Concept

Four-vector

Summary
In special relativity, a four-vector (or 4-vector) is an object with four components, which transform in a specific way under Lorentz transformations. Specifically, a four-vector is an element of a four-dimensional vector space considered as a representation space of the standard representation of the Lorentz group, the (1/2,1/2) representation. It differs from a Euclidean vector in how its magnitude is determined. The transformations that preserve this magnitude are the Lorentz transformations, which include spatial rotations and boosts (a change by a constant velocity to another inertial reference frame). Four-vectors describe, for instance, position x''μ'' in spacetime modeled as Minkowski space, a particle's four-momentum p''μ'', the amplitude of the electromagnetic four-potential A''μ''(x) at a point x in spacetime, and the elements of the subspace spanned by the gamma matrices inside the Dirac algebra. The
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