four-vector
Sign in to saveIn special relativity, a four-vector (or 4-vector, sometimes Lorentz vector) is an element of a four-dimensional vector space object with four components, which transform under Lorentz transformations with respect to a change of basis. Its magnitude is determined by an indefinite quadratic form, the preservation of which defines the Lorentz transformations, which include spatial rotations and boosts (a change by a constant velocity to another reference frame).
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Article
41 sectionsContents
- Notation
- Four-vector algebra
- Four-vectors in a real-valued basis
- Lorentz transformation
- Pure rotations about an arbitrary axis
- Pure boosts in any direction
- Properties
- Linearity
- Minkowski tensor
- Standard basis, (+−−−) signature
- Standard basis, (−+++) signature
- Dual vectors
- Four-vector calculus
- Derivatives and differentials
- Fundamental four-vectors
- Four-position <span class="anchor" id="Position"></span>
- Four-gradient
- Kinematics
- Four-velocity
- Four-acceleration
- Dynamics
- Four-momentum
- Four-force
- Thermodynamics
- Four-heat flux
- Four-baryon number flux
- Four-entropy
- Electromagnetism
- Four-current
- Four-potential
- Waves
- Four-frequency
- Four-wavevector
- Quantum theory
- Four-probability current
- Four-spin
- Other formulations
- Four-vectors in the algebra of physical space
- Four-vectors in spacetime algebra
- See also
- References
In special relativity, a four-vector (or 4-vector, sometimes Lorentz vector) is an element of a four-dimensional vector space object with four components, which transform under Lorentz transformations with respect to a change of basis. Its magnitude is determined by an indefinite quadratic form, the preservation of which defines the Lorentz transformations, which include spatial rotations and boosts (a change by a constant velocity to another reference frame).
Four-vectors describe, for instance, position in spacetime modeled as Minkowski space, a particle's four-momentum , the amplitude of the electromagnetic four-potential at a point in spacetime, and the elements of the subspace spanned by the gamma matrices inside the Dirac algebra.