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]

Technical Report · Mon Jan 01 04:00:00 EST 1979

DOI:https://doi.org/10.2172/5970844· OSTI ID:5970844

Sternberg, S; Santilli, R M

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
• OSTI ID: 5970844
• Report Number(s): COO-4742-1
• Country of Publication: United States
• Language: English

Related Subjects

645400* -- High Energy Physics-- Field Theory
657002 -- Theoretical & Mathematical Physics-- Classical & Quantum Mechanics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ALGEBRA
BASIC INTERACTIONS
CLASSICAL MECHANICS
DIFFERENTIAL EQUATIONS
ELEMENTARY PARTICLES
EQUATIONS
EQUATIONS OF MOTION
FIELD THEORIES
FINE STRUCTURE
FUNCTIONS
GEOMETRY
HADRONS
HAMILTONIANS
HEISENBERG PICTURE
INTEGRALS
INTERACTIONS
INVERSE SCATTERING PROBLEM
KINETICS
LAGRANGIAN FUNCTION
LIE GROUPS
MATHEMATICAL OPERATORS
MATHEMATICS
MECHANICS
NUCLEAR STRUCTURE
PARTICLE STRUCTURE
PAULI PRINCIPLE
QUANTUM FIELD THEORY
QUANTUM OPERATORS
RESEARCH PROGRAMS
SPECTRA
STRONG INTERACTIONS
SYMMETRY GROUPS