Affine connections in special relativity

Journal Article · Fri Sep 15 00:00:00 EDT 1978 · Phys. Rev., D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.18.1837· OSTI ID:6637159

Epstein, K J

Affine geometry, implemented by a ''Lorentz connection'' for accelerated frames of reference in pseudo-Euclidean space-times, a ''Fourier connection'' for abstract Hilbert spaces associated with classical Fourier analysis, and a ''quantum connection'' for quantum-mechanical Hilbert spaces, give snew perspectives on special relativity, where affine connections are usually interpreted phenomenologically, in a manner which obscures theri geometric significance. The connections are determined by ''absolute constants,'' whose covariant derivatives, expressed in terms of the connection coefficients, vanish identically. In the deterministic theory of prequantum physics, the space-time connection is expressed in terms of ''local Lorentz transformations,'' which represent the motion of accelerated frames relative to inertial frames. In quantum theory, relative motion is not well defined, but local Lorentz transformations, represented by locally isomorphic symmetry groups, remain well defined, and become the basis of quantum field theory.

• Research Organization: 2025 W. Granville Avenue, Chicago, Illinois 60659
• OSTI ID: 6637159
• Journal Information: Phys. Rev., D; (United States), Vol. 18:6
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
RELATIVITY THEORY
SPACE-TIME
HILBERT SPACE
LORENTZ TRANSFORMATIONS
MINKOWSKI SPACE
QUANTUM FIELD THEORY
BANACH SPACE
FIELD THEORIES
GENERAL RELATIVITY THEORY
MATHEMATICAL SPACE
SPACE
TRANSFORMATIONS
645400* - High Energy Physics- Field Theory
657003 - Theoretical & Mathematical Physics- Relativity & Gravitation