Recent content by xboy

OK, I didn't phrase that right. What I meant was that the real line has a discrete topology. Now I take the group of translations on it. My question was whether this group would be any different from the group of translations on a (real line with usual topology) and I think that they would be...

Hi. I wanted to know in what way the group of translations on a real line with discrete topology (let's call it Td) will be different from the group of translations on a real line with the usual topology (lets call it Tu)? Is Td a Lie Group? Will it have the same generator as Tu?

What I meant is this : suppose I have a function f(x,y). Can you write down the total derivative of f w.r.t x i.e df/dx in terms of the partial derivatives \partial_{x}f and \partial_{y}f ? If you can do that for f and x, go ahead and do it for rho and t. If you aren't sure of which equation...

For part a, how'd you write the total time derivative of rho in terms of its partial derivatives? For part b, what do you think the relevant equations are?

Turin, can you please tell me how you interpret ' bounded region of each spacelike hypersurface x^0 = const. Does it mean that x^0 = const. are closed hypersurfaces ? Or is it something else?

I don't like this solution either. For one, it does not really use the formula mentioned. The only way out is to say that the surface isn't closed. But if that's not what Schutz meant, what did he mean by that sentence?

If it vanishes, that means it's a constant and independent of x^0 In your first post you did not use the fact that we are dealing here with a closed hypersurface, which is what Schutz seems to be implying.

Turin, If I combine this with divergence theorem shouldn't the integral just vanish, as a consequence of the conservation of energy-momentum?

Maria, I suspect this question would be better answered were you to post it in the Solid State forum. After all, this is not a homework question. Anyways, here's what I can tell you: We do know that in solids ions are periodically arranged, and we can expect that their electrostatic potentials...

I checked the question on Schutz and it says that the stress energy tensor is non zero 'only in some bounded region of each spacelike hypersurface x^0 = const. '. I don't understand what that's supposed to mean. Does it mean we're working with closed surfaces and Gauss' law applies. What do you...

So you agree that you need to use another law. The argument can be stated this way: Let us consider a system of particles. According to N1L none of the momentums of each particle remains constant unless forces act on it. Here the forces are all forces of interaction. So the total rate of...

When you use F = ma, N1L is automatically implied, is it not.

Walia, your derivation seems correct to me. I can't think of a case of your derivation being invalid except for the metric being non-symmetric. But I don't know if the metric can be non-symmetric at all.

I think it would be fair to say that it's a consequence of both first and third laws.

You remember what x^2 - y^2 equals to?