抽象的な対相互作用モデルのスペクトル解析

浅原, 啓輔

doi:10.14943/doctoral.k13552

書誌事項

タイトル: 抽象的な対相互作用モデルのスペクトル解析

タイトル別名

Spectral analysis of an abstract pair interaction model

著者: 浅原, 啓輔

学位授与大学: 北海道大学

取得学位: 博士(理学)

学位授与番号: 甲第13552号

学位授与年月日: 2019-03-25

説明

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.