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Degenerate perturbation theory for models of quantum field theory with symmetries

Hasler, David and Lange, Markus (2023) Degenerate perturbation theory for models of quantum field theory with symmetries. Annales Henri Poincaré. Springer Nature. doi: 10.1007/s00023-023-01359-1. ISSN 1424-0637.

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Official URL: https://doi.org/10.1007/s00023-023-01359-1


We consider Hamiltonians of models describing non-relativistic quantum mechanical matter coupled to a relativistic field of bosons. If the free Hamiltonian has an eigenvalue, we show that this eigenvalue persists also for nonzero coupling. The eigenvalue of the free Hamiltonian may be degenerate provided there exists a symmetry group acting irreducibly on the eigenspace. Furthermore, if the Hamiltonian depends analytically on external parameters then so does the eigenvalue and eigenvector. Our result applies to the ground state as well as resonance states. For our results, we assume a mild infrared condition. The proof is based on operator theoretic renormalization. It generalizes the method used in (https://doi.org/10.1007/s00023-023-01359-1) to non-degenerate situations, where the degeneracy is protected by a symmetry group, and utilizes Schurs lemma from representation theory.

Item URL in elib:https://elib.dlr.de/197689/
Document Type:Article
Title:Degenerate perturbation theory for models of quantum field theory with symmetries
AuthorsInstitution or Email of AuthorsAuthor's ORCID iDORCID Put Code
Lange, MarkusUNSPECIFIEDhttps://orcid.org/0000-0001-7198-2871147094635
Date:3 October 2023
Journal or Publication Title:Annales Henri Poincaré
Refereed publication:Yes
Open Access:Yes
Gold Open Access:No
In ISI Web of Science:Yes
Publisher:Springer Nature
Keywords:Degenerate Eigenvalues, Spin Boson model, Symmetries
HGF - Research field:other
HGF - Program:other
HGF - Program Themes:other
DLR - Research area:Digitalisation
DLR - Program:D - no assignment
DLR - Research theme (Project):D - ELEVATE
Location: Ulm
Institutes and Institutions:Institute for AI Safety and Security
Deposited By: Lange, Dr. Markus
Deposited On:21 Nov 2023 12:42
Last Modified:21 Nov 2023 12:42

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