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Lie-admissible structure of Hamilton`s original equations with external terms

Technical Report:

Abstract

As a necessary additional step in preparation of our operator studies of closed nonhamiltonian systems, in this note we consider the algebraic structure of the original equations proposed by Lagrange and Hamilton, those with external terms representing precisely the contact nonpotential forces of the interior dynamical problem. We show that the brackets of the theory violate the conditions to characterize any algebra. Nevertheless, when properly written, they characterize a covering of the Lie-isotopic algebras called Lie-admissible algebras. It is indicated that a similar occurrence exists for conventional operator treatments, e.g. for nonconservative nuclear cases characterized by nonhermitean Hamiltonians. This occurrence then prevents a rigorous treatment of basic notions, such as that of angular momentum and spin spin, which are centrally dependent on the existence of a consistent algebraic structure. The emergence of the Lie-admissible algebras is therefore expected to be unavoidable for any rigorous operator treatment of open systems with nonlinear, nonlocal and nonhamiltonian external forces. (author). 14 refs, 1 fig.
Authors:
Publication Date:
Sep 01, 1991
Product Type:
Technical Report
Report Number:
IC-91/266
Reference Number:
SCA: 661100; PA: AIX-23:015324; SN: 92000647053
Resource Relation:
Other Information: PBD: Sep 1991
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CLASSICAL MECHANICS; MATHEMATICAL OPERATORS; ALGEBRA; HAMILTON-JACOBI EQUATIONS; LAGRANGE EQUATIONS; SYMMETRY; 661100; CLASSICAL AND QUANTUM MECHANICS
OSTI ID:
10113300
Research Organizations:
International Centre for Theoretical Physics (ICTP), Trieste (Italy)
Country of Origin:
IAEA
Language:
English
Other Identifying Numbers:
Other: ON: DE92615216; TRN: XA9130263015324
Availability:
OSTI; NTIS (US Sales Only); INIS
Submitting Site:
INIS
Size:
13 p.
Announcement Date:
Jun 30, 2005

Technical Report:

Citation Formats

Santilli, R M. Lie-admissible structure of Hamilton`s original equations with external terms. IAEA: N. p., 1991. Web.
Santilli, R M. Lie-admissible structure of Hamilton`s original equations with external terms. IAEA.
Santilli, R M. 1991. "Lie-admissible structure of Hamilton`s original equations with external terms." IAEA.
@misc{etde_10113300,
title = {Lie-admissible structure of Hamilton`s original equations with external terms}
author = {Santilli, R M}
abstractNote = {As a necessary additional step in preparation of our operator studies of closed nonhamiltonian systems, in this note we consider the algebraic structure of the original equations proposed by Lagrange and Hamilton, those with external terms representing precisely the contact nonpotential forces of the interior dynamical problem. We show that the brackets of the theory violate the conditions to characterize any algebra. Nevertheless, when properly written, they characterize a covering of the Lie-isotopic algebras called Lie-admissible algebras. It is indicated that a similar occurrence exists for conventional operator treatments, e.g. for nonconservative nuclear cases characterized by nonhermitean Hamiltonians. This occurrence then prevents a rigorous treatment of basic notions, such as that of angular momentum and spin spin, which are centrally dependent on the existence of a consistent algebraic structure. The emergence of the Lie-admissible algebras is therefore expected to be unavoidable for any rigorous operator treatment of open systems with nonlinear, nonlocal and nonhamiltonian external forces. (author). 14 refs, 1 fig.}
place = {IAEA}
year = {1991}
month = {Sep}
}