- #1
Gene Naden
- 321
- 64
I am continuing to work through Lessons on Particle Physics. The link is
https://arxiv.org/PS_cache/arxiv/pdf/0906/0906.1271v2.pdf
I am on page 22, equation (1.5.58). The authors are deriving the Hermitian conjugate of the Dirac equation (in order to construct the current). I am able to reproduce (1.5.58) except for one difference:
I have ##-i\gamma^0 \frac{\partial}{\partial t} \psi^\dagger - i\frac{\partial}{\partial x_k} \psi^\dagger (-\gamma^k)=0##
while the authors have ##-i\gamma^0 \frac{\partial}{\partial t} \psi^\dagger - i\frac{\partial}{\partial x^k} \psi^\dagger (-\gamma^k)=0##
I think, but I am not sure, that they are saying ##(\frac{\partial \psi}{\partial x_\mu})^\dagger=\frac{\partial \psi^\dagger}{\partial x^\mu}##
I would like clarification on whether this is in fact the root of my error. Thanks.
https://arxiv.org/PS_cache/arxiv/pdf/0906/0906.1271v2.pdf
I am on page 22, equation (1.5.58). The authors are deriving the Hermitian conjugate of the Dirac equation (in order to construct the current). I am able to reproduce (1.5.58) except for one difference:
I have ##-i\gamma^0 \frac{\partial}{\partial t} \psi^\dagger - i\frac{\partial}{\partial x_k} \psi^\dagger (-\gamma^k)=0##
while the authors have ##-i\gamma^0 \frac{\partial}{\partial t} \psi^\dagger - i\frac{\partial}{\partial x^k} \psi^\dagger (-\gamma^k)=0##
I think, but I am not sure, that they are saying ##(\frac{\partial \psi}{\partial x_\mu})^\dagger=\frac{\partial \psi^\dagger}{\partial x^\mu}##
I would like clarification on whether this is in fact the root of my error. Thanks.