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arXiv · 1910.13487

Explicit Diagonalization of Pair Interaction Models

Yasumichi Matsuzawa·Itaru Sasaki·Kyosuke Usami
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Abstract

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.

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Yasumichi Matsuzawa, Itaru Sasaki, Kyosuke Usami. 2020-11-04. Explicit Diagonalization of Pair Interaction Models. https://doi.org/10.1007/s13324-021-00486-4

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