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In relativistic physics, Lorentz symmetry or Lorentz invariance, named after the Dutch physicist Hendrik Lorentz, is an equivalence of observation or observational symmetry due to special relativity implying that the laws of physics stay the same for all observers that are moving with respect to one another within an inertial frame. It has also ...
This form is invariant under the Lorentz group, so that for S ∈ SL(2, C) one has , = , This defines a kind of "scalar product" of spinors, and is commonly used to defined a Lorentz-invariant mass term in Lagrangians. There are several notable properties to be called out that are important to physics.
The following notations are used very often in special relativity: Lorentz factor = where = and v is the relative velocity between two inertial frames.. For two frames at rest, γ = 1, and increases with relative velocity between the two inertial frames.
It may include a rotation of space; a rotation-free Lorentz transformation is called a Lorentz boost. In Minkowski space—the mathematical model of spacetime in special relativity—the Lorentz transformations preserve the spacetime interval between any two events. They describe only the transformations in which the spacetime event at the ...
The difference between this and the spacetime interval = in Minkowski space is that = is invariant purely by the principle of relativity whereas = requires both postulates. The "principle of relativity" in spacetime is taken to mean invariance of laws under 4-dimensional transformations.
The covariant formulation of classical electromagnetism refers to ways of writing the laws of classical electromagnetism (in particular, Maxwell's equations and the Lorentz force) in a form that is manifestly invariant under Lorentz transformations, in the formalism of special relativity using rectilinear inertial coordinate systems. These ...
A simple Lorentz scalar in Minkowski spacetime is the spacetime distance ("length" of their difference) of two fixed events in spacetime. While the "position"-4-vectors of the events change between different inertial frames, their spacetime distance remains invariant under the corresponding Lorentz transformation.
The corresponding result for superstring theory is again deduced demanding Lorentz invariance, but now with supersymmetry. In these theories the Poincaré algebra is replaced by a supersymmetry algebra which is a Z 2-graded Lie algebra extending the Poincaré algebra. The structure of such an algebra is to a large degree fixed by the demands of ...