- #1
infiniteen
- 2
- 0
Hiya,
just stumbled upon this forum searching out 'Peskin errata' when trying to figure out a simple QFT calculation in the textbook. Apparently, there is no mention of the simple derivation that I'm struggling with, so there must be something wrong with my own working. I would really appreciate any help with this.
Anyway, here's the derivation -
basically, the I'd like to ask how (2.38) results from (2.35) and (2.37).
[tex]|\textbf{p}\rangle = \sqrt{2E_{\textbf{p}}}a^{t}_{\textbf{p}}|0\rangle[/tex]
[tex]U(\Lambda)|\textbf{p}\rangle = |\Lambda\textbf{p}\rangle[/tex]
[tex]U(\Lambda)a^{t}_{\textbf{p}}U^{-1}(\Lambda) = \sqrt{\frac{E_{\Lambda\textbf{p}}}{E_{\textbf{p}}}}a^{t}_{\Lambda\textbf{p}}[/tex]
It looks like something that you could hardly go wrong with, but I get the following instead:
[tex]U(\Lambda)a^{t}_{\textbf{p}} = \sqrt{\frac{E_{\Lambda\textbf{p}}}{E_{\textbf{p}}}}a^{t}_{\Lambda\textbf{p}}[/tex]
Thanks in advance for any help rendered :)
just stumbled upon this forum searching out 'Peskin errata' when trying to figure out a simple QFT calculation in the textbook. Apparently, there is no mention of the simple derivation that I'm struggling with, so there must be something wrong with my own working. I would really appreciate any help with this.
Anyway, here's the derivation -
basically, the I'd like to ask how (2.38) results from (2.35) and (2.37).
[tex]|\textbf{p}\rangle = \sqrt{2E_{\textbf{p}}}a^{t}_{\textbf{p}}|0\rangle[/tex]
(2.35)
[tex]U(\Lambda)|\textbf{p}\rangle = |\Lambda\textbf{p}\rangle[/tex]
(2.37)
[tex]U(\Lambda)a^{t}_{\textbf{p}}U^{-1}(\Lambda) = \sqrt{\frac{E_{\Lambda\textbf{p}}}{E_{\textbf{p}}}}a^{t}_{\Lambda\textbf{p}}[/tex]
(2.38)
It looks like something that you could hardly go wrong with, but I get the following instead:
[tex]U(\Lambda)a^{t}_{\textbf{p}} = \sqrt{\frac{E_{\Lambda\textbf{p}}}{E_{\textbf{p}}}}a^{t}_{\Lambda\textbf{p}}[/tex]
Thanks in advance for any help rendered :)