covariant derivative वाक्य
उदाहरण वाक्य
मोबाइल
- In the special case of inertial frames, the Fermi Walker derivatives reduce to covariant derivatives.
- Note that the partial derivatives may be written in terms of covariant derivatives and Christoffel symbols as
- Where \ nabla _ \ mu is the general-relativistic covariant derivative of a spinor.
- We introduce an arbitrary covariant derivative via
- The gauge covariant derivative transforms similarly.
- That is we trace the covariant derivative on the " first two " covariant indices.
- Ricci calculus is the modern formalism and notation for tensor indices : indicating partial and covariant derivatives.
- Of particular note is their concept of a "'dynamical covariant derivative " '.
- The symbol \ partial _ k denotes partial derivative, while \ nabla _ k denotes covariant derivative.
- The covariant derivative \ nabla _ a is defined to annihilate the tetrad E _ a ^ I.
- This is the tactic taken by the covariant derivative approach to connections : good behavior is equated with covariance.
- Thus they quickly supplanted the classical notion of covariant derivative in many post-1950 treatments of the subject.
- By definition, a covariant derivative of a scalar field is equal to the regular derivative of the field.
- In differential geometry, the covariant derivative makes a choice for taking directional derivatives of vector fields along curves.
- Thus one might want a derivative with some of the features of a functional derivative and the covariant derivative.
- With the classical covariant derivatives, covariance is an " a posteriori " feature of the derivative.
- Then decompose the ambient covariant derivative of ? along " X " into tangential and normal components:
- Where we have taken advantage of the first covariant derivative of a function being the same as its ordinary derivative.
- Cartan connections induce covariant derivatives and other differential operators on certain associated bundles, hence a notion of parallel transport.
- Furthermore, many of the features of the covariant derivative still remain : parallel transport, curvature, and holonomy.
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