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The Buchholz Algebra from the Universal Resolvent Algebra--Particle Structure, Gibbs States, and Closed-Path Expansions without Fock Representations
Yoshitsugu Sekine
We construct the Buchholz algebra without a Fock representation, as the bounded inverse limit of intrinsic particle-cutoff quotients of the gauge-fixed resolvent algebra, with isom…
Interacting Lattice Bosons on the Concrete Buchholz Algebra -- All-Temperature Equilibrium States from Functional-Integral Local-Number Bounds
Yoshitsugu Sekine
Interacting Bose--Hubbard dynamics is formulated on the concrete Buchholz algebra in Fock space. Under repulsive finite-range interactions and a low-activity gap, a discrete functi…
Notes on the Optical-Lattice Hard-Core Bose Gas of Aizenman--Lieb--Seiringer--Solovej--Yngvason
Yoshitsugu Sekine
These are detailed expository notes on the staggered optical-lattice hard-core Bose gas of Aizenman, Lieb, Seiringer, Solovej and Yngvason. They restate and expand the arguments an…
An Operator-Algebraic Exposition of the Thirring-Wehrl Theory of the Quasi-Spin BCS Model
Yoshitsugu Sekine
This expository review reformulates the BCS analyses of Haag, Emch--Guenin, and Thirring--Wehrl, together with subsequent operator-algebraic mean-field results of Bóna, Raggio--Wer…
Mean-Field Bose--Einstein Condensation and Condensate Ideals in the Resolvent Algebra
Yoshitsugu Sekine
This paper studies the imperfect Bose gas after the Kac density law and the mean-field Euler equations have selected a condensed density with positive zero-mode excess. In this BEC…
No-Go Theorem for BEC in the Nelson and Pauli--Fierz Models
Yoshitsugu Sekine
We construct KMS states for the Nelson model, the spinless Pauli--Fierz model, and the Pauli--Fierz model with spin by functional integral representations, and study point-source m…
A Note on the Resolvent Algebra and Functional Integral Approach to the van Hove Model
Yoshitsugu Sekine
This paper is a collection of the author's computational notes on the van Hove model and contains no essentially new results. We discuss, from both the operator-algebraic perspecti…
No-Go Theorem for Quasiparticle BEC
Yoshitsugu Sekine
We discuss a no-go theorem for Bose-Einstein condensation (BEC) of quasiparticles (phonons) from the viewpoint of operator algebras, using the van Hove model. The -KMS states of…
A Note on the Resolvent Algebra and Functional Integral Approach to the Free Bose Einstein Condensation
Yoshitsugu Sekine
We present a systematic description of the structure of Bose-Einstein condensation (BEC) in the free Bose gas from the viewpoint of the correspondence between the operator-algebrai…
No-Go Theorem for Quasiparticle BEC in the Spin-Boson Model
Yoshitsugu Sekine
We analyze the possibility of Bose-Einstein condensation (BEC) at finite temperature in the spin-boson model within the frameworks of functional integral representations and the re…
Constructive Quantum Field Theory and Rigorous Statistical Mechanics via Operator Algebras and Probability Theory -- Guiding Principles and Research Perspectives
Yoshitsugu Sekine
We present a hierarchical viewpoint on the operator-algebraic formulation of quantum systems, in which -algebras are responsible for the universal and intrinsic description,…
Phonon Bose-Einstein condensation in a Hubbard-phonon interacting system with infrared divergence
Yoshitsugu Sekine
We show that a finite Hubbard-phonon interacting system exhibits phonon BEC at sufficiently low temperature. We also have the gauge symmetry breaking for phonons. The key tools are…
Magnetism and infrared divergence in a Hubbard-phonon interacting system
Yoshitsugu Sekine
We show that a finite Hubbard-phonon interacting system has ferromagnetic or unique spin-singlet ground state under the infrared singular condition. The key tool is a unitary trans…