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.

中文翻译：

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对相互作用模型的显式对角化

我们提供了构造对角线化一类二次哈密顿量的Bosonic Bogoliubov变换的通用方法。这些哈密顿主义者描述了配对相互作用模型。Bogoliubov变换是代数构造的，所得的哈密顿量成为显式单粒子哈密顿量的第二个量化。此外，给出了基态能量的明确公式。我们的方法系统地对角化了各种量子场论模型，包括耦合到Bose场的谐波振荡器模型和偶极近似中的Pauli-Fierz模型。