Recent content by JuanC97

Ok guys, I've already answer my own question: . Yeah, the equations of motion for higher order perturbed fields remain unchanged, I checked this using XAct for Mathematica. I suppose that the difference with the case of adding a background-dependent-zero is that in that case any perturbation...

Intuitively, I'd say that adding a 4-divergence to the Lagrangian should not affect the eqs of motion since the integral of that 4-divergence (of a vector that vanishes at ∞) can be rewritten as a surface term equal to zero, but... In some theories, the addition of a term that is equal to zero...

Yeah, you're right, I should've called it a "change of coordinates" instead of "a clockwise rotation". And... about this, what do you think?

Hello guys, I have a question regarding commutators of vector fields and its pushforwards. Let me define a clockwise rotation in the plane \,\phi:\mathbb{R}^2\rightarrow\mathbb{R}^2 \,.\; [\,\partial_x\,,\,\partial_y\,]=0 \,, \;(\phi_{*}\partial_x) = \partial_r and \,(\phi_{*}\partial_y) =...

Just teacher and student discussions. Our classes follow my teacher's hand-written lecture notes and new demonstrations he prepares for each specific class to exhibit an interesting fact of the topic under exposition. There's no book, he just writes down his demonstrations and we discuss it with...

Sadly, I'd have to write my lecture notes in PDF in order to give you more details about it but I think that would take a long time, more than desired. I'm going to wait a bit more to see what comments arrive now and... maybe, some days later I can upload my notes and then tag you to them...

I know a way to deduce the solution in terms of one factor A(r) that has to be (##1-2GM/r##). In order to complete the solution and find the equivalence between both terms you have to use perturbation theory to make that factor consistent with special relativity, ie: if I do so at first order...

Hello guys, I'm wondering if there are some important restrctions on the 'applicability' of first order perturbation theory. I know there's a way to deduce Schwarzschild's solution to Einstein's field equations that assummes one can decompose the 4D metric ##g_{\mu\nu}## as Minkowski...

Well, you're right, the massless case shouldn't be called 'proca' but mathematically, it exists and corresponds to a lagrangian of the form (kinetic term) - (potential). Also, when I said I was interested in 'generalizing proca', I should've said it was in the sense of adding extra terms to the...

Hello guys, In 90% of the papers I've read about diferent ways to achieve generalizations of the Proca action I've found there's a common condition that has to be satisfied, i.e: The number of degrees of freedom allowed to be propagated by the theory has to be three at most (two if the fields...

Maybe I should rephrase the statement. Before thinking a little bit about it I concluded that ## A_\mu^a=0 ## doesn't imply that is impossible to define a connection, it implies that it's not necessary since the partial derivative of a scalar field would be already a gauge covariant derivative...

Hi, this question is related to global and local SU(n) gauge theories. First of all, some notation: ##A## will be the gauge field of the theory (i.e: the 'vector potential' in the case of electromagnetic interactions) also known as 'connection form'. In components: ##A_\mu## can be expanded in...

Hello, I just want to clarify some things with a simple exercise: I have the equation ## \frac{\partial^2 f}{\partial A^\mu \,\partial A^\nu} = 0## and I want to integrate it once assuming that ## f=f(A^1,A^2,...,A^n)=f(A^\rho) ##. I think the solution should be ## \frac{\partial f}{\partial...

This was really useful Peter, just as you pointed out is not possible to set ## G=c=\hbar=1 ##. I thought about this too. Redefining or the Planck charge or the electric charge ## e ## you could have ## \epsilon_0=1 ##, then ## \mu_0=1 ## is satisfied if the unit system is natural ( ##...

Hello, I've been told that 'natural units' ensure ##\hbar=G=c=\mu_0=1## but... when I look for it in Wikipedia I find that there are (mainly) two kinds of natural/geometrized units: The Planck ones and the Stoney ones, (https://en.wikipedia.org/wiki/Geometrized_unit_system) Also, some...