Knowra Lorentz group Lorentz group The group of linear transformations that preserves the Minkowski metric. It describes changes of inertial frame and spacetime symmetries that leave the speed of light invariant.
Minkowski metric : The indefinite metric used to measure spacetime intervals in special relativity. The Lorentz group consists precisely of linear transformations preserving this metric.
Minkowski spacetime : The flat spacetime model equipped with the Minkowski metric. The Lorentz group acts as a symmetry group of this spacetime.
Special relativity : The theory of spacetime, motion, and physical laws in inertial frames, with invariant light speed. Its transformations between inertial frames are Lorentz transformations.
Euclidean group : The group of rigid motions preserving distances in Euclidean space. It preserves a positive-definite metric, unlike the Lorentz group’s spacetime metric.
Lorentz transformation : A linear transformation of spacetime coordinates that preserves the Minkowski metric. Each group element acts on spacetime as a Lorentz transformation.
Group theory : The mathematical study of sets equipped with associative operations, identities, and inverses. Closure, composition, and inverses make Lorentz transformations a group.
Poincaré group : The group of spacetime translations combined with Lorentz transformations. It extends Lorentz symmetry to include changes in spacetime origin.
Galilean group : The spacetime symmetry group of classical mechanics, including absolute time and Galilean boosts. Its boosts do not preserve a finite invariant speed.
Lorentz boost : A Lorentz transformation relating inertial frames moving at constant velocity relative to one another. Boosts are the group’s transformations that mix time with spatial coordinates.
Lie group : A group that is also a smooth manifold, with smooth multiplication and inversion. The Lorentz group is continuous and has a smooth local structure.
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