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  2. Mathematical descriptions of the electromagnetic field

    en.wikipedia.org/wiki/Mathematical_descriptions...

    In three dimensions, the derivative has a special structure allowing the introduction of a cross product: = + = + from which it is easily seen that Gauss's law is the scalar part, the Ampère–Maxwell law is the vector part, Faraday's law is the pseudovector part, and Gauss's law for magnetism is the pseudoscalar part of the equation.

  3. Mathisson–Papapetrou–Dixon equations - Wikipedia

    en.wikipedia.org/wiki/Mathisson–Papapetrou...

    Other equations with similar names and mathematical forms are the Mathisson–Papapetrou equations and Papapetrou–Dixon equations. All three sets of equations describe the same physics. These equations are named after Myron Mathisson, [1] William Graham Dixon, [2] and Achilles Papapetrou, [3] who worked on them.

  4. 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. These ...

  5. Linear programming - Wikipedia

    en.wikipedia.org/wiki/Linear_programming

    Linear programming (LP), also called linear optimization, is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements and objective are represented by linear relationships. Linear programming is a special case of mathematical programming (also known as mathematical optimization).

  6. Postulates of special relativity - Wikipedia

    en.wikipedia.org/wiki/Postulates_of_special...

    Thus, if a fundamental physical law is expressed with a mathematical equation in one inertial frame, it must be expressed by an identical equation in any other inertial frame, provided both frames are parameterised with charts of the same type. (The caveat on charts is relaxed, if we employ connections to write the law in a covariant form.) 2.

  7. Mathematical formulation of the Standard Model - Wikipedia

    en.wikipedia.org/wiki/Mathematical_formulation...

    This article describes the mathematics of the Standard Model of particle physics, a gauge quantum field theory containing the internal symmetries of the unitary product group SU(3) × SU(2) × U(1). The theory is commonly viewed as describing the fundamental set of particles – the leptons , quarks , gauge bosons and the Higgs boson .

  8. Mathematical formulation of quantum mechanics - Wikipedia

    en.wikipedia.org/wiki/Mathematical_formulation...

    The first complete mathematical formulation of this approach, known as the Dirac–von Neumann axioms, is generally credited to John von Neumann's 1932 book Mathematical Foundations of Quantum Mechanics, although Hermann Weyl had already referred to Hilbert spaces (which he called unitary spaces) in his 1927 classic paper and book.

  9. Formulations of special relativity - Wikipedia

    en.wikipedia.org/wiki/Formulations_of_special...

    The minimal subgroup in question can be described as follows: The stabilizer of a null vector is the special Euclidean group SE(2), which contains T(2) as the subgroup of parabolic transformations. This T(2), when extended to include either parity or time reversal (i.e. subgroups of the orthochronous and time-reversal respectively), is ...