| Softcover ISBN: | 978-2-85629-893-0 |
| Product Code: | AST/404 |
| List Price: | $52.50 |
| AMS Member Price: | $42.00 |
| Softcover ISBN: | 978-2-85629-893-0 |
| Product Code: | AST/404 |
| List Price: | $52.50 |
| AMS Member Price: | $42.00 |
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Book DetailsAstérisqueVolume: 404; 2018; 110 ppMSC: Primary 47; 60; 81
The authors derive Feynman-Kac formulas for the ultra-violet renormalized Nelson Hamiltonian with a Kato decomposable external potential and for corresponding fiber Hamiltonians in the translation invariant case. They simultaneously treat massive and massless bosons. Furthermore, they present a non-perturbative construction of a renormalized Nelson Hamiltonian in a non-Fock representation defined as the generator of a corresponding Feynman-Kac semi-group.
The authors' novel analysis of the vacuum expectation of the Feynman-Kac integrands shows that if the external potential and the Pauli principle are dropped, then the spectrum of the \(N\)-particle renormalized Nelson Hamiltonian is bounded from below by some negative universal constant times \(g^{4}n^{3}\) for all values of the coupling constant \(g\). A variational argument also yields an upper bound of the same form for large \(g^{2}N\).
The authors further verify that the semi-groups generated by the ultra-violet renormalized Nelson Hamiltonian and its non-Fock version are positivity improving with respect to a natural self-dual cone if the Pauli principle is ignored. In another application, they discuss continuity properties of elements in the range of the semi-group of the renormalized Nelson Hamiltonian.
A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.
ReadershipGraduate students and research mathematicians.
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The authors derive Feynman-Kac formulas for the ultra-violet renormalized Nelson Hamiltonian with a Kato decomposable external potential and for corresponding fiber Hamiltonians in the translation invariant case. They simultaneously treat massive and massless bosons. Furthermore, they present a non-perturbative construction of a renormalized Nelson Hamiltonian in a non-Fock representation defined as the generator of a corresponding Feynman-Kac semi-group.
The authors' novel analysis of the vacuum expectation of the Feynman-Kac integrands shows that if the external potential and the Pauli principle are dropped, then the spectrum of the \(N\)-particle renormalized Nelson Hamiltonian is bounded from below by some negative universal constant times \(g^{4}n^{3}\) for all values of the coupling constant \(g\). A variational argument also yields an upper bound of the same form for large \(g^{2}N\).
The authors further verify that the semi-groups generated by the ultra-violet renormalized Nelson Hamiltonian and its non-Fock version are positivity improving with respect to a natural self-dual cone if the Pauli principle is ignored. In another application, they discuss continuity properties of elements in the range of the semi-group of the renormalized Nelson Hamiltonian.
A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.
Graduate students and research mathematicians.
