Accession Number : AD0467414

Title :   CLASSICAL FIELDS AND GRAVITATION,

Corporate Author : ARMY MISSILE RESEARCH DEVELOPMENT AND ENGINEERING LAB REDSTONE ARSENAL AL PHY SICAL SCIENCES DIRECTORATE

Personal Author(s) : Garber, Vitalij ; Coulter, C. A.

Report Date : 10 MAY 1965

Pagination or Media Count : 41

Abstract : This report deals with classical field theory and gravitation. The discussion begins with consideration of the Lagrangian formalism in four-dimensional space-time. Hamilton's principle is applied to obtain the Euler-Lagrange equations of motion. Criteria for Lorentz covariance are developed. Treatment of interacting fields by use of the Lagrangian formulation is illustrated by the consideration of charged particles in an electromagnetic field. Noether's theorem and its connection with conservation laws are outlined, and the application to the particular case of ortochronour Lorentz transformations is described. Following a review of gravitational experiments supporting the general theory of relativity, the concepts of gravitational and inertial mass equivalence, general covariance, the metric tensor, Riemannian space, and covariant differentiation are developed. The Bianchi identities are derived from the symmetry properties of the affine connection the the Riemannian metric space. Subsequently, gravitational field equations for gravitational fields only and in the presence of other fields are derived. The necessity for explicitly introducing an interaction term in the conventional and quantum mechanical theory is contrasted with the automatic, implicit interaction found in the gravitational field theory. Exact solutions are obtained for the spherically-symmetric Schwarzschild case. The approximate theory for the weak field case is discussed. (Author)

Descriptors :   (*GRAVITY, FIELD THEORY), (*FIELD THEORY, GRAVITY), NUMERICAL INTEGRATION, CHARGED PARTICLES, ELECTROMAGNETIC FIELDS, QUANTUM THEORY, ALGEBRAIC TOPOLOGY, GROUPS(MATHEMATICS).

Distribution Statement : APPROVED FOR PUBLIC RELEASE