# Covariant

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

### Some articles on covariant:

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 ... presentation of these topics, see Covariant formulation of classical electromagnetism ...
Classical Electromagnetism And Special Relativity - Covariant Formulation in Vacuum - Maxwell's Equations in Tensor Form
... 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 tensor, and ...
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 components this becomes and ... The covariant derivative of a function (scalar) is just its usual differential Because the Levi-Civita connection is metric-compatible, the covariant derivatives of ...
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 covariant derivative ... 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 covariant derivative of X can thus be ... By definition, a covariant derivative of a scalar field is equal to the regular derivative of the field ...
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 ...