I Understanding the Spin-Statistics Theorem: A Modern Notation Approach

[filip97]

i read that question and Weinberg book (A,B)-Representation of Lorentz Group: Coefficient functions of fields

why u(a,b)=Cab/sqrt(2m) ?

where Cab is Clebsch-Gordan coefficients, and m is mass of particle

 

[DarMM]

i read that question and Weinberg book (A,B)-Representation of Lorentz Group: Coefficient functions of fields

why u(a,b)=Cab/sqrt(2m) ?

where Cab is Clebsch-Gordan coefficients, and m is mass of particle

Basically because transformations on $u_{ab}(0,\sigma)$ for a massive particle are transformations that don't alter momentum by boosting to another frame, i.e. occur in one frame and don't involve translation. The only transformations then are rotations, thus they are Clebsch-Gordan coefficients.

 

[filip97]

Basically because transformations on $u_{ab}(0,\sigma)$ for a massive particle are transformations that don't alter momentum by boosting to another frame, i.e. occur in one frame and don't involve translation. The only transformations then are rotations, thus they are Clebsch-Gordan coefficients.

Formulas please

 

[DarMM]

Formulas please

Weinberg has all the formulae, I'd just be repeating him. I thought you wanted the reasoning as such, what gap does Weinberg's text have for you?

 

[filip97]

Weinberg has all the formulae, I'd just be repeating him. I thought you wanted the reasoning as such, what gap does Weinberg's text have for you?

I think formulas in modern notation, i don't understand weinberg notation for sst , thanks !