be the bottom of the spectrum of H. Suppose that the infimum of ω is m> 0. Then it is shown that σ ess (H)=[E+ m,∞). In particular the existence of the ground state of H can be proven.