Lorentz Transformation on Left & Right Chiral Spinors

[Phys_Reason]

I will start with a summary of my confusion: I came across seemingly contradictory transformation rules for left and right chiral spinor in 2 books, and am unable to understand what part is Physics and what part is convention. Or is it that one of the two books incorrectly writes the transformation rules?

In the following, I hope I have expressed my confusion in more detail and in a somewhat clear language, but please let me know if it is unclear:

I started reading Patrick Labelle's book on SUSY. But I noticed that, when in equation 2.32, Labelle's tranformation for the left and right chiral spinors are the opposite of what Ryder writes in equations 2.73 and 2.74. That is, what Ryder says is the tranformation rule for left chiral spinor is the transformation rule for Labelle's right chiral spinor, and vice versa.

As far as I can tell, both Labelle and Ryder use the same convention for relative positioning of the right and left chiral spinors in the whole 4 component spinor, i.e. - the upper two components make the right and the lower two components make the left chiral spinor.

I am unable to see how these two are equivalent, if they at all are products of different but equivalent conventions.

 

[vanhees71]

In my own manuscript I agree with Labelle's result. Peskin&Schröder has the opposite sign for the entire infinitesimal transformation (that's just a sign convention and mathematically equivalent). I'd say that's 3:1 for Labelle :-).