Schroedinger equation for non-associative quantum mechanics and No-Go theorem
Conference
·
· Hadronic J.; (United States)
OSTI ID:6293899
Within an algebraic framework of non-associative quantum mechanics, a Hilbert space and the corresponding Schroedinger equation have been introduced into the theory as follows. The underlying non-associative operator algebra A is assumed to be flexible and Lie-admissible so that it is compatible with the Heisenberg equation of motion and quantization. A Hilbert space can be introduced into the theory as a faithful representation of the associated Lie algebra A/sup -/ of the Lie-admissible algebra A. However, if A/sup -/ is the standard Heisenberg algebra, and if the representation is irreducible, then it is shown that A must be associative, reproducing the standard associative quantum mechanics. Some discussions to circumvent this No-Go theorem are discussed. Especiallyyu if we are interested in the formulation of infinite component wave equations, then this difficulty can be avoided.
- Research Organization:
- Univ. of Rochester, NY
- OSTI ID:
- 6293899
- Report Number(s):
- CONF-820136-
- Conference Information:
- Journal Name: Hadronic J.; (United States) Journal Volume: 5:5
- Country of Publication:
- United States
- Language:
- English
Similar Records
Foundations of the hadronic generalization of the atomic mechanics. I. Generalization of Heisenberg's and Schroedinger's representations
Possible incompatibility of Lie-admissible local powers of a quantum field with the Wightman axioms and the spin-statistics theorem
Initiation of the representation theory of Lie-admissible algebras of operators on bimodular Hilbert spaces
Conference
·
Tue Jun 01 00:00:00 EDT 1982
· Hadronic J.; (United States)
·
OSTI ID:6296839
Possible incompatibility of Lie-admissible local powers of a quantum field with the Wightman axioms and the spin-statistics theorem
Journal Article
·
Tue Aug 01 00:00:00 EDT 1978
· Hadronic J.; (United States)
·
OSTI ID:6486368
Initiation of the representation theory of Lie-admissible algebras of operators on bimodular Hilbert spaces
Conference
·
Fri Nov 30 23:00:00 EST 1979
· Hadronic J.; (United States)
·
OSTI ID:6484260
Related Subjects
657002 -- Theoretical & Mathematical Physics-- Classical & Quantum Mechanics
658000* -- Mathematical Physics-- (-1987)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGEBRA
BANACH SPACE
DIFFERENTIAL EQUATIONS
EQUATIONS
HILBERT SPACE
LIE GROUPS
MATHEMATICAL OPERATORS
MATHEMATICAL SPACE
MATHEMATICS
MECHANICS
PARTIAL DIFFERENTIAL EQUATIONS
QUANTUM MECHANICS
SCHROEDINGER EQUATION
SPACE
SYMMETRY GROUPS
WAVE EQUATIONS
658000* -- Mathematical Physics-- (-1987)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGEBRA
BANACH SPACE
DIFFERENTIAL EQUATIONS
EQUATIONS
HILBERT SPACE
LIE GROUPS
MATHEMATICAL OPERATORS
MATHEMATICAL SPACE
MATHEMATICS
MECHANICS
PARTIAL DIFFERENTIAL EQUATIONS
QUANTUM MECHANICS
SCHROEDINGER EQUATION
SPACE
SYMMETRY GROUPS
WAVE EQUATIONS