Search results
Results from the WOW.Com Content Network
Lorentz covariance has two distinct, but closely related meanings: A physical quantity is said to be Lorentz covariant if it transforms under a given representation of the Lorentz group . According to the representation theory of the Lorentz group , these quantities are built out of scalars , four-vectors , four-tensors , and spinors .
A Lorentz scalar may be generated from, e.g., the scalar product of vectors, or by contracting tensors. While the components of the contracted quantities may change under Lorentz transformations, the Lorentz scalars remain unchanged. A simple Lorentz scalar in Minkowski spacetime is the spacetime distance ("length" of their difference) of two ...
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.
The covariant quantities are four-scalars, four-vectors etc., of the Minkowski space (and also more complicated objects like bispinors and others). An example of a covariant equation is the Lorentz force equation of motion of a charged particle in an electromagnetic field (a generalization of Newton's second law)
A scalar (also called type-0 or rank-0 tensor) is an object that does not vary with the change in basis. An example of a physical observable that is a scalar is the mass of a particle. The single, scalar value of mass is independent to changes in basis vectors and consequently is called invariant.
The explicit form of a covariant transformation is best introduced with the transformation properties of the derivative of a function. Consider a scalar function f (like the temperature at a location in a space) defined on a set of points p, identifiable in a given coordinate system , =,, … (such a collection is called a manifold).
While both the scalar and vector potential depend upon the frame, the electromagnetic four-potential is Lorentz covariant. Like other potentials, many different electromagnetic four-potentials correspond to the same electromagnetic field, depending upon the choice of gauge.
Modern formulations of classical field theories generally require Lorentz covariance as this is now recognised as a fundamental ... The action is a Lorentz scalar, ...