I see, I still have one question then. In the question above, it is also mentioned that " This should then be interpreted as meaning that the sum of the inertial
and the gravitational acceleration could be made equal to zero everywhere. " Why sum? How was this interpreted? I mean interpretation...
In attempt to describe the consequences of the Equivalence Principle, this is almost said:
When there are gravitational accelerations present, as for example in the
gravitational field of the earth, the space cannot be the flat Minkowski space. Indeed,
in the Minkowski space we can have...
Do you mean that I should have derived wrt A? Well, because what I am trying to find is ##G_{\mu\nu}=\delta S/\delta F^{\mu\nu}##. The formula that I have come across in the web says so, maybe in few resources it says so, in some others, it says ##G_{\mu\nu}=\epsilon_{\mu\nu\rho\sigma}\delta...
Hello @fzero ! Sorry I am reviving the thread again but as I was reviewing what I learned yesterday, I am wondering about something:
In this one, now in order to proceed like we did in our first case, I should lower indices in ##F^{I\rho\sigma}## right? So I can also use the ##\epsilon## for...
I have one question, as I said above ##N_{IJ}## is a complex symmetric matrix, that is I do not know if we should consider ##I## and ##J## to be functional here and embed them in a Kronecker delta or should I consider them as if they were not there because those are things that span the space...
I guess, the question is not clear enough.
My confusion is in the following, if in the least usage of words: If ##L = \frac{1}{2}N_{IJ}F_{\mu\nu}^I\tilde{F}^{J\mu\nu} ##, what is ##\delta L/\delta F^{\rho\sigma J}##?
No, here "I" is related to the "I" in ##N_{IJ}## which is a matrix. F is a rank 2 tensor. Suppose there were no "I" or "J" to start with, how can I derive ##1/2 N_{IJ}F_{\mu\nu}\tilde{F}^{\mu\nu} ## wrt ##F^{\rho\sigma}## meanwhile it has no ##\rho## nor ##\sigma## in it?
Hello, I am very new to tensors and GR and would like to ask for guidance to understand how tensor simplification works.
If we have this term $$\frac{1}{2}N_{IJ}F_{\mu\nu}^I\tilde{F}^{J\mu\nu} $$ and I want to derive w.r.t ##F^{\rho\sigma I}##
where
- ##N_{IJ}## is a symmetric complex matrix
-...
I am reading the book Supergravity.
In chapter 4, section 4.3.2
- Duality for gauge fields and complex scalar:
The simplest case of electromagnetic duality in an interacting field theeory occurs with one abelian gauge field ##A_{\mu}(x)## and a complex scalar field ##Z(x)##. The...