Spectral analysis of an abstract pair interaction model

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Bibliographic Information

Title
Spectral analysis of an abstract pair interaction model
Other Title
  • 抽象的な対相互作用モデルのスペクトル解析
Author
浅原, 啓輔
University
Hokkaido University
Types of degree
博士(理学)
Grant ID
甲第13552号
Degree year
2019-03-25

Description

We consider an abstract pair-interaction model in quantum field theory with a coupling constant λ ∈ R and analyze the Hamiltonian H(λ) of the model. In the massive case, there exist constants λc < 0 and λc,0 < λc such that, for each λ ∈ (λc,0,λc) ∪ (λc,∞), H(λ) is diagonalized by a proper Bogoliubov transformation, so that the spectrum of H(λ) is explicitly identified, where the spectrum of H(λ) for λ > λc is different from that for λ ∈ (λc,0,λc). As for the case λ < λc,0, we show that H(λ) is unbounded from above and below. In the massless case, λc coincides with λc,0.

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