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Lorentz generators can be added together, or multiplied by real numbers, to obtain more Lorentz generators. In other words, the set of all Lorentz generators V = { ζ ⋅ K + θ ⋅ J } {\displaystyle V=\{{\boldsymbol {\zeta }}\cdot \mathbf {K} +{\boldsymbol {\theta }}\cdot \mathbf {J} \}} together with the operations of ordinary matrix ...
The Lorentz group is a subgroup of the Poincaré group—the group of all isometries of Minkowski spacetime. Lorentz transformations are, precisely, isometries that leave the origin fixed. Thus, the Lorentz group is the isotropy subgroup with respect to the origin of the isometry group of Minkowski spacetime.
In theoretical physics, the composition of two non-collinear Lorentz boosts results in a Lorentz transformation that is not a pure boost but is the composition of a boost and a rotation. This rotation is called Thomas rotation, Thomas–Wigner rotation or Wigner rotation.
Such converters act on the fluid using the Lorentz force to operate in two possible ways: either as an electric generator called an MHD generator, extracting energy from a fluid in motion; or as an electric motor called an MHD accelerator or magnetohydrodynamic drive, putting a fluid in motion by injecting energy. MHD converters are indeed ...
In the fundamental branches of modern physics, namely general relativity and its widely applicable subset special relativity, as well as relativistic quantum mechanics and relativistic quantum field theory, the Lorentz transformation is the transformation rule under which all four-vectors and tensors containing physical quantities transform from one frame of reference to another.
The boost generators K and rotation generators J can be combined into one generator for Lorentz transformations; M the antisymmetric angular momentum tensor, with components = =, =. and correspondingly, the boost and rotation parameters are collected into another antisymmetric four-dimensional matrix ω, with entries: = =, =, where the ...