Covariant

  • (adj): Changing so that interrelations with another variable quantity or set of quantities remain unchanged.

Some articles on covariant:

Mathematics Of General Relativity - Tensorial Derivatives - The Covariant Derivative
... The formula for a covariant derivative of along associated with connection turns out to give curve-independent results and can be used as a "physical definition" of a ... It can be expressed using connection coefficients The expression in brackets, called a covariant derivative of (with respect to the connection) and denoted by, is more often used in calculations A ... By definition, a covariant derivative of a scalar field is equal to the regular derivative of the field ...
List Of Formulas In Riemannian Geometry - Christoffel Symbols, Covariant Derivative
... The covariant derivative of a vector field with components is given by and similarly the covariant derivative of a -tensor field with components is given by For a -tensor field with ... The covariant derivative of a function (scalar) is just its usual differential Because the Levi-Civita connection is metric-compatible, the covariant derivatives of metrics vanish, The geodesic ...
Classical Electromagnetism And Special Relativity - Covariant Formulation in Vacuum - 4-potential
... in the Lorenz gauge, an alternative manifestly-covariant formulation can be found in a single equation (a generalization of an equation due to Bernhard Riemann by Arnold Sommerfeld, known as the Riemann–Sommerfeld ... For a more comprehensive presentation of these topics, see Covariant formulation of classical electromagnetism ...
Inhomogeneous Electromagnetic Wave Equation - Covariant Form of The Inhomogeneous Wave Equation
... See also Covariant formulation of classical electromagnetism The relativistic Maxwell's equations can be written in covariant form as where J is the four-current , is the 4-gradient and the electromagnetic four ...
Classical Electromagnetism And Special Relativity - Covariant Formulation in Vacuum - Maxwell's Equations in Tensor Form
... Using these tensors, Maxwell's equations reduce to Maxwell's equations (Covariant formulation) where the partial derivatives may be written in various ways, see 4-gradient ... These tensor equations are manifestly-covariant, meaning the equations can be seen to be covariant by the index positions ... Another covariant electromagnetic object is the electromagnetic stress-energy tensor, a covariant rank-2 tensor which includes the Poynting vector, Maxwell stress ...