manifestly covariant

12 examples (0.03 sec)
  • It is a manifestly covariant equation, but at the same time its three-dimensional structure is evident.
  • The laws and mathematical objects in classical electromagnetism can be written in a form which is manifestly covariant.
  • Writing an equation in manifestly covariant form is useful because it guarantees general covariance upon quick inspection.
  • The equation above contains partial derivatives and is therefore not manifestly covariant.
  • An equation may be Lorentz covariant even if it is not manifestly covariant.
  • These tensor equations are manifestly-covariant, meaning the equations can be seen to be covariant by the index positions.
  • In general relativity, a manifestly covariant equation is one in which all expressions are tensors.
  • Third, it motivates a compact and convenient notation for the laws of electromagnetism, namely the "manifestly covariant" tensor form.
  • Tensor densities, especially integrands and variables of integration, may be allowed in manifestly covariant equations if they are clearly weighted by the appropriate power of the determinant of the metric.
  • Unlike the Breit equation, it is manifestly covariant and free from the types of singularities that prevent a strictly nonperturbative treatment of the Breit equation.
  • If an equation is manifestly covariant, and if it reduces to a correct, corresponding equation in special relativity when evaluated instantaneously in a local inertial frame, then it is usually the correct generalization of the special relativistic equation in general relativity.
  • In quantum field theory, and in the significant subfields of quantum electrodynamics and quantum chromodynamics, the two-body Dirac equations (TBDE) of constraint dynamics provide a three-dimensional yet manifestly covariant reformulation of the Bethe-Salpeter equation for two spin-1/2 particles.