NDLI: The Translation Invariant Massive Nelson Model: II. The Continuous Spectrum below the Two-Boson Threshold

Content Provider	Springer Nature Link
Author	Møller, Jacob Schach Rasmussen, Morten Grud
Copyright Year	2012
Abstract	In this paper we continue the study of the energy-momentum spectrum of a class of translation invariant, linearly coupled, and massive Hamiltonians from non-relativistic quantum field theory. The class contains the Hamiltonians of E. Nelson (J Math Phys 5:1190–1197, 1964) and H. Fröhlich (Adv Phys 3:325–362, 1954). In Møller (Ann Henri Poincaré 6:1091–1135, 2005; Rev Math Phys 18:485–517, 2006) one of us previously investigated the structure of the ground state mass shell and the bottom of the continuous energy-momentum spectrum. Here we study the continuous energy-momentum spectrum itself up to the two-boson threshold, the threshold for energetic support of two-boson scattering states. We prove that non-threshold embedded mass shells have finite multiplicity and can accumulate only at thresholds. We furthermore establish the non-existence of singular continuous energy-momentum spectrum. Our results hold true for all values of the particle-field coupling strength but only below the two-boson threshold. The proof revolves around the construction of a certain relative velocity vector field used to construct a conjugate operator in the sense of Mourre.
Starting Page	793
Ending Page	852
Page Count	60
File Format	PDF
ISSN	14240637
Journal	Annales Henri Poincaré
Volume Number	14
Issue Number	4
e-ISSN	14240661
Language	English
Publisher	SP Birkhäuser Verlag Basel
Publisher Date	2012-10-20
Publisher Place	Basel
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Theoretical, Mathematical and Computational Physics Dynamical Systems and Ergodic Theory Quantum Physics Mathematical Methods in Physics Classical and Quantum Gravitation, Relativity Theory Elementary Particles, Quantum Field Theory
Content Type	Text
Resource Type	Article
Subject	Statistical and Nonlinear Physics Nuclear and High Energy Physics Mathematical Physics

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

The Translation Invariant Massive Nelson Model: III. Asymptotic Completeness Below the Two-Boson Threshold

The translation Invariant Massive Nelson Model: II. The Continuous Spectrum Below the Two-boson Threshold

2 The translation Invariant Massive Nelson Model: II. The Continuous Spectrum Below the Two-boson Threshold (2014)

The Translation Invariant Massive Nelson Model: I. The Bottom of the Spectrum

Absolutely Continuous Spectrum for Multi-type Galton Watson Trees

Absolutely Continuous Spectrum for the Anderson Model on Some Tree-like Graphs

Absence of Absolutely Continuous Spectrum for the Kirchhoff Laplacian on Radial Trees

Ground States in the Spin Boson Model

Continuous Limits of Classical Repeated Interaction Systems

The Translation Invariant Massive Nelson Model: II. The Continuous Spectrum below the Two-Boson Threshold

Similar Documents

The Translation Invariant Massive Nelson Model: III. Asymptotic Completeness Below the Two-Boson Threshold

The translation Invariant Massive Nelson Model: II. The Continuous Spectrum Below the Two-boson Threshold

2 The translation Invariant Massive Nelson Model: II. The Continuous Spectrum Below the Two-boson Threshold (2014)

The Translation Invariant Massive Nelson Model: I. The Bottom of the Spectrum

Absolutely Continuous Spectrum for Multi-type Galton Watson Trees

Absolutely Continuous Spectrum for the Anderson Model on Some Tree-like Graphs

Absence of Absolutely Continuous Spectrum for the Kirchhoff Laplacian on Radial Trees

Ground States in the Spin Boson Model

Continuous Limits of Classical Repeated Interaction Systems

The Translation Invariant Massive Nelson Model: II. The Continuous Spectrum below the Two-Boson Threshold