2025/06/05 by Jorge R. Bolaños-Servín, Bolaños-Servín, Jorge R., Roberto Quezada +3
Mathematics · Physics and Astronomy · #60B15 #Advanced Operator Algebra Research #FOS: Physical sciences #Mathematical Physics (math-ph) #Noncommutative and Quantum Gravity Theories #Primary 81S05 #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #Secondary 78M05
paper · pdf · doi:10.48550/arxiv.2506.04537
openalex publication_date 2025/06/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
We develop an analytical approach to quantum Gaussian states in infinite-mode representation of the Canonical Commutation Relations (CCR's), using Yosida approximations to define integrability of possibly unbounded observables with respect to a state ρ (ρ-integrability). It turns out that all elements of the commutative *-algebra generated by a possibly unbounded ρ-integrable observable A, denoted by ⟨ A⟩, are normal and ρ -integrable. Besides, ⟨ A⟩ can be endowed with the well-defined norm ‖⋅‖ρ:= \rm tr (ρ|⋅| ). Our approach allows us to rigorously establish fundamental properties and derive key formulae for the mean value vector and the covariance operator. We additionally show that the covariance operator S of any Gaussian state is real, bounded, positive, and invertible, with the property that S-iJ≥ 0, being J the multiplication operator by -i on ℓ2(\mathbb N).