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  2. Lorentz transformation - Wikipedia

    en.wikipedia.org/wiki/Lorentz_transformation

    The most general proper Lorentz transformation Λ(v, θ) includes a boost and rotation together, and is a nonsymmetric matrix. As special cases, Λ(0, θ) = R(θ) and Λ(v, 0) = B(v). An explicit form of the general Lorentz transformation is cumbersome to write down and will not be given here.

  3. 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 ...

  4. Classical electromagnetism and special relativity - Wikipedia

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

    A derivation for the transformation of the Lorentz force for the particular case u = 0 is given here. [4] A more general one can be seen here. [5] The transformations in this form can be made more compact by introducing the electromagnetic tensor (defined below), which is a covariant tensor.

  5. 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.

  6. Covariant formulation of classical electromagnetism - Wikipedia

    en.wikipedia.org/wiki/Covariant_formulation_of...

    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.

  7. Electromagnetic four-potential - Wikipedia

    en.wikipedia.org/wiki/Electromagnetic_four-potential

    In special relativity, the electric and magnetic fields transform under Lorentz transformations. This can be written in the form of a rank two tensor – the electromagnetic tensor . The 16 contravariant components of the electromagnetic tensor, using Minkowski metric convention (+ − − −) , are written in terms of the electromagnetic four ...

  8. Dyadics - Wikipedia

    en.wikipedia.org/wiki/Dyadics

    In mathematics, specifically multilinear algebra, a dyadic or dyadic tensor is a second order tensor, written in a notation that fits in with vector algebra. There are numerous ways to multiply two Euclidean vectors. The dot product takes in two vectors and returns a scalar, while the cross product [a] returns a pseudovector.

  9. Four-gradient - Wikipedia

    en.wikipedia.org/wiki/Four-gradient

    "Any physical law which can be expressed in tensor notation in SR has exactly the same form in a locally inertial frame of a curved spacetime." The 4-gradient commas (,) in SR are simply changed to covariant derivative semi-colons (;) in GR, with the connection between the two using Christoffel symbols. This is known in relativity physics as ...