Riemann surfaces are Riemann sphere, torus, and pretzel-shaped surface. Their angles are the same as in Euclidean space. Riemann surfaces can define field theories {conformal field theory} that pair with string theory.
General-relativity dynamics {geometrodynamics}| is three-dimensional Riemann-space dynamics, using a method {ADM formalism} {canonical quantization} developed by Paul Dirac and later Richard Arnowitt, Stanley Deser, and Charles Misner.
Geometric optics {geometric optics}| models plane waves in flat space-time. Geometric optics applies if wave-packet wavelengths are much less than wave-front space-time curvature radius. Wave photons have same momentum and polarization. Photon number determines ray amplitude. Like adiabatic flow, photon number conserves. Light rays are null geodesics. Polarization vector is perpendicular to rays and propagates along rays.
Quantum general-relativity gravitation theories {relational quantum theory} have different observers whose calculations are the same at corresponding space-time points.
5-Physics-Relativity-General Relativity-Theory
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Date Modified: 2022.0225