On some groups of automorphisms of von Neumann algebras with cyclic and separating vector
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Citations
Around Property (T) for Quantum Groups
Fully Coupled Pauli-Fierz Systems at Zero and Positive Temperature
Nonabelian special K-flows
On generalizations of the kms-boundary condition
Relatively independent joinings and subsystems of W*-dynamical systems
References
On the equilibrium states in quantum statistical mechanics
Statistical mechanics of quantum spin systems. III
Invariant states and asymptotic abelianness
Asymptotically abelian systems
Related Papers (4)
Frequently Asked Questions (10)
Q2. what is the eigenvalue of the "Momentum" p?
In particular, for each discrete eigenvalue of the "momentum" p the authors construct two unitary operators p ζ 21 and p ζ 2Γ such thatIt is shown that for each such p, the vector ψP = pΩ also describes the state of thermal equilibrium, with the same temperature as Ω.
Q3. What is the definition of the group G?
Let G -> 23^ be a unitary representation of the group G on a Hubert space Jf. Let Q be the group of all (bounded) characters of the group G. With χ in ύ the authors say that χ is in a point spectrum of 23# if there is 0 =f= ψ ζ 3tf such thatVgψ = χ(g)ψ for all g £G . (*) 10 Commun.math.
Q4. What is the goal of this paper?
The goal of their paper is to study a general situation, when there is given a von Neumann algebra 21, the group Λ-^VgΛV^1 of automorphisms of 21 and the vector Ω invariant under all Vg and cyclic for 21 and 2Γ.
Q5. What is the simplest way to prove the KMS-Algebra?
At = VtA V-1 is in 2ί0 for each A ζ 2ί0 and t ζ R, b) lim \\\\At -A\\\\=0 for each A ζ 2ί0,c) VtΩ = Ω for all t ζR; 5. the involution J such that JAΩ = TA*Ωioτ each A ζ 21 = (2ίo)//, where T = exp(~ jS£Γ/2) and Vt = exp(iHt), 6. The 3-parameter, strongly continuous group of unitary operators {Ux} such thata)
Q6. What is the proof of the KMS?
It is easy to see that the existence of a conjugation Jsatisfying 5. is a necessary and sufficient condition for the state ω : A-^ (Ω, AΩ) to satisfy the KMS boundary conditions (see [2]).
Q7. What is the point spectrum of 93$?
Then the point spectrum of 93$ is a group and for each χ ζσ{^ΰG) there exists a unitary operator χ in 21' such thatχ') for each χ '
Q8. What is the state of thermal equilibrium of an infinite system?
It has been shown in [1] that the state of thermal equilibrium of an infinite system is mathematically described by the state ω (over the 0*- algebra of observables 21̂ ) satisfying the KMS boundary conditions.
Q9. What is the point spectrum of 93#?
if 93# is abelian, n-parameter and strongly continuous then JF(Δ)J = F{-Δ) for each Borel set Δ C Rn.The authors drope an easy proof of this theorem.
Q10. what is the spectrum of vf and 7?
Thena) the spectrum of {Vf} and {̂ 7̂ } is additive (see 3.4); b) the point spectrum of {t^} is a group and for each p in a(Ux)there exist two unitary operators: φ ζ 21 and p ξ 2Γ such that (see 3.5)Uxp = e^ xp Ux ,pE(q)p* = E(p + q) if also qζσ(Ua)9where p denotes either p or p c) for each p ζ σ (Ux) the authors have E (p) < FQ.