Classical Physics: Spacetime and Fields

Abstract

We present a self-contained introduction to the classical theory of spacetime and fields. This exposition is based on the most general principles: the principle of general covariance (relativity) and the principle of least action. The order of the exposition is: 1. Spacetime (principle of general covariance and tensors, affine connection, curvature, metric, space and time, tetrad and spin connection, Lorentz group, spinors); 2. Fields (principle of least action, gravitational field, matter, symmetries and conservation laws, particle limit of field, gravitational field equations, spinor fields, electromagnetic field). In this order, a particle is a special case of a field existing in spacetime, and classical mechanics can be derived from field theory.

151 pages, 3 figures

Cited by in corpus (14)

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• Charged Wormhole Solutions in Einstein-Cartan gravity
• Dynamic wormhole solutions in Einstein-Cartan gravity
• The dynamics of Bianchi I universes in $R^n$ cosmologies with torsion
• A nonsingular, anisotropic universe in a black hole with torsion and particle production
• General-relativistic wave$-$particle duality with torsion
• Neutrino oscillations induced by chiral torsion
• Consistent solution of Einstein-Cartan equations with torsion outside matter
• Black holes in the expanding Universe
• Affine Dynamics with Torsion
• On the real representations of the Poincare group
• Spin-Torsion effect on collapsing of first generation stars into neutron stars rather than black holes in Einstein-Cartan-Sciama-Kibble theory
• Comment on `Relativistic wave-particle duality for spinors'
• The appearance of non trivial torsion for some Ricci dependent theories in the Palatini formalism