Four-vector
In special relativity, a four-vector is an object with four in general complex components that transform in a specific way under Lorentz transformations. Specifically, a four-vector is an element of a 4-dimensional vector space considered as a representation space of the standard representation of the Lorentz group, the (½,½) representation. It differs from a Euclidean vector in how its magnitude is determined. The transformations that preserve this magnitude are the Lorentz transformations. They include spatial rotations, boosts (a change by a constant velocity to another inertial reference frame), and temporal and spatial inversions.
Four-vectors describe, for instance, position xμ in spacetime modeled as Minkowski space, a particles 4-momentum pμ, the amplitude of the electromagnetic four-potential Aμ(x) at a point x in spacetime, and the elements of the subspace spanned by the gamma matrices inside the Dirac algebra.
The Lorentz group may be represented by 4×4 matrices Λ. The action of a Lorentz transformation on a general contravariant four-vector X (like the examples above), regarded as a column vector with Cartesian coordinates with respect to an inertial frame in the entries, is given by
Podcasts:
-
by Fear Factory
-
by Fear Factory
-
by Fear Factory
-
by Fear Factory
-
by Fear Factory
-
by Fear Factory
-
by Fear Factory
-
by Fear Factory
-
by Fear Factory
-
by Fear Factory
-
by Fear Factory
-
by Fear Factory
-
by Fear Factory
-
by Fear Factory
-
by Fear Factory
-
by Fear Factory
-
by Fear Factory
-
by Fear Factory
-
by Fear Factory
-
by Fear Factory
-
by Fear Factory
-
by Fear Factory
-
by Fear Factory
-
by Fear Factory
-
by Fear Factory
-
by Fear Factory
-
by Fear Factory
-
by Fear Factory
-
by Fear Factory
-
by Fear Factory
-
by Fear Factory
-
by Fear Factory
-
by Fear Factory
-
by Fear Factory
-
by Fear Factory
-
by Fear Factory
-
by Fear Factory
-
by Fear Factory
-
by Fear Factory
-
by Fear Factory
-
by Fear Factory
-
by Fear Factory
-
by Fear Factory
-
by Fear Factory
-
by Fear Factory
-
by Fear Factory
-
by Fear Factory
-
by Fear Factory
-
by Fear Factory
-
by Fear Factory
Corporate Cloning
by: Fear FactoryA Clone force mass produced
Simulate, introduce
Delinquint, rank and file
Incodent, stamped and styled
Ill-affected progeny
Tasteless iconography
A half-life in the line
Industry, by design
Plastic thoughts in my mind
Thus begins my demise
This year's model dims and fades
Last year's model is erased
Prototype
By design
Prototype
Stand in line
(Fading) Another fading idol
(Falling) Another fallen icon
(Fading) Another fading idol
(Falling) Another fallen icon
Life and sex share a mind
Deviance is a crime
Delinquint, rank and file
Incodent, stamped and styled
Ill-affected progeny
Tasteless iconography
This years model dims and fades
Last years model is erased
Prototype
By design
Prototype
Stand in line
(Fading) Another fading idol
(Falling) Another fallen icon
(Fading) Another fading idol
(Falling) Another fallen icon
Another fallen icon
Sometimes I wish I were deaf and blind
(Fading) Another fading idol
(Falling) Another fallen icon
(Fading) Another fading idol
(Falling) Another fallen icon
(Fading) Another fading idol
(Falling) Another fallen icon
(Fading) Another fading idol
Latest News for: four-vector
When 3D meets 4D: Scientists decode the strange physics of quasicrystals
- 1