Recent content by aries0152

Yes. there is a inverse laplacian. It's a problem of M.Sc. And I am stuck with this term :frown:

I would like to integrate by parts this term- \mu^2 (\nabla^2)^{-1} (\nabla\times B)\dot{B} Here B is a vector and \dot{B} is the time derivative of B. And \mu is just a constant. Can anyone help me?

Yes, when I have run the command @canonicalise!(@); it got stuck. Adding the bracket solve my problem. Thank you. :smile: :smile:

Ok, I figured it out :smile: . I have to declare two substitution by two different name- GaG := G_{a b c} -> \partial_{a}\phi_{b c}+\partial_{b}\phi_{c a}+\partial_{c}\phi_{a b}; GbG := G^{a b c} -> \partial^{a}\phi^{b c}+\partial^{b}\phi^{c a}+\partial^{c}\phi^{a b}; Then substitute...

Thanks that's really helpful. But if I want to calculate GG := G_{a b c} G^{a b c}; How can I substitute the term 'G^{a b c}' with upper indices? I mean G := G^{a b c} -> \partial_{a}\phi^{b c}+\partial_{b}\phi^{c a}+\partial_{c}\phi^{a b}; Because declaring G := G_{a b c} ->...

That is what I did- Are my steps correct? Actually these 9 terms are not my final result. I have posted the general formate of the equation. After the multiplication, I have to separate the terms in time and space coordinates. It will give me about 12-14 separate terms from each of the 9...

sweet springs many many Thanx :-)

I was searching for a software that can calculate the tensor. I found in this forum some people suggest Cadabra (http://cadabra.phi-sci.com/) to calculate the tensors for relativity and field theory. Can anyone help me how can I calculate the product of two antisymmetric tensor using Cadabra...

Actually I want to separate this in space and time component. There is some hint in the "Classical Electrodynamics by Jackson" section 11.6 I can separate the space and time component for two indices (like: F_{\mu\nu} ) but I am not sure how to do it when there are three indices. can...

\phi_{\nu\rho} is a antisymmetric tensor field.

For -\frac{1} {4} F_{\mu\nu} F^{\mu\nu} We can write -\frac{1} {4} F_{i j} F^{ij} -\frac{1}{2}F_{0i} F^{0i} Where F_{\mu\nu} \equiv \partial_\mu W_\nu-\partial_\nu W\mu If there are 3 indices how can I separate them like this? I want to separate \frac{1} {12} G_{\mu\nu\rho}...

I have searched in web and go through some papers. But the use of Dirac Bracket in constraint still unclear to me. It would be better if I have some examples. Can anyone please help me by suggesting books/references where I can find details about using Dirac Bracket?

How can we go from the configuration space of the system to the phase space when velocity can be expressed in terms of momenta?