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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 :)