Recent content by dpopchev

Homework Statement If I have the following expansion f(r,t) \approx g(r) + \varepsilon \delta g(r,t) + O(\varepsilon^2) This means for other function U(f(r,t)) U(f(r,t)) = U( g(r) + \varepsilon \delta g(r,t)) \approx U(g) + \varepsilon \delta g \dfrac{dU}{dg} + O(\varepsilon^2) Then up to...

R_SOLUTION: I should have been more careful with the indices juggling, keeping track in which spacetime I am working and definitions. The definition of Rieman tensor comes from the commutator of two covariant derivatives acting on vector field \left[ \nabla_{\mu}, \nabla_{\nu} \right]...

SOLUTION: I should have been more careful with the indices juggling, keeping track in which spacetime I am working and definitions. The definition of Rieman tensor comes from the commutator of two covariant derivatives acting on vector field \left[ \nabla_{\mu}, \nabla_{\nu} \right] V^\alpha...

Here I will post detailed calculations, also will reorganize the post as a whole since as I see it now, it is very chaotic. For the rest of the post I am working with torsion free connection, and thus my Christoffel symbols will be defined as \Gamma^\sigma_{\mu\nu} = \dfrac{1}{2}...

I am trying to calculate the Ricci tensor in terms of small perturbation hμν over arbitrary background metric gμν whit the restriction \left| \dfrac{h_{\mu\nu}}{g_{\mu\nu}} \right| << 1 Following Michele Maggiore Gravitational Waves vol 1 I correctly expressed the Chirstoffel symbol in terms...

I found this pdf where question 1 is similar: http://users.wpi.edu/~physics/ph1130c06/Images/ppset05.PDF

Should not have the need for initial energy: https://www.hep.wisc.edu/~prepost/407/compton/compton.pdf EDIT: made a calculation mistake, have no idea how to approach this questions

I think OP is missing the basic concepts and needs to catch up with them. When I stumble upon such problem, as already suggested, I use google to find an appropriate way to handle it. From what I see in the syllabus maybe more appropriate book is something like this...

The dependent variable changes with respect to the independent one, thus dependent = function of independent. To solve the equation is to find a function of the independent variable, which has this special property that its second derivative + first derivative to the power of 3 - 3 times the...

Can you give more information from where you took this example as it seems a little out of context. From what I see the i stands for the identity matrix, and id for the 0 matrix, the O with the cross stands for tensor product, and take into account that < | and | > come from bra - ket notation...

You tried with simple examples ? See here and if more questions arose don't hesitate to ask: https://en.wikipedia.org/wiki/Set_theory#Basic_concepts_and_notation

So easy ! https://www.physicsforums.com/threads/relativistic-energy-derivation.753362/ Outline: m\;u.du/dt (...)^{-1/2} + mu.du/dt \;u.u/c^2 (...)^{-3/2} = mu.du/dt (...)^{-3/2} \left( (...)^{-1/2+3/2} + u.u/c^2 \right) = ...

Be careful of the u^3 as despite not explicitly labelled with a arrow it is a vector, thus always respect the dot and write it. In this case do it as u.u u The easiest way to think about it is by writing it by components using Einstein summation convection with upper and lower indexes...

EDIT: poor replay skills I followed Griffits and I am stuck in the calculation. The scalar field is not time dependent as actually it is the mass of a test particle, so his original γ becomes \eta \equiv m In the calculation we want to derive the work-energy theorem thus W = \int...

I have been an A and IGCSE level physics tutor for the past 3 years in a school in Bulgaria. Also I am on the CIE examination reserves. I am interested in developing my teaching skills in this syllabuses also on several similar as Pre-U and etc. EDIT: also math related as I am theoretical...