- #1
Gene Naden
- 321
- 64
I am working through the first chapter of Lessons on Particle Physics by Luis Anchordoqui and Francis Halzen. The link is https://arxiv.org/PS_cache/arxiv/pdf/0906/0906.1271v2.pdf
I am on page 22. Equation 1.5.61:
##L_{Dirac}=\psi \bar ( i\gamma^\mu \partial_\mu-m)\psi##
where ##\psi bar = \psi^\dagger \gamma^0##
The authors state that this is invariant. I already proved the invariance of the mass term, but I don't see how to prove the invariance of the term involving ##\partial_\mu##.
The authors seem to feel that the invariance of (1.5.61) follows directly from the transformation properties of ##\psi \bar \gamma^\mu \psi##, which are:
##\psi \bar \prime \gamma^\mu \psi \prime = \Lambda^\mu_{\phantom \alpha} \psi \bar \gamma^\alpha \psi##
My question is how do I see the invariance of ##L_{Dirac}##; how to see the invariance of the first term, which is proportional to ##\psi bar \gamma^\mu \partial_\mu \psi##?
A related question: how to render ##\psi bar## in Tex. When I use \bar or \overline, the bar ends up too far to the right.
I am on page 22. Equation 1.5.61:
##L_{Dirac}=\psi \bar ( i\gamma^\mu \partial_\mu-m)\psi##
where ##\psi bar = \psi^\dagger \gamma^0##
The authors state that this is invariant. I already proved the invariance of the mass term, but I don't see how to prove the invariance of the term involving ##\partial_\mu##.
The authors seem to feel that the invariance of (1.5.61) follows directly from the transformation properties of ##\psi \bar \gamma^\mu \psi##, which are:
##\psi \bar \prime \gamma^\mu \psi \prime = \Lambda^\mu_{\phantom \alpha} \psi \bar \gamma^\alpha \psi##
My question is how do I see the invariance of ##L_{Dirac}##; how to see the invariance of the first term, which is proportional to ##\psi bar \gamma^\mu \partial_\mu \psi##?
A related question: how to render ##\psi bar## in Tex. When I use \bar or \overline, the bar ends up too far to the right.