Some fun (yet nice) questions on QFT

[ChrisVer]

I was looking through some problems on QFT, and I found these exercises:
http://www.damtp.cam.ac.uk/user/tong/qft/oh4.pdf
I was wondering about questions 9 and 10...
Q9 : speaking I guess aftermatch ,why was there a factor of 2 wrong in the published result? To be honest I don't quiet understand the question posed by Pauli, was he asking for something like: \gamma \rightarrow \phi \phi or \gamma \gamma \rightarrow \phi \phi or even \phi \phi ( \rightarrow \gamma \rightarrow ) \phi \phi?
Q10: any hint for why classical physicists hadn't introduced fields for the particles like electrons? was that because QM and wavefunctions were not existent at that time?

 

[Q.B.]

Hi,

Q9: I think he meant $\gamma \rightarrow \phi \phi$. The factor 2 might be due to a symmetry factor that has to be taken into account when outgoing particles are identical (a consequence of Pauli's own principle).

Q10: I would say that indeed fields have their interest when particles cannot be described in terms on trajectories only (i.e. when we go quantum mechanical) and/or when we need to describe the different possibilities for representing the Lorentz group.

 

[nrqed]

I was looking through some problems on QFT, and I found these exercises:
http://www.damtp.cam.ac.uk/user/tong/qft/oh4.pdf
I was wondering about questions 9 and 10...
Q9 : speaking I guess aftermatch ,why was there a factor of 2 wrong in the published result? To be honest I don't quiet understand the question posed by Pauli, was he asking for something like: \gamma \rightarrow \phi \phi or \gamma \gamma \rightarrow \phi \phi or even \phi \phi ( \rightarrow \gamma \rightarrow ) \phi \phi?
Q10: any hint for why classical physicists hadn't introduced fields for the particles like electrons? was that because QM and wavefunctions were not existent at that time?

I agree with QB for Q9, it must be \gamma \rightarrow \phi \phi (well, this is not possible for an on-shell photon so it must be off-shell) and the factor of two is almost certainly the symmetry factor due to the indistinguishability of the two final particles. As for Q10, the key point is that there can be no coherent states for fermions. The E and B fields we observed in experiments are coherent states of the photon fields and there is no such state for fermions fields.