On ground states for CCR algebras and Bogoliubov automorphism groups. (English) Zbl 0848.46043
Summary: Let \(A_{\text{CCR}} (L)\) be the CCR algebra over a Hilbert space \(L\), and let \(\{\sigma_t \}_{t\in \mathbb{R}}\) be a Bogoliubov automorphism group of \(A_{\text{CCR}} (L)\) induced by a strongly continuous one-parameter unitary group on \(L\). In this paper, we introduce some continuity for linear functionals on \(A_{\text{CCR}} (L)\) and, under this continuity, we study existence, uniqueness, and non-uniqueness of ground states for \(\{A_{\text{CCR}} (L), \{\sigma_t \}_{t\in \mathbb{R}}\}\).
Keywords:
CCR algebra; Bogoliubov automorphism group; strongly continuous one-parameter unitary group; ground statesReferences:
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