The Limiting Absorption Principle for Massless Dirac Operators, Properties of Spectral Shift Functions, and an Application to the Witten Index of Non-Fredholm Operators
Applying the theory of strongly smooth operators, we derive a limiting absorption principle (LAP) on any compact interval on the real line away from zero for the *n*-dimensional free massless Dirac operator *H*, and then use this to demonstrate the absence of singular continuous spectrum of interact...
Enregistré dans:
| Auteurs principaux: | , , , , , |
|---|---|
| Format: | Livre numérique |
| Langue: | Anglais |
| Publié: |
Berlin :
European Mathematical Society
2023.
Berlin : |
| Collection: | Memoirs of the European Mathematical Society
4 |
| Accès en ligne: | Accès sur la plateforme EMS Press Accès sur la plateforme ISTEX Accès Université d'Orléans Accès INSA CVL |
| Note: |
European Mathematical Society (Licence nationale) European Mathematical Society (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • The Limiting Absorption Principle for Massless Dirac Operators, Properties of Spectral Shift Functions, and an Application to the Witten Index of Non-Fredholm Operators, 978-3-98547-049-5 |
| Résumé: | Applying the theory of strongly smooth operators, we derive a limiting absorption principle (LAP) on any compact interval on the real line away from zero for the *n*-dimensional free massless Dirac operator *H*, and then use this to demonstrate the absence of singular continuous spectrum of interacting massless Dirac operators *H* *H* + *V*, where the entries of the (essentially bounded) matrix-valued potential *V* decay appropriately at spatial infinity. This includes the special case of electromagnetic potentials. In addition, we derive a one-to-one correspondence between embedded eigenvalues of *H* (away from zero) and the eigenvalue 1 of an underlying Birman-Schwinger-type operator. In addition, expressing the spectral shift function for the pair (*H*,*H*) as normal boundary values of associated regularized Fredholm determinants to the real axis, we then prove that under appropriate additional decay hypotheses on *V*, the spectral shift function for (*H*,*H*) is continuous away from zero and that its left and right limits at zero exist. This fact is then used to express the resolvent regularized Witten index of the non-Fredholm operator *D* *A* (*d*/*dt*) + *A*, where *A* represents the direct integral over a family operators *A*(*t*) that has asymptotes *A* and *A* as *t* tends to + infinity and infinity (in the norm resolvent sense), respectively, in terms of the spectral shift function for the pair (*H*,*H*). |
|---|---|
| Description: | European Mathematical Society (Licence nationale) European Mathematical Society (Licence nationale) |
| ISBN: | 9783985475490 |
| ISSN: | 2747-9099 |
| Accès: | Accès en ligne pour les établissements français bénéficiaires des licences nationales Accès soumis à abonnement pour tout autre établissement Conditions particulières de réutilisation pour les bénéficiaires des licences |