The discussion revolves around the Spin-Statistics Theorem and its representation within the context of the Lorentz Group, specifically focusing on the coefficient functions of fields as described in Weinberg's work. Participants are exploring the mathematical formulations and reasoning behind the Clebsch-Gordan coefficients and their application to massive particles.
Participants appear to have differing levels of understanding regarding Weinberg's notation and the specific formulas related to the Spin-Statistics Theorem. There is no consensus on the clarity of Weinberg's text or the need for additional formulas.
Participants express uncertainty regarding the notation used by Weinberg and the specific mathematical formulations, indicating potential limitations in understanding the material presented in the text.
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 said: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 said: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.
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 said:Formulas please
I think formulas in modern notation, i don't understand weinberg notation for sst , thanks !DarMM said: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?