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?
The Spin Statistics Theorem states that particles with integer spin must obey Bose-Einstein statistics, while particles with half-integer spin must obey Fermi-Dirac statistics.
The Spin Statistics Theorem was first proposed by Wolfgang Pauli in 1926.
The Spin Statistics Theorem is closely related to the exclusion principle, which states that no two particles can occupy the same quantum state simultaneously. This is because particles with half-integer spin (fermions) must follow Fermi-Dirac statistics, which leads to the exclusion principle.
The Spin Statistics Theorem is a fundamental principle in particle physics and has important implications for the behavior of particles at the quantum level. It helps to explain the observed behavior of particles and is essential for understanding phenomena such as superconductivity and superfluidity.
Particles with zero spin, such as photons, are exempt from the Spin Statistics Theorem and do not follow either Bose-Einstein or Fermi-Dirac statistics. Instead, they follow Maxwell-Boltzmann statistics, which does not impose any restrictions on the occupation of quantum states.