Towards a nonpotential scattering theory

Journal Article · Wed May 01 04:00:00 EDT 1985 · Hadronic J.; (United States)

OSTI ID:6419159

Mignani, R

We present a formal approach to nonpotential scattering theory (i.e. scattering under unrestricted nonlocal non-Hamiltonian forces), based on the generalization of the concept of scattering matrix (and related topics) to the Lie-isotopic and Lie-admissible case. In the time-dependent formalism, the main taks is the determination of the evolution operator, from which the S matrix is found as a double infinite limit. The study of time-development operators is carried out in detail in the isotopic case, and involves the isotopic generalizations of Moller wave operators, in- and out-states, and temporal (retarded and advanced) propagators. We give also expansion techniques for the S matrix, which extend to the Lie-isotopic formulation the Feynman-Dyson perturbation series, the Magnus expansion, and the Wei-Norman theorem. In the time-independent approach, we solve the isotopic Schroedinger eigenvalue equation by exploiting the properties of isotopic Green operators, Lippmann-Schwinger equations, and incoming and outgoing states, which turn out to be suitable generalizations of the conventional ones. The changes in cross sections due to nonpotential forces are explicitly worked out in some simple cases. A purely algebraic approach to nonpotential scattering, essentially based on the properties of the isowave operators, is presented. The Lie-admissible formulation of the main results is briefly outlined.

• Research Organization: Dipartimento di Fisica, I Universita di Roma ''La Sapienza,'' P. le A. Moro, 2-00185 Roma, Italy and Division of Physics, Institute for Basic Research, 96 Prescott Street, Cambridge, Massachusetts 02138
• OSTI ID: 6419159
• Journal Information: Hadronic J.; (United States), Journal Name: Hadronic J.; (United States) Vol. 8:3; ISSN HAJOD
• Country of Publication: United States
• Language: English

Related Subjects

645500* -- High Energy Physics-- Scattering Theory-- (-1987)
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BANACH SPACE
CROSS SECTIONS
DIFFERENTIAL EQUATIONS
EIGENVALUES
ELEMENTARY PARTICLES
EQUATIONS
HADRONS
HILBERT SPACE
INTEGRAL EQUATIONS
LIPPMANN-SCHWINGER EQUATION
MATHEMATICAL SPACE
MATRICES
PARTIAL DIFFERENTIAL EQUATIONS
S MATRIX
SCATTERING
SCHROEDINGER EQUATION
SERIES EXPANSION
SPACE
TIME DEPENDENCE
WAVE EQUATIONS