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...
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| Päätekijät: | , , , , , |
|---|---|
| Aineistotyyppi: | Livre numérique |
| Kieli: | Anglais |
| Julkaistu: |
Berlin :
European Mathematical Society
2023.
Berlin : |
| Sarja: | Memoirs of the European Mathematical Society
4 |
| Linkit: | Accès sur la plateforme EMS Press Accès sur la plateforme ISTEX Accès Université d'Orléans Accès INSA CVL |
| Huomautus: |
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 |
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| 008 | 240415q2023 xxe ||| |||| 00| 0 eng d | ||
| 009 | PPN277058414 | ||
| 020 | |a 9783985475490 | ||
| 041 | 0 | |a eng | |
| 084 | |a 35P25. 2020 | ||
| 084 | |a 35Q40. 2020 | ||
| 084 | |a 81Q10. 2020 | ||
| 084 | |a 47A10. 2020 | ||
| 084 | |a 47A40. 2020 | ||
| 084 | |a 35P25. 2020 | ||
| 100 | 1 | |a Carey, Alan L., |d 1949- | |
| 245 | 1 | 0 | |a The Limiting Absorption Principle for Massless Dirac Operators, Properties of Spectral Shift Functions, and an Application to the Witten Index of Non-Fredholm Operators |c Alan Carey, Fritz Gesztesy, Galina Levitina, Roger Nichols, Fedor Sukochev, Dmitriy Zanin. |
| 260 | |a Berlin : |b European Mathematical Society. | ||
| 260 | |a Berlin : |b European Mathematical Society, |c 2023. | ||
| 490 | 0 | |a Memoirs of the European Mathematical Society |x 2747-9099 |v 4 | |
| 500 | |a European Mathematical Society (Licence nationale) | ||
| 500 | |a European Mathematical Society (Licence nationale) | ||
| 506 | |a Accès en ligne pour les établissements français bénéficiaires des licences nationales | ||
| 506 | |a Accès soumis à abonnement pour tout autre établissement | ||
| 506 | |a Conditions particulières de réutilisation pour les bénéficiaires des licences | ||
| 520 | |a 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*). | ||
| 700 | 1 | |a Gesztesy, Fritz, |d 1953- |4 aut | |
| 700 | 1 | |a Levitina, Galina. |4 aut | |
| 700 | 1 | |a Nichols, Roger, |d 19..-...., |c mathématicien. |4 aut | |
| 700 | 1 | |a Sukochev, Fedor, |d 1962- |4 aut | |
| 700 | 1 | |a Zanin, Dmitriy, |d 19..- |4 aut | |
| 776 | 0 | |t The Limiting Absorption Principle for Massless Dirac Operators, Properties of Spectral Shift Functions, and an Application to the Witten Index of Non-Fredholm Operators |z 978-3-98547-049-5 | |
| 856 | 4 | |u https://doi.org/10.4171/mems/4 |z Accès sur la plateforme EMS Press | |
| 856 | 4 | |u https://revue-sommaire.istex.fr/ark:/67375/8Q1-QPHXSDL1-K |z Accès sur la plateforme ISTEX | |
| 856 | 4 | |5 452349901:833133373 |u https://ezproxy.univ-orleans.fr/login?url=https://doi.org/10.4171/mems/4 |z Accès Université d'Orléans | |
| 856 | 4 | |5 180339901:833135872 |u https://ezproxy.univ-orleans.fr/login?url=https://doi.org/10.4171/mems/4 |z Accès INSA CVL | |
| 997 | |0 1243114 |1 Livre numérique |a Ressource numérique |b INSA |b ENSA |c 0/Bibliothèque numérique/ |c 1/Bibliothèque numérique/Autre ressource numérique/ | ||