covariant in a sentence

1. As a covariant vector, its rule for transforming from one coordinate system to another is

2. In particular, certain variables that could be interpreted as time and energy turned out to be covariant.

3. The electromagnetic potential is a covariant vector, Aα which is the undefined primitive of electromagnetism.

4. The use of non-covariant objects like pseudotensors was heavily criticized in 1917 by Erwin Schrödinger and others.

5. In general relativity, we have to use the covariant derivative instead of the partial derivative in d'Alembert's equation, so we get:

6. The electromagnetic field is a covariant antisymmetric rank 2 tensor which can be defined in terms of the electromagnetic potential by

7. The bra ⟨ f | {\displaystyle \langle f|} is a covariant vector and the ket | g ⟩ {\displaystyle |g\rangle } is a contra-variant vector.

8. He gave up looking for fully generally covariant tensor equations, and searched for equations that would be invariant under general linear transformations only.

9. According to the principle of equivalence, (1a) describes in general covariant form a gravitational field of a special kind, when the functions gik satisfy the Riemann condition.

10. It is also possible that a rule which defines instantaneousness is contingent, by emerging dynamically from relativistic covariant laws combined with particular initial conditions.

11. More specifically, every morphism in C must be assigned to a morphism in D. In other words, a contravariant functor acts as a covariant functor from the opposite category Cop to D.

12. If the laws of this field are in general covariant, that is, are not dependent on a particular choice of coordinate system, then the introduction of an independent (absolute) space is no longer necessary.

13. For them to be independent of (or covariant with, to be more precise) motion, Einstein postulated that the speed of light had to be a constant regardless of whether you were going toward it or away from it.

14. The procedure Christoffel employed in his solution of the equivalence problem is what Gregorio Ricci-Curbastro later called covariant differentiation, Christoffel also used the latter concept to define the basic Riemann-Christoffel curvature tensor. ...

15. In order that this may be possible, the functions gik must satisfy certain general covariant equations of condition, which were derived by B. Riemann more than half a century before the formulation of the general theory of relativity (“Riemann condition”).

16. 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.