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Scattering theory of classical and quantum N-particle systems
0. Introduction.- 1. Classical Time-Decaying Forces.- 2. Classical 2-Body Hamiltonians.- 3. Quantum Time-Decaying Hamiltonians.- 4. Quantum 2-Body Hamiltonians.- 5. Classical N-Body Hamiltonians.- 6.…
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Asymptotic Completeness in Quantum Field Theory. A Class of Galilei-Covariant Models
0. Introduction 192 1. General Definitions 195 1.1. Hilbert spaces 195 1.2. Homomorphisms of commutative C∗and W ∗-algebras 196 1.3. Permutations 197 1.4. Clusters 197 1.5. Cartesian and tensor…
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Scattering Theory of Infrared Divergent Pauli-Fierz Hamiltonians
Abstract. We consider in this paper the scattering theory of infrared divergent massless Pauli-Fierz Hamiltonians. We show that the CCR representations obtained from the asymptotic field contain…
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Return to Equilibrium for Pauli-Fierz Systems
Abstract. We study ergodic properties of Pauli-Fierz systems – W*-dynamical systems often used to describe the interaction of a small quantum system with a bosonic free field at temperature $ T \geq…
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Perturbation Theory of W*-Dynamics, Liouvilleans and KMS-States
Given a W*-algebra ${\mathfrak M}$ with a W*-dynamics τ, we prove the existence of the perturbed W*-dynamics for a large class of unbounded perturbations. We compute its Liouvillean. If τ has a β-KMS…
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Spectral Theory of Pauli–Fierz Operators
Abstract We study spectral properties of Pauli–Fierz operators which are commonly used to describe the interaction of a small quantum system with a bosonic free field. We give precise estimates of…
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Homogeneous Schrödinger Operators on Half-Line
The differential expression $${L_m=-\partial_x^2+(m^2-1/4)x^{-2}}$$ defines a self-adjoint operator Hm on L2(0, ∞) in a natural way when m2 ≥ 1. We study the dependence of Hm on the parameter m show…
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Mathematics of Quantization and Quantum Fields
Preface 1. Vector spaces 2. Operators in Hilbert spaces 3. Tensor algebras 4. Analysis in L2(Rd) 5. Measures 6. Algebras 7. Anti-symmetric calculus 8. Canonical commutation relations 9. CCR on Fock…
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ASYMPTOTIC COMPLETENESS IN QUANTUM IN FIELD THEORY: MASSIVE PAULI–FIERZ HAMILTONIANS
Spectral and scattering theory of massive Pauli–Fierz Hamiltonians is studied. Asymptotic completeness of these Hamiltonians is shown. The proof consists of three parts. The first is a construction…
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Spectral and Scattering Theory¶of Spatially Cut-Off P(ϕ)2 Hamiltonians
Abstract:We study spatially cut-off P(ϕ)2 Hamiltonians. We show the local finiteness of the pure point spectrum outside of thresholds, the limiting absorption principle and asymptotic completeness of…
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