Titlebook: Special Relativity in General Frames; From Particles to As éric Gourgoulhon Textbook 2013 Springer-Verlag Berlin Heidelberg 2013 Limits of

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Maxwell Equations,lated, first in terms of the electromagnetic field tensor, before being expressed in terms of the electric and magnetic fields with respect to some observer. It is shown that, as a consequence of Maxwell equations, the electric charge is conserved. The solution to Maxwell equations is searched by me

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,Energy–Momentum Tensor,of quantities measurable by a given observer: energy density, linear-momentum density, energy-flux 1-form and stress tensor. The principle of energy–momentum conservation is stated, and its local expression is written in terms of the divergence of the energy–momentum tensor. The notion of four-force

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CULP

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Lorentz Group,lies of spatial rotations, Lorentz boosts, null rotations and four-screws. The polar decomposition of restricted Lorentz transformations is presented. The properties of boosts are studied in detail. Finally the composition of boosts is investigated, leading to the concept of Thomas rotation.

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Lorentz Group as a Lie Group,, the link between the restricted Lorentz group and the special linear group . is established via the spinor map. The Lie algebras of these two groups are shown to be identical (up to some isomorphism).

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,Inertial Observers and Poincaré Group,ormations corresponding to a change of inertial observers. It is shown to be the semidirect product of the translation group and the Lorentz group. Finally the Lie group structure of the Poincaré group is analysed, yielding to its Lie algebra, its generators and its structure constants.

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Principle of Least Action,ticle in scalar, vector or second-rank tensor fields are treated. The Noether theorem is presented. The generalized four-momentum and the Hamiltonian are introduced for a single particle, and the canonical equations of Hamilton are written. Finally, systems of many particles are discussed by means of the Tetrode–Fokker action.