On Nelson-Type Hamiltonians and Abstract Boundary Conditions

We construct Hamiltonians for systems of nonrelativistic particles linearly coupled to massive scalar bosons using abstract boundary conditions. The construction yields an explicit characterisation of the domain of self-adjointness in terms of boundary conditions that relate sectors with different n...

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Bibliographic Details
Published inCommunications in mathematical physics Vol. 367; no. 2; pp. 629 - 663
Main Authors Lampart, Jonas, Schmidt, Julian
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.04.2019
Springer Nature B.V
Springer Verlag
Subjects
Bosons
Boundary conditions
Classical and Quantum Gravitation
Complex Systems
Mathematical and Computational Physics
Mathematical Physics
Mathematics
Physics
Physics and Astronomy
Quantum Physics
Relativity Theory
Theoretical
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Summary:We construct Hamiltonians for systems of nonrelativistic particles linearly coupled to massive scalar bosons using abstract boundary conditions. The construction yields an explicit characterisation of the domain of self-adjointness in terms of boundary conditions that relate sectors with different numbers of bosons. We treat both models in which the Hamiltonian may be defined as a form perturbation of the free operator, such as Fröhlich’s polaron, and renormalisable models, such as the massive Nelson model.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0010-3616
1432-0916
DOI:10.1007/s00220-019-03294-x