Recent content by orentago

Does anyone have any hints for this, or should I have another stab and post my findings?

I'm still stuck on this. I tried to go for the former of the two approaches mentioned above. I let \psi\rightarrow\psi_L and \overline{\psi}\rightarrow\overline{\psi}_L, then: L=c\overline{\psi}_L\left(\mathrm{i}\hbar\gamma^\mu\partial_\mu-mc\right)\psi_L Splitting this into two terms and...

Homework Statement From Mandl and Shaw (exercise 4.5): Deduce the equations of motion for the fields: \psi_L(x)\equiv{1 \over 2} (1-\gamma_5)\psi(x) \psi_R(x)\equiv{1 \over 2} (1+\gamma_5)\psi(x) for non-vanishing mass, and show that they decouple in the limit m=0. Hence show that the...

Ah no, problem solved. I evaluated my commutators wrongly (they should be the negative of the Kronecker delta, not the positive).

Homework Statement Given that, for operators A and B: \mathrm{e}^{\mathrm{i} \alpha A} B \mathrm{e}^{-\mathrm{i} \alpha A} = \sum_{n=0}^{\infinity} {(\mathrm{i}\alpha)^n \over n!} B_n where B_0 = B and B_n = [A, B_{n-1}] for n=1,2,... show that: P_1...

Actually no worries I've sorted it: applying charge conjugation twice takes one back to the original state. It's so simple I don't know why I didn't think of it!

Does anyone have any ideas for the second question, or should I supply more information?

I have another question. It can be shown that C a(\mathbf{k})C^{-1}=\eta_c b(\mathbf{k}) and C b(\mathbf{k})C^{-1}=\eta_c^* a(\mathbf{k}). I can show the first one fairly easily by just substituting the full expressions of the fields into the transformation condition above. I'm a little...

Homework Statement Show that the complex Klein-Gordon Lagrangian density: L=N\left(\partial_\alpha\phi^{\dagger}(x)\partial^\alpha\phi(x)-\mu^2\phi^{\dagger}(x)\phi(x)\right) is invariant under charge conjugation: \phi(x)\rightarrow C\phi(x)C^{-1}=\eta_c \phi^\dagger (x) Where C...

Ah therein would lie part of my confusion: this isn't stated formally in the book. All sorted now. Thanks for humouring me on this one.

Okay, I've pretty much arrived at the answer, except I still need to remove a factor of V somehow. After I integrate I get this: \omega_{\mathbf{k'}} \sum_{\mathbf{k}} \sqrt{\frac{2 \hbar c^2 }{V \omega_{\mathbf{k}}}} \left( a(\mathbf{k}) \delta_{kk'} + a^\dagger (\mathbf{k})...

Awesome. That's really helpful! I feel I have enough information to progress now. Thanks a lot! Actually one last thing. How would you represent the second of the Dirac deltas (with the plus in) in Kronecker delta format? Or would it be eliminated in the integral by default? EDIT: actually how...

Right, I've had another go at this. Here's my working so far. First I'll just outline the Fourier transform I'll be using (in one dimension). \int^\infty_{-\infty} \mathrm{e}^{\mathrm{i}a x} \mathrm{e}^{-\mathrm{i}w x}\mathrm{d}x=2\pi \delta(w-a) And the inverse: \int^\infty_{-\infty}...

Except mine apparently. I did Fourier transforms but the course skipped over delta functions. Thanks for the help. I'll read around a bit more, have another stab at it and let you know if I run into any more problems.

I'm self-teaching from Mandl and Shaw, and haven't seen anything like that yet :-S. I'm basically attempting exercise 3.1, from chapter 3 on the Klein Gordon field.