A special class of infinite dimensional Dirac operators on the abstract boson-fermion Fock space
A special class of infinite dimensional Dirac operators on the abstract boson-fermion Fock space
复制标题
抽象玻色子-费米子福克空间上一类特殊的无限维狄拉克算子
DOI：
10.1155/2014/713690
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发表时间：
2014
影响因子：
1.4
通讯作者：
Asao Arai
中科院分区：
文献类型：
--
作者：
Ｒｉｋｉｏ Ｙｏｎｅｄａ;Teturo Kamae and Li Peng;Asao Arai
研究了一类特殊的无穷维Dirac算子Q（α）在与复Hilbert空间对（λ，λ）相关联的抽象玻色费米子Fock空间λ（λ，λ）上的谱性质，其中λ是一个扰动参数（物理学中的耦合常数），未扰动算子Q（0）被取为自由的无穷维Dirac算子.给出了Q（α）核的各种形式。它被证明，有情况下，对于所有足够大的|α|当α< 0时，即使Q（0）没有非零特征值，Q（α）也有无穷多个非零特征值。同时讨论了Q（α）的Fredholm性质，并将其限制在一个子空间上.𝒦
Spectral properties of a special class of infinite dimensional Dirac operatorsQ(α) on the abstract boson‐fermion Fock spaceℱ(ℋ,𝒦) associated with the pair (ℋ,𝒦) of complex Hilbert spaces are investigated, whereis a perturbation parameter (a coupling constant in the context of physics) and the unperturbed operatorQ(0) is taken to be a free infinite dimensional Dirac operator. A variety of the kernel ofQ(α) is shown. It is proved that there are cases where, for all sufficiently large |α| withα< 0,Q(α) has infinitely many nonzero eigenvalues even ifQ(0) has no nonzero eigenvalues. Also Fredholm property ofQ(α) restricted to a subspace ofℱ(ℋ,𝒦) is discussed.