- #1

TerryW

Gold Member

- 179

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- Homework Statement:
- I really don't understand what is going on here - can anyone shed any light please?

- Relevant Equations:
- Contained in attachments

At the start of this section §22.5 (Geometric Optics in curved Spacetime), the amplitude of the vector potential is given as:

The Amplitude is then re=expressed a "two-length-scale" expansion (fine!) but it then is modified further to (22.25) by

introducing a "useful" parameter ε...

But this amplitude is now varying at a quite different rate (if ε is anything other than unity) so it isn't equivalent to the original vector potential.

When we get into the calculations, (22.7) is readily derived but I have a problem with the gathering terms O(##\frac {1}{ε}##) or O(ε) etc because, if ε reverts to its eventual value unity thereby recovering the original rate of variation, justification for (22.28) and (22.9) looks a bit thin.

Can anyone explain what is going on here and why this is all reasonable?

Regards

TerryW

**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 (22.25) by

introducing a "useful" parameter ε...

But this amplitude is now varying at a quite different rate (if ε is anything other than unity) so it isn't equivalent to the original vector potential.

When we get into the calculations, (22.7) is readily derived but I have a problem with the gathering terms O(##\frac {1}{ε}##) or O(ε) etc because, if ε reverts to its eventual value unity thereby recovering the original rate of variation, justification for (22.28) and (22.9) looks a bit thin.

Can anyone explain what is going on here and why this is all reasonable?

Regards

TerryW