In special relativity, a four-vector (or 4-vector, sometimes Lorentz vector) is an object with four components, which transform in a specific way under...

spacetime. Momentum is a vector in three dimensions; similarly four-momentum is a four-vector in spacetime. The contravariant four-momentum of a particle...

particular in special relativity and general relativity, a four-velocity is a four-vector in four-dimensional spacetime that represents the relativistic counterpart...

An electromagnetic four-potential is a relativistic vector function from which the electromagnetic field can be derived. It combines both an electric...

charge per unit time per unit area. Also known as vector current, it is used in the geometric context of four-dimensional spacetime, rather than separating...

the natural sciences, a vector quantity (also known as a vector physical quantity, physical vector, or simply vector) is a vector-valued physical quantity...

a wave four-vector can be defined, combining the (angular) wave vector and (angular) frequency. The terms wave vector and angular wave vector have distinct...

four-acceleration is a four-vector (vector in four-dimensional spacetime) that is analogous to classical acceleration (a three-dimensional vector, see...

operations on the above sorts of vectors. A vector space formed by geometric vectors is called a Euclidean vector space, and a vector space formed by tuples is...

transformation matrix is universal for all four-vectors, not just 4-dimensional spacetime coordinates. If A is any four-vector, then in tensor index notation A...

The four-frequency of a massless particle, such as a photon, is a four-vector defined by N a = ( ν , ν n ^ ) {\displaystyle N^{a}=\left(\nu ,\nu {\hat...

physics, and engineering, a Euclidean vector or simply a vector (sometimes called a geometric vector or spatial vector) is a geometric object that has magnitude...

quantity to a spacelike vector quantity, and we have 4d vectors, or "four-vectors", in Minkowski spacetime. The components of vectors are written using tensor...

In differential geometry, the four-gradient (or 4-gradient) ∂ {\displaystyle {\boldsymbol {\partial }}} is the four-vector analogue of the gradient ∇ →...

spacetime represented as a four-vector (t, x, y, z). A Lorentz transformation is represented by a matrix that acts on the four-vector, changing its components...

electromagnetic four-potential is a covariant four-vector containing the electric potential (also called the scalar potential) ϕ and magnetic vector potential...

In geometry, a position or position vector, also known as location vector or radius vector, is a Euclidean vector that represents a point P in space....

of relativity, four-force is a four-vector that replaces the classical force. The four-force is defined as the rate of change in the four-momentum of a...

perpendicular to the light's wavefronts (and is therefore collinear with the wave vector). A slightly more rigorous definition of a light ray follows from Fermat's...

For instance, many times the time-based terms are placed first in the four-vectors, with the spatial terms following. Also, sometimes η is replaced with...

potential and the magnetic vector potential. The electric potential and the magnetic vector potential together form a four-vector, so that the two kinds of...

In classical electromagnetism, magnetic vector potential (often denoted A) is the vector quantity defined so that its curl is equal to the magnetic field...

object. It is a vector quantity, possessing a magnitude and a direction. If m is an object's mass and v is its velocity (also a vector quantity), then...

example of a bilinear form that is not an inner product would be the four-vector product. The definition of a bilinear form can be extended to include...

Poincaré group (the inhomogeneous Lorentz group). Thus, a is a real Lorentz four-vector representing the change of spacetime origin x ↦ x − a, where x is in...

In mathematics, vector multiplication may refer to one of several operations between two (or more) vectors. It may concern any of the following articles:...

operations of vector addition and scalar multiplication must satisfy certain requirements, called vector axioms. Real vector spaces and complex vector spaces...

momentarily at rest, the proper acceleration 3-vector, combined with a zero time-component, yields the object's four-acceleration, which makes proper-acceleration's...

phenomenological theory of spin. The wave functions in the Dirac theory are vectors of four complex numbers (known as bispinors), two of which resemble the Pauli...

of the Lorentz group, these quantities are built out of scalars, four-vectors, four-tensors, and spinors. In particular, a Lorentz covariant scalar (e...