Premium
Representations for the Three‐Body T‐Matrix, Scattering Matrices and Resolvent in Unphysical Energy Sheets
Author(s) -
Motovilov Alexander K.
Publication year - 1997
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.19971870110
Subject(s) - resolvent , mathematics , matrix (chemical analysis) , scattering , mathematical analysis , fundamental matrix (linear differential equation) , analytic continuation , pure mathematics , mathematical physics , algebra over a field , physics , quantum mechanics , materials science , composite material
Abstract Explicit representations for the Faddeev components of the three‐body T‐matrix continued analytically into unphysical sheets of the energy Riemann surface are formulated. According to the representations, the T‐matrix in unphysical sheets is explicitly expressed in terms of its components taken in the physical sheet only. The representations for the T‐matrix are then used to construct similar representations for the analytic continuation of the three‐body scattering matrices and the resolvent. Domains on unphysical sheets are described where the representations obtained can be applied. A method for finding three‐body resonances based on the Faddeev differential equations is proposed.