What is the meaning of the notation \partial \betaD\alpha in General Relativity?

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Discussion Overview

The discussion revolves around the notation \partial \betaD\alpha in the context of General Relativity, specifically exploring its meaning and implications within mathematical formulations.

Discussion Character

  • Technical explanation, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant suggests that \partial \betaD\alpha represents the set of all partial derivatives of a vector function, although they express uncertainty about this interpretation.
  • Another participant clarifies that if the notation is \partial_{\beta}D^{\alpha}, it is shorthand for the partial derivative \frac{\partial D^{\alpha}}{\partial x^{\beta}}.
  • A third participant notes that the notation could also refer to a boundary, prompting a request for context to clarify its meaning.
  • A later reply supports the interpretation of the notation as the "outer derivative" of the vector, aligning with the previous explanation about the derivative of the \alpha component of D with respect to x^\beta.

Areas of Agreement / Disagreement

Participants express differing interpretations of the notation, with some proposing it refers to partial derivatives while others suggest it may indicate a boundary. The discussion remains unresolved regarding a definitive meaning.

Contextual Notes

The discussion lacks specific context that could clarify the intended meaning of the notation, leaving interpretations dependent on assumptions about its usage in General Relativity.

Reedeegi
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What does the notation [tex]\partial[/tex] [tex]\beta[/tex]D[tex]\alpha[/tex]
mean? I came across it in General Relativity, so I think it's the set of all partial derivatives of the vector function, i.e.
[tex]\partial[/tex]0D1, [tex]\partial[/tex]0D[tex]2[/tex]

and so on... but I'm not entirely sure.
 
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If you mean [itex]\partial_{\beta}D^{\alpha}[/itex], then it is short hand for [tex]\frac{\partial D^{\alpha}}{\partial x^{\beta}}[/tex]
 
Depending on the context, it can also mean boundary. What is the context?
 
Since Reedeegi said it was from General Relativity I suspect the context is as cristo assumed and it is the "outer derivative" of the vector- the tensor represented by array in which the "[itex]\alpha\beta[/itex]" component is the derivative of the [itex]\alpha[/itiex] component of D with respect to [itex]x^\beta[/itex]- which is, of course, just what cristo said.[/itex]
 

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