- #1
gdumont
- 16
- 0
Hi,
I'm trying to do problem 3.5 of Peskin & Schroeder and I don't know where to start.
First of all,
I need to get the hermitian conjugate of the following expression
[tex]\delta \chi = \epsilon F + \sigma^\mu \partial_\mu \phi \sigma^2 \epsilon^\ast[/tex]
where [itex]\epsilon[/itex] is a 2 component-spinor of grassmann numbers, F a complex scalar field [itex]\sigma^\mu = (I,\sigma^i)[/itex] for [itex]i=1,...,3[/itex] and the [itex]\sigma^i[/itex] are the Pauli matrices, [itex]\phi[/itex] is a complex scalar field.
I think the hermitian conjugate would be something like
[tex]\delta \chi^\dagger = \epsilon^\dagger F^\ast + \epsilon^T \sigma^2 \sigma^\mu \partial_\mu \phi^\ast[/tex]
Am I right?
Thanks
Guillaume
Moderator note: I took the liberty of editing in your LaTeX tags.
-TM
I'm trying to do problem 3.5 of Peskin & Schroeder and I don't know where to start.
First of all,
I need to get the hermitian conjugate of the following expression
[tex]\delta \chi = \epsilon F + \sigma^\mu \partial_\mu \phi \sigma^2 \epsilon^\ast[/tex]
where [itex]\epsilon[/itex] is a 2 component-spinor of grassmann numbers, F a complex scalar field [itex]\sigma^\mu = (I,\sigma^i)[/itex] for [itex]i=1,...,3[/itex] and the [itex]\sigma^i[/itex] are the Pauli matrices, [itex]\phi[/itex] is a complex scalar field.
I think the hermitian conjugate would be something like
[tex]\delta \chi^\dagger = \epsilon^\dagger F^\ast + \epsilon^T \sigma^2 \sigma^\mu \partial_\mu \phi^\ast[/tex]
Am I right?
Thanks
Guillaume
Moderator note: I took the liberty of editing in your LaTeX tags.
-TM
Last edited by a moderator: