Integrability conditions for the existence of a Lagrangian in Newtonian mechanics and field theory. Annual progress report, March 1, 1978-May 31, 1979. [Summaries of research activities at Harvard University]
Studies of general covariance and its application to particle motion and continuum mechanics were continued. Also developed was a new method in microlocal analysis which has applications to integral geometry, geometrical quantization and the fine structure of certain types of spectra. The classical aspect of a program was studied by a comprehensive analysis of the integrability conditions for the existence of a Lagrangian or, independently, of a Hamiltonian for the representation of given Newtonian systems with forces nonderivable from a potential, as well as the methods for the computation of these functions from the equations of motion. The study of a classical, complementary, methodological approach to the same class of systems was also initiated. It consists of the representation of systems with forces nonderivable from a potential via a generalization of Hamilton's equations posessing a Lie-admissible algebraic structure. The problem of the quantization of forces nonderivable from a potential was then studied via the use of these complementary methods. The use of the integrability conditions for the existence of a Hamiltonian representation (the inverse problem) yielded, under certain restrictions, the conventional Heisenberg's equations, but expressed in terms of a generalized Hamiltonian structure. The use of the Lie-admissible formulations yielded a generalization of Heisenberg's equations possessing a generalized (Lie-admissible) algebraic structure, but expressed in terms of a conventional Hamiltonian structure. These preliminary studies were then applied to the investigation of the old idea that the strong interactions are of the type considered, local and nonderivable from a potential, as an approximation of expected nonlocal settings. The experimental verification of the validity or invalidity of Pauli's exclusion principle and other basic physical laws for the nuclear and the hadronic structure was proposed. Publications are listed.
- Research Organization:
- Harvard Univ., Cambridge, MA (USA). Science Center
- DOE Contract Number:
- ER-78-S-02-4742
- OSTI ID:
- 5970844
- Report Number(s):
- COO-4742-1; TRN: 79-019616
- Country of Publication:
- United States
- Language:
- English
Similar Records
Lie-admissible structure of statistical mechanics
Closed systems with nonconservative internal forces
Related Subjects
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
CLASSICAL MECHANICS
LAGRANGIAN FUNCTION
QUANTUM FIELD THEORY
ALGEBRA
EQUATIONS OF MOTION
FINE STRUCTURE
GEOMETRY
HADRONS
HAMILTONIANS
HEISENBERG PICTURE
INTEGRALS
INVERSE SCATTERING PROBLEM
KINETICS
LIE GROUPS
NUCLEAR STRUCTURE
PARTICLE STRUCTURE
PAULI PRINCIPLE
RESEARCH PROGRAMS
SPECTRA
STRONG INTERACTIONS
BASIC INTERACTIONS
DIFFERENTIAL EQUATIONS
ELEMENTARY PARTICLES
EQUATIONS
FIELD THEORIES
FUNCTIONS
INTERACTIONS
MATHEMATICAL OPERATORS
MATHEMATICS
MECHANICS
QUANTUM OPERATORS
SYMMETRY GROUPS
645400* - High Energy Physics- Field Theory
657002 - Theoretical & Mathematical Physics- Classical & Quantum Mechanics