Matrix-valued Schrödinger operators over local fields

Autor:	David Weisbart, Trond Digernes
Rok vydání:	2009
Předmět:	Pure mathematics Nuclear operator General Mathematics Mathematical analysis Hilbert space Displacement operator Compact operator Operator space symbols.namesake Ladder operator symbols Hamiltonian (quantum mechanics) Ornstein–Uhlenbeck operator Mathematics
Zdroj:	P-Adic Numbers, Ultrametric Analysis, and Applications. 1:136-144
ISSN:	2070-0474 2070-0466
DOI:	10.1134/s2070046609020058
Popis:	We consider quantum systems that have as their configuration spaces finite dimensional vector spaces over local fields. The quantum Hilbert space is taken to be a space with complex coefficients and we include in our model particles with internal symmetry. The Hamiltonian operator is a pseudo-differential operator that is initially only formally defined. For a wide class of potentials we prove that this Hamiltonian is well-defined as an unbounded self-adjoint operator. The free part of the operator gives rise to ameasure on the Skorokhod space of paths,D[0,∞), and with respect to this measure there is a path integral representation for the semigroup associated to the Hamiltonian. We prove this Feynman-Kac formula in the local field setting as a consequence of the Hille-Yosida theory of semi-groups.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::74f4887cd5769ea33b255e138d485386 https://doi.org/10.1134/s2070046609020058 Zobrazit plný text záznamu Full text from SpringerLink