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In physics and mathematics, the Lorentz group is the group of all Lorentz transformations of Minkowski spacetime, the classical and quantum setting for all (non-gravitational) physical phenomena. The Lorentz group is named for the Dutch physicist Hendrik Lorentz. For example, the following laws, equations, and theories respect Lorentz symmetry:
Many of the representations, both finite-dimensional and infinite-dimensional, are important in theoretical physics. Representations appear in the description of fields in classical field theory, most importantly the electromagnetic field, and of particles in relativistic quantum mechanics, as well as of both particles and quantum fields in quantum field theory and of various objects in string ...
If C ≠ 0, this is an inhomogeneous Lorentz transformation or Poincaré transformation. [24] [25] If C = 0, this is a homogeneous Lorentz transformation. Poincaré transformations are not dealt further in this article.
By combining the Lorentz force law above with the definition of electric current, the following equation results, in the case of a straight stationary wire in a homogeneous field: [30] =, where ℓ is a vector whose magnitude is the length of the wire, and whose direction is along the wire, aligned with the direction of the conventional current I.
At any time after t = t′ = 0, xx′ is not zero, so dividing both sides of the equation by xx′ results in =, which is called the "Lorentz factor". When the transformation equations are required to satisfy the light signal equations in the form x = ct and x ′ = ct ′, by substituting the x and x'-values, the same technique produces the ...
Hendrik Lorentz was a major influence on Einstein's theory of special relativity. Lorentz laid the fundamentals for the work by Einstein and the theory was originally called the Lorentz-Einstein theory. After 1905 Lorentz wrote several papers on what he called "Einstein's principle of relativity". Einstein, Albert (1905-06-30).
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.
Lorentz transformations can be parametrized by rapidity φ for a boost in the direction of a three-dimensional unit vector ^ = (,,), and a rotation angle θ about a three-dimensional unit vector ^ = (,,) defining an axis, so ^ = (,,) and ^ = (,,) are together six parameters of the Lorentz group (three for rotations and three for boosts). The ...