- #1
oliveriandrea
- 9
- 0
Hello,
sorry for my english..
I have a problem with weyl's spinors notation.
I'm confused, becouse i read more books (like Landau, Srednicki and Peskin) and it's seems to me that all of them use different and incompatible notations..
If i define
[itex]M=\exp\left(-\frac{1}{2}(i\theta+\beta)\sigma\right)[/itex]
as a generic lorentz transformation in left spinor rappresentation
if [itex] \psi_\alpha [/itex] represent left covariant spinor that transform with M
[itex] \psi^\alpha [/itex] represent left contravariant spinor that transform with M^(-1) right?
so how do i represent covariant and contravariant right spinor in dotted notation?
and how do they transform in connection with M matrix?
if i transform covariant left spinor with [itex]\epsilon^{\alpha\beta}[/itex] I obtain a contravariant left spinor or not?
the inner product involves dotted-dotted spinors (covariant and contravariant) or dotted-undotted spinors?
thank you :)
sorry for my english..
I have a problem with weyl's spinors notation.
I'm confused, becouse i read more books (like Landau, Srednicki and Peskin) and it's seems to me that all of them use different and incompatible notations..
If i define
[itex]M=\exp\left(-\frac{1}{2}(i\theta+\beta)\sigma\right)[/itex]
as a generic lorentz transformation in left spinor rappresentation
if [itex] \psi_\alpha [/itex] represent left covariant spinor that transform with M
[itex] \psi^\alpha [/itex] represent left contravariant spinor that transform with M^(-1) right?
so how do i represent covariant and contravariant right spinor in dotted notation?
and how do they transform in connection with M matrix?
if i transform covariant left spinor with [itex]\epsilon^{\alpha\beta}[/itex] I obtain a contravariant left spinor or not?
the inner product involves dotted-dotted spinors (covariant and contravariant) or dotted-undotted spinors?
thank you :)