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2. Lorentz transformation - Wikipedia

   en.wikipedia.org/wiki/Lorentz_transformation

   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. This property is the defining property of a Lorentz transformation.

3. Derivations of the Lorentz transformations - Wikipedia

   en.wikipedia.org/wiki/Derivations_of_the_Lorentz...

   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.

4. Lorentz group - Wikipedia

   en.wikipedia.org/wiki/Lorentz_group

   Since every proper, orthochronous Lorentz transformation can be written as a product of a rotation (specified by 3 real parameters) and a boost (also specified by 3 real parameters), it takes 6 real parameters to specify an arbitrary proper orthochronous Lorentz transformation. This is one way to understand why the restricted Lorentz group is ...

5. Classical electromagnetism and special relativity - Wikipedia

   en.wikipedia.org/wiki/Classical_electromagnetism...

   Lorentz boost of an electric charge. Top: The charge is at rest in frame F , so this observer sees a static electric field. An observer in another frame F ′ moves with velocity v relative to F , and sees the charge move with velocity − v with an altered electric field E due to length contraction and a magnetic field B due to the motion of ...

6. Symmetry in quantum mechanics - Wikipedia

   en.wikipedia.org/wiki/Symmetry_in_quantum_mechanics

   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 ...

7. Light front quantization - Wikipedia

   en.wikipedia.org/wiki/Light_front_quantization

   The light-front boost is a Lorentz boost that leaves the light front invariant. The light-front boosts are not only members of the light-front kinematic subgroup, but they also form a closed three-parameter subgroup. This has two consequences.

8. Four-vector - Wikipedia

   en.wikipedia.org/wiki/Four-vector

   Given two inertial or rotated frames of reference, a four-vector is defined as a quantity which transforms according to the Lorentz transformation matrix Λ: ′ =. In index notation, the contravariant and covariant components transform according to, respectively: ′ =, ′ = in which the matrix Λ has components Λ μ ν in row μ and column ν, and the matrix (Λ −1) T has components Λ ...

9. Wigner rotation - Wikipedia

   en.wikipedia.org/wiki/Wigner_rotation

   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.