Foundations of the hadronic generalization of the atomic mechanics. I. Generalization of Heisenberg's and Schroedinger's representations

Conference · Tue Jun 01 04:00:00 UTC 1982 · Hadronic J.; (United States)

OSTI ID:6296839

Santilli, R M

This paper deals with the part of of the Hadronic Mechanics called of Lie-isotopic type, which: (1) is conceived for the exterior strong non-Hamiltonian treatment; (2) is based on the isotopic generalization of the associative algebra of operators on a Hilbert space; and (3) admits as a classical limit the recently achieved Birkhoffian generalization of the Hamiltonian Mechanics. We first review the Hadronic-isotopic covering of Heisenberg's representation with particular reference to the generalization of: Heisenberg's equations; canonical commutation rules; canonical quantization; Heisenberg's uncertainty principle; Planck's constant; Galilei's relativity; and the representation theory. A possible, single, unifying postulate for the covering theory is introduced. We then pass to the construction of the corresponding generalization of Schroedinger's representation. For this purpose, we first construct the Birkhoffian generalization of the Hamilton-Jacobi theory for local non-Hamiltonian systems. We then show that the latter theory admits a consistent quantization into a generalization of Schroedinger's equations. Some essential properties of the emerging hadronic generalization of the atomic wave theory, are presented. In particular, we identify the general solution of the hadronic wave packets under the most general possible local Hamiltonian and non-Hamiltonian forces, which has no counterpart in the Atomic Mechanics.

• Research Organization: Inst. for Basic Research, Cambridge, MA
• DOE Contract Number: AC02-80ER10651
• OSTI ID: 6296839
• Report Number(s): CONF-820136-
• Conference Information: Journal Name: Hadronic J.; (United States) Journal Volume: 5:4
• Country of Publication: United States
• Language: English

Related Subjects

645204* -- High Energy Physics-- Particle Interactions & Properties-Theoretical-- Strong Interactions & Properties
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BASIC INTERACTIONS
CLASSICAL MECHANICS
DIFFERENTIAL EQUATIONS
DOCUMENT TYPES
ELEMENTARY PARTICLES
EQUATIONS
HADRONS
HAMILTONIANS
HEISENBERG PICTURE
INTERACTIONS
LIE GROUPS
MATHEMATICAL OPERATORS
MECHANICS
PARTIAL DIFFERENTIAL EQUATIONS
QUANTUM MECHANICS
QUANTUM OPERATORS
REVIEWS
SCHROEDINGER EQUATION
STATISTICAL MECHANICS
STRONG INTERACTIONS
SYMMETRY BREAKING
SYMMETRY GROUPS
WAVE EQUATIONS