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Interpolating Asymptotic Constants for the Poincaré Group, in Particular on Fock Space
Author(s) -
Baumgärtel H.,
Wollenberg M.
Publication year - 1984
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19841190103
Subject(s) - mathematics , fock space , bounded function , invariant (physics) , hilbert space , poincaré group , lorentz group , lorentz space , group (periodic table) , pure mathematics , euclidean space , euclidean geometry , lorentz transformation , mathematical analysis , mathematical physics , quantum mechanics , geometry , physics
Starting from a representation of the restricted Poincaré group ζ + →on a Hilbert space χ and from arbitrary bounded Poincaré invariant operators X + and X − we describe a method for the construction of bounded operators X whose time evolutions e itH Xe − itH tend “very fast” to the given operators X + and X − as t goes to + ∞ and ‐ ∞, respectively. Additionally these operators X (interpolating asymptotic constants) are Lorentz (or Euclidean) invariant and satisfy a certain boundedness condition with respect to H .