Foundations of the hadronic generalization of the atomic mechanics. I. Generalization of Heisenberg's and Schroedinger's representations
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-
- Journal Information:
- Hadronic J.; (United States), Vol. 5:4; Conference: 1. international conference on non-potential interactions and their Lie-admissible treatment, Orleans, France, 5 Jan 1982
- Country of Publication:
- United States
- Language:
- English
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STRONG INTERACTIONS
QUANTUM MECHANICS
CLASSICAL MECHANICS
HADRONS
HAMILTONIANS
HEISENBERG PICTURE
LIE GROUPS
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SCHROEDINGER EQUATION
STATISTICAL MECHANICS
SYMMETRY BREAKING
BASIC INTERACTIONS
DIFFERENTIAL EQUATIONS
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ELEMENTARY PARTICLES
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PARTIAL DIFFERENTIAL EQUATIONS
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WAVE EQUATIONS
645204* - High Energy Physics- Particle Interactions & Properties-Theoretical- Strong Interactions & Properties