Tagged Questions
9
votes
1answer
214 views
Is there a “covariant derivative” for conformal transformation?
A primary field is defined by its behavior under a conformal transformation $x\rightarrow x'(x)$:
$$\phi(x)\rightarrow\phi'(x')=\left|\frac{\partial x'}{\partial x}\right|^{-h}\phi(x)$$
It's fairly ...
1
vote
2answers
69 views
What is path of light in the accelerating elevator?
Mathematically, (by mathematically I means by equations) what is path of light in the accelerating elevator?
What is the difference between an ordinary derivative and covariant derivative (which is ...
4
votes
1answer
143 views
Do partial derivatives commute on tensors?
For example; is $$\partial_{\rho}\partial_{\sigma}h_{\mu\nu} - \partial_{\sigma}\partial_{\rho}h_{\mu\nu}=0$$ correct?
0
votes
1answer
134 views
How to find the intrinsic covariant derivative component?
How to find the intrinsic covariant derivative component?
In general relativity the elements of the acceleration four-vector are related to the elements of the four-velocity through a covariant ...
0
votes
1answer
350 views
How to get the gradient potential in polar coordinate
In polar coordinate,
$$\nabla U = \frac{\partial U}{\partial r}\hat{\mathbf{r}} + \frac{1}{r}\frac{\partial U}{\partial \theta}\hat{\mathbf{\theta}} .$$
Can anyone show me how to get this result?
11
votes
5answers
3k views
Laplace operator's interpretation
What is your interpretation of Laplace operator? When evaluating Laplacian of some scalar field at a given point one can get a value. What does this value tell us about the field or it's behaviour in ...
