Physics Electroweak Theory Left-Handed Doublets and Hypercharge in the SU(2) x U(1)L Framework
The core principle of Electroweak Theory posits that weak and electromagnetic interactions unify under a single gauge group $SU(2)_L \times U(1)_Y$, where only left-handed fermions transform as doublets ($I=1/2$) while right-handed fermions are singlets ($I=0$). A conserved quantum number termed "weak hypercharge" ($Y_W$) is assigned to these multiplets such that electric charge $Q$ satisfies the relation $Q = I_3 + Y_W/2$. This framework establishes the mechanism distinguishing chiral generations within particle physics by defining how gauge transformations mix weak bosons and photon fields.
Physics Electroweak Theory Left-Handed Doublets and Hypercharge in the SU(2) x U(1)L Framework
The core principle of Electroweak Theory posits that weak and electromagnetic interactions unify under a single gauge group $SU(2)_L \times U(1)_Y$, where only left-handed fermions transform as doubl…