Explicit diagonalization of pair interaction models
Explicit diagonalization of pair interaction models
复制标题
配对交互模型的显式对角化
DOI：
10.1007/s13324-021-00486-4
复制
发表时间：
2021
影响因子：
1.7
通讯作者：
Usami Kyosuke
中科院分区：
文献类型：
--
作者：
Matsuzawa Yasumichi;Sasaki Itaru;Usami Kyosuke
我们提供了一个一般的方法来构造玻色子Bogoliubov变换，对角化一般类的二次哈密顿。这些哈密顿量描述了对相互作用模型。Bogoliubov变换被代数地构造，并且所得到的哈密顿量成为显式单粒子哈密顿量的二次量子化。此外，给出了基态能量的显式表达式。我们的方法系统地对角化量子场论的各种模型，包括耦合到玻色场的谐振子模型和偶极近似中的Pauli-Fierz模型。
We provide a general method for constructing bosonic Bogoliubov transformations that diagonalize a general class of quadratic Hamiltonians. These Hamiltonians describe the pair interaction models. Bogoliubov transformations are constructed algebraically, and the resulting Hamiltonians become the second quantizations of explicit one-particle Hamiltonians. Moreover, an explicit formula for the ground state energies is given. Our method systematically diagonalizes various models of quantum field theory, including a model of a harmonic oscillator coupled to a Bose field and the Pauli-Fierz models in the dipole approximation.