Thanks for replying vanhees71,
I'll see if I can find something about the WKB approximation or singular perturbation theory - it doesn't look like I can get a free download of Sommerfield Vol IV. Maybe I can find something in my ancient copy of the Feynman lectures.
Regards
Terry W
Thanks TSny,
I'd already decided that I didn't need ##\varepsilon## and that I could get to all the results by "remembering" the order of the terms, but your reply is helpful in reassuring me that I wan't missing something crucial.
Cheers
Terry
At the start of this section §22.5 (Geometric Optics in curved Spacetime), the amplitude of the vector potential is given as:
A = ##\mathfrak R\{Amplitude \ X \ e^{i\theta}\} ##
The Amplitude is then re=expressed a "two-length-scale" expansion (fine!) but it then is modified further to...
Hi Etotheipi,
Thanks for getting back to me on this.
I'll spend a bit of time comparing your working with mine to see if it generates any further ideas
I hadn't thought of doing this, I just took ##\partial_{\mu} (nu^{\mu}) = 0 ##
I know that the Lorentz frame was used earlier to help...
I've come to a grinding halt with this and I can't see a way forward.
Can someone please take a look at what I've done so far and let me know if what I have done is OK and then if it is, give me a hint on how to proceed.
First up,
Is ## u \cdot \nabla \cdot T = u_\alpha...
Hi JTMetz,
I've just come across your post more or less by accident. I have worked my way through Schaum and (I think) have done all the problems and supplementaries. I reckoned that there were loads of errors in the book, mainly bad typesetting and poor proof reading and I sent an email off to...
##4\pi\mathcal L = -\mathcal e \frac{\partial A_i }{\partial t} - \phi\mathcal E^i{}_{,i} -\frac{1}{2}N\gamma^{\frac{1}{2}}g_{ij}(\mathcal E^i \mathcal E^j +\mathcal B^i\mathcal B^j) +N^i [ijk]\mathcal E^i\mathcal B^j## MTW (21.100)
I'm trying to produce the result required by the problem...
I'm having a bit of trouble getting a clear picture of what is going on here, so if anyone can shed any light, it will be greatly appreciated.
1. I can see how the metric coefficients provide the six numbers per spacepoint, but it can't always be possible to transform the metric into a diagonal...
Hi Peter,
Looking back, I was trying to use this formula to get to an equation for ##\psi ( r )## using the ##\Gamma ## terms but it didn't get anywhere. To do this I had to (completely unjustifiably ) set ##\frac {\partial g_{ij}}{\partial t} ## = 0 so it is no surprise that it didn't work...
Hi Peter and TSny
FollowingTSny's suggestion of using 21.137 and 21.136, I've produced the required result, so thanks for that!
I'm still going to try to get the result by working out R in terms of derivatives of ##\psi## just for the satisfaction of seeing it all come out.
One question...
Hi Peter and TSny,
All I've done here is put ##K_{ik} = 0 ## and ##\Gamma_{pik}## with ##\frac{1}{2}(g_{pi,k} + g_{pk,i} - g_{ki,p})##
I think I'll go with this idea for the moment. (Using 21.137 looks more complicated!) - I can see that quite a bit of work is going to be required and I won't...
Hi Peter,
I'm still not quite getting this!
I've explored the use of the formula:
##N_{i,j} + N_{j,i} - \frac{\partial g_{ij}}{\partial t} = N^p(g_{pi,j} +g_{pj,i} -g_{ij,p} )## derived from 21.67
Using the three components of the metric ##g_{rr}##, ##g_{\theta \theta}## and ##g_{\phi...