The diffeomorphism group approach to nonlinear quantum systems

Journal Article · Mon Jun 01 04:00:00 EDT 1992 · International Journal of Modern Physics B; (United States)

DOI:https://doi.org/10.1142/S0217979292000931· OSTI ID:7109972

Goldin, G A ^[1]

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1. Rutgers--the State Univ., New Brunswick, NJ (United States)

Unitary representations of diffeomorphism groups predict some unusual possibilities in quantum theory, including non-standard statistics and certain nonlinear effects. Many of the fundamental physical properties of anyons were first derived from their study by R. Menikoff, D.H. Sharp, and the author. This paper surveys new applications in two other domains: first (with Menikoff and Sharp) some surprising conclusions about the nature of quantum vortex configurations in ideal, incompressible fluids; second (with H.-D. Doebner) a natural description of dissipative quantum mechanics by means of a nonlinear Schrodlinger equation different from the sort usually studied. The authors' equation follows from including a diffusion current in the equation of continuity.

• OSTI ID: 7109972
• Journal Information: International Journal of Modern Physics B; (United States), Journal Name: International Journal of Modern Physics B; (United States) Vol. 6:11-12; ISSN 0217-9792; ISSN IJPBE
• Country of Publication: United States
• Language: English

Related Subjects

661100 -- Classical & Quantum Mechanics-- (1992-)
662110* -- General Theory of Particles & Fields-- Theory of Fields & Strings-- (1992-)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ANYONS
DIFFERENTIAL EQUATIONS
DIFFUSION
EQUATIONS
FIELD THEORIES
FLUID FLOW
FLUIDS
INCOMPRESSIBLE FLOW
MAGNETIC FLUX
MECHANICS
NONLINEAR PROBLEMS
PARTIAL DIFFERENTIAL EQUATIONS
QUANTUM FIELD THEORY
QUANTUM MECHANICS
QUASI PARTICLES
SCHROEDINGER EQUATION
SURVEYS
SYMMETRY
UNITARY SYMMETRY
WAVE EQUATIONS