- #1
CGH
- 7
- 0
Hi there,
i have a very simple question, but still, i don't know what the answer is, her it goes.
I havew Dirac spinor [itex]\psi[/itex] and its hermitian timex [itex]\gamma^0[/itex], [itex]\bar \psi[/itex].
My question is the following:
we can think of [itex]\psi[/itex] as a vector and [itex]\bar \psi[/itex] as a row vector, then, if i take
[tex][\psi,\bar \psi]_+=\psi\bar \psi+\bar\psi \psi[/tex]
the first term is a matrix, and the second one is a number! What did i do wrong?
I tried writting
[itex]\psi=\int (\tex{something})(b u e^{-ipx}+d^\dagger v e^{ipx})[/itex]
in that case, the first term of the anticommutator gives something like [itex]u\bar u[/itex] (a matrix) and the second [itex]\bar u u[/itex] (a number). The problem is still there, my question is: what did i do wrong?
i have a very simple question, but still, i don't know what the answer is, her it goes.
I havew Dirac spinor [itex]\psi[/itex] and its hermitian timex [itex]\gamma^0[/itex], [itex]\bar \psi[/itex].
My question is the following:
we can think of [itex]\psi[/itex] as a vector and [itex]\bar \psi[/itex] as a row vector, then, if i take
[tex][\psi,\bar \psi]_+=\psi\bar \psi+\bar\psi \psi[/tex]
the first term is a matrix, and the second one is a number! What did i do wrong?
I tried writting
[itex]\psi=\int (\tex{something})(b u e^{-ipx}+d^\dagger v e^{ipx})[/itex]
in that case, the first term of the anticommutator gives something like [itex]u\bar u[/itex] (a matrix) and the second [itex]\bar u u[/itex] (a number). The problem is still there, my question is: what did i do wrong?