Nonlinear operators. II

Journal Article · Tue Jul 01 04:00:00 EDT 1997 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.532070· OSTI ID:530089

Schwartz, C ^[1]

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1. Department of Physics, University of California, Berkeley, California 94720 (United States)

This work extends the previous development of new mathematical machinery for nonlinear operators acting on a vector space. Starting from the usual concept of inner product, we find that Hermitian, anti-Hermitian, and unitary nonlinear operators can be defined without bringing in the ideas of a dual vector space or adjoint operators. After looking briefly at how these general ideas might be used in classical mechanics and to extend the linear Schr{umlt o}dinger equation of quantum theory, the topic of Lie groups and Lie algebras is studied. Many, but not all, of the familiar features of that topic are extended to nonlinear operators. New representations are found for a few simple cases of interest to physics, and some provocative implications for elementary particle theory are discussed. {copyright} {ital 1997 American Institute of Physics.}

• OSTI ID: 530089
• Journal Information: Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 7 Vol. 38; ISSN JMAPAQ; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
ALGEBRA
CLASSICAL MECHANICS
HERMITIAN OPERATORS
LIE GROUPS
MATHEMATICAL OPERATORS
NONLINEAR PROBLEMS
QUANTUM OPERATORS
SCHROEDINGER EQUATION
UNITARITY
VECTORS