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Yoshitsugu Sekine

Publications and source records attributed to Yoshitsugu Sekine.

13 recordsLinked to original sources
arXiv2026

The Buchholz Algebra from the Universal Resolvent Algebra--Particle Structure, Gibbs States, and Closed-Path Expansions without Fock Representations

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 isometric particle-degree coordinates. Its finite matrix corners carry canonical traces, KMS states, and trace-norm product formulas, together with closed-path expansions that lay the groundwork for path-integral representations. The known Fock-space description and a proper quasilocal subalgebra arise as realizations.

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arXiv2026

Interacting Lattice Bosons on the Concrete Buchholz Algebra -- All-Temperature Equilibrium States from Functional-Integral Local-Number Bounds

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 functional integral gives volume-uniform exponential local-number bounds at all temperatures. These bounds remove the local-moment hypothesis and yield finite-volume approximation and KMS accumulation states in arXiv:2505.13170.

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arXiv2026

Constructive Quantum Field Theory and Rigorous Statistical Mechanics via Operator Algebras and Probability Theory -- Guiding Principles and Research Perspectives

We present a hierarchical viewpoint on the operator-algebraic formulation of quantum systems, in which $C^{*}$-algebras are responsible for the universal and intrinsic description, whereas von Neumann algebras provide the detailed account obtained after fixing a state compatible with the dynamics. From this standpoint, for bosonic many-body systems the resolvent algebra, rather than the Weyl algebra, is the natural object; in particular, its nuclearity, trivial center, and rich ideal structure faithfully reflect purely quantum-mechanical structures. Macroscopic variables or sector structures associated with phase transitions are captured as the center appearing in the weak closure of the GNS representation. Moreover, the equivalence between representations of operator algebras and functional integrals allows powerful probabilistic methods to be employed. Taking these as guiding principles, we outline research perspectives on concrete objects in constructive quantum field theory and rigorous statistical mechanics.

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arXiv2026

Notes on the Optical-Lattice Hard-Core Bose Gas of Aizenman--Lieb--Seiringer--Solovej--Yngvason

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 and their principal inputs in a common notation, and describe the central and orbitwise decompositions of thermodynamic-limit equilibrium states. The purpose is to make compressed or delegated steps explicit, not to introduce a new method, strengthen the estimates, or otherwise improve the cited results.

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arXiv2026

An Operator-Algebraic Exposition of the Thirring-Wehrl Theory of the Quasi-Spin BCS Model

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--Werner, and Bru--de Siqueira Pedra, in the language of quasi-local $C^{\ast}$-algebras and state decompositions. The quasi-spin model is realized on the UHF algebra of type $2^{\infty}$, with product sectors described by von Neumann's incomplete infinite tensor products. This framework distinguishes strong limits of intensive observables, domain-restricted limits of extensive observables, and sectorwise Bogoliubov--Haag limits, including their operator criterion, gap equation, and limiting dynamics. In the degenerate model, the ground-state and thermal gauge averages admit central direct-integral decompositions over the gauge circle, and the thermal decomposition converges to the ground-state decomposition at zero temperature. Adjoining the gauge phase as a central classical variable combines the phase-dependent Bogoliubov dynamics into one automorphism group on $C(\mathbb{S}^{1},\mathcal{A})$.

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arXiv2026

Mean-Field Bose--Einstein Condensation and Condensate Ideals in the Resolvent Algebra

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 regime the selected chemical potential cancels the mean-field shift, so the selected one-particle Hamiltonian is exactly the free one. The resulting zero-mode covariance defines a mean-field BEC ideal in the resolvent algebra, while the nonregular quotient and the direct-integral center record distinct representation-theoretic data. Occupation-number and Brownian-loop formulations recover the same density selection, excess density, ODLRO data, local tests, and the separation between finite-density BEC and Buchholz's stricter infinite-occupation proper-condensate criterion.

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arXiv2026

No-Go Theorem for BEC in the Nelson and Pauli--Fierz Models

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 models after removal of the infrared and ultraviolet cutoffs. If the physical test-function space can distinguish the zero mode, the absence of off-diagonal long-range order, the vanishing of the zero-mode form, the vanishing of the condensate density, the order-parameter criterion, and the triviality of the BEC directions and the BEC ideal are equivalent. We also describe the infrared quotient and the BEC ideal in the resolvent algebra uniformly for the three models, and formulate an operator-algebraic sufficient condition for separately given spatially translation-invariant KMS states.

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arXiv2026

No-Go Theorem for Quasiparticle BEC in the Spin-Boson Model

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 resolvent algebra. Because a sesquilinear form arising from the zero mode appears, analogous to the case of the free Bose gas, a BEC-type component is also formally present in the spin-boson model. However, according to arxiv:1207.4621, quasiparticles do not undergo BEC, so we have to exclude this possibility. A no-go theorem for BEC is obtained, but we find that the spin-boson model is not a model that follows the criterion in arxiv:1207.4621.

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arXiv2026

A Note on the Resolvent Algebra and Functional Integral Approach to the van Hove Model

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 perspective via the Weyl algebra and the resolvent algebra and the functional integral approach, the removal of infrared and ultraviolet cutoffs and the existence of the ground state and $β$-KMS states in the case of a point source. In the infinite-volume system at finite temperature, Bose--Einstein condensation can arise.

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arXiv2026

No-Go Theorem for Quasiparticle BEC

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 $β$-KMS states of the van Hove model satisfy the self-consistency condition of arXiv:1207.4621. However, the self-consistency condition is a constraint concerning the definition of the field, and is insufficient to establish the no-go theorem for BEC. In this paper, we prove the no-go theorem for BEC via two routes. First, imposing time cluster properties on the $β$-KMS states precludes BEC. Second, under nonlinear dispersion with $s > 2$, the treatment of infrared divergences automatically reduces the algebra of physical observables, and BEC is mathematically excluded on the reduced algebra. In particular, the latter property admits an interpretation in terms of the ideal theory of the resolvent algebra.

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arXiv2026

A Note on the Resolvent Algebra and Functional Integral Approach to the Free Bose Einstein Condensation

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-algebraic formulation based on the resolvent algebra and the functional integral representation. By clarifying the representation-theoretic structure of finite-temperature BEC states and rigorously analyzing the correspondence between their direct integral decomposition and the ergodic decomposition of the associated probability measures, we provide a framework in which general features of phase transitions-such as the emergence of order parameters, the decomposition of states, and clustering properties-are explicitly described using BEC in the free Bose gas as a concrete example. Furthermore, we construct in detail the correspondence between the decomposition of measures in the functional integral approach and that of operator-algebraic representations, thereby establishing the equivalence between the probabilistic and algebraic aspects, and providing a guiding principle for isolating the essential structures by disentangling the additional mathematical complications arising from the treatment of infrared singularities in interacting systems. These results lay a foundation for the rigorous analysis of phase transitions in non-relativistic constructive quantum field theory and quantum statistical mechanics, and serve as a starting point for extensions to interacting models.

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arXiv2011

Magnetism and infrared divergence in a Hubbard-phonon interacting system

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 transformation introduced by Arai and Hirokawa. We construct a concrete infrared singular representation using the operator algebraic method. The method is essentially same as one for the van Hove model using the Wightman functional method.

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