Recent content by Baela

Varying ##\partial_\lambda\phi\,\partial^\lambda\phi## wrt the metric tensor ##g_{\mu\nu}## in two different ways gives me different results. Obviously I'm doing something wrong. Where am I going wrong? Method 1: \begin{equation} (\delta g_{\mu\nu})\,\partial^\mu\phi\,\partial^\nu\phi...

Sorry about the long delay in my reply. I've had a very busy couple of months with deadlines to meet. After having met some of my deadlines, I have returned to reply to your questions as soon as I could manage. Generally the main purpose of a gauge transformation is to keep the action...

Let us consider an action ##S=S(a,b,c)## which is a functional of the fields ##a,\, b,\,## and ##c##. The solution of the field ##c## is given by the expression ##f(a,b)##. On taking into account the relations obtained from the solutions for ##a## and ##b##, we find that ##f(a,b)=0##. If the...

We know that a metric tensor raises or lowers the indices of a tensor, for e.g. a Levi-Civita tensor. If we are in ##4D## spacetime, then \begin{align} g_{mn}\epsilon^{npqr}=\epsilon_{m}{}^{pqr} \end{align} where ##g_{mn}## is the metric and ##\epsilon^{npqr}## is the Levi-Civita tensor. The...

As per the answer given by Demystifier here: https://www.physicsforums.com/threads/are-equations-of-motion-invariant-under-gauge-transformations.1052060/post-6879952 , equations of motion of an action are not necessarily required to be invariant under the gauge transformations of the action. So...

Which symbol do you need clarification for? My question is pretty general. I can't see what part you are confused about.

If a Lagrangian has the fields ##a##, ##b## and ##c## whose equations of motion are denoted by ##E_a, E_b## and ##E_c## respectively, then if \begin{align} E_a=f_1(a,b,c)\,E_b+f_2(a,b,c)\,E_c \end{align} where ##f_1## and ##f_2## are some functions of the fields, if ##E_b## and ##E_c## are...

Thanks!

We know that all actions are invariant under their gauge transformations. Are the equations of motion also invariant under the gauge transformations? If yes, can you show a mathematical proof (instead of just saying in words)?

I need to prove that under an infinitesimal coordinate transformation ##x^{'\mu}=x^\mu-\xi^\mu(x)##, the variation of a vector ##U^\mu(x)## is $$\delta U^\mu(x)=U^{'\mu}(x)-U^\mu(x)=\mathcal{L}_\xi U^\mu$$ where ##\mathcal{L}_\xi U^\mu## is the Lie derivative of ##U^\mu## wrt the vector...

Supergravity transformations in curved spacetime.

What is the expression for the covariant derivative of a Weyl spinor?

It'll take some time to show that. Will try to do it when I get enough time for it.

The equations of motion are invariant also under the gauge transformations which are undefined on-shell. ##E_a,\,E_b,## and ##E_c## can be shown to be invariant under such gauge transformations. I would be happy to come to know of some reasoning which rules out the gauge-transformations that...

Then eq. (2) becomes undefined. Such a gauge-transformation is undefined on-shell. But that does not mean that such a gauge transformation is not possible or not allowed.