Spectral Theory of Automorphism Groups and Particle Structures in Quantum Field Theory

Dybalski, Wojciech

doi:10.48550/arxiv.0901.3127

Cited by 3 publications

(4 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…An important consequence is the non-vanishing of the limits defining the scattering states and it is the essential ingredient to establish the extension of wave operators to the full asymptotic Fock spaces (cf. [Dy09] App. A).…”

Section: Convergence Of Scattering State Approximantsmentioning

confidence: 99%

See 1 more Smart Citation

Strengthened Reeh–Schlieder Property and Scattering in Quantum Field Theories Without Mass Gaps

Duell

2017

Commun. Math. Phys.

View full text Add to dashboard Cite

We develop Haag-Ruelle scattering theory for Wigner particles in local relativistic Quantum Field Theory without assuming mass gaps or any other restrictions on the spectrum of the mass operator near the particle masses. Our approach is based on the Reeh-Schlieder property of the vacuum state. It is shown that a strengthened variant of this property, concerning the relative approximation error for single-particle states, implies the existence of scattering states.

show abstract

Section: Convergence Of Scattering State Approximantsmentioning

confidence: 99%

“…Under the above assumptions, (HK1) -(HK4), (HK5'), and (HK6'), our results from Sections 7 and 8 below allow to construct wave-operators and the S-matrix in the usual manner (see e.g. [Dy09] App. A).…”

Section: Introductionmentioning

confidence: 99%

Strengthened Reeh–Schlieder Property and Scattering in Quantum Field Theories Without Mass Gaps

Duell

2017

Commun. Math. Phys.

View full text Add to dashboard Cite

show abstract

“…Important motivation for the present study comes from the refined spectral theory of translation automorphisms [15]. The aim of this theory is to decompose the algebra of observables A into subspaces which differ in their behavior under translation automorphisms R s+1 ∋ x → α x .…”

Section: Introductionmentioning

confidence: 99%

“…The results presented in this paper were included in the PhD thesis of the author [15] completed at the University of Göttingen.…”

Section: Introductionmentioning

confidence: 99%

Coincidence arrangements of local observables and uniqueness of the vacuum in QFT

Dybalski¹

2009

J. Phys. A: Math. Theor.

Self Cite

View full text Add to dashboard Cite

A new phase space criterion, encoding the physically motivated behavior of coincidence arrangements of local observables, is proposed in this work. This condition entails, in particular, uniqueness and purity of the energetically accessible vacuum states. It is shown that the qualitative part of this new criterion is equivalent to a compactness condition proposed in the literature. Its novel quantitative part is verified in massive free field theory.

show abstract

Mourre Theory and Asymptotic Observables in Local Relativistic Quantum Field Theory

Kruse

2024

Commun. Math. Phys.

View full text Add to dashboard Cite

We prove the convergence of Araki–Haag detectors in any Haag–Kastler quantum field theory with an upper and lower mass gap. We cover the case of a single Araki–Haag detector on states of bounded energy, which are selected from the absolutely continuous part of the energy-momentum spectrum sufficiently close to the lower boundary of the multi-particle spectrum. These states essentially encompass those states in the multi-particle spectrum lying below the three-particle threshold. In our proof, we draw on insights from proofs of asymptotic completeness in quantum mechanics. Notably, we apply Mourre’s conjugate operator method for the first time within the framework of Haag–Kastler quantum field theory. Furthermore, we discuss applications of our findings for the problem of asymptotic completeness in local relativistic quantum field theory.

show abstract

Spectral Theory of Automorphism Groups and Particle Structures in Quantum Field Theory

Cited by 3 publications

References 19 publications

Strengthened Reeh–Schlieder Property and Scattering in Quantum Field Theories Without Mass Gaps

Strengthened Reeh–Schlieder Property and Scattering in Quantum Field Theories Without Mass Gaps

Coincidence arrangements of local observables and uniqueness of the vacuum in QFT

Mourre Theory and Asymptotic Observables in Local Relativistic Quantum Field Theory

Contact Info

Product

Resources

About