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Qmechanic ♦
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Bosoneando
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I'm reading the book "massive"Massive neutrinos in physics and astrophysics", by R. N. Mohapatra and P. B. Pal, and have a question about its notation. The Equation 2.10, it says: $$ q_{L}=\binom{u_{L}}{d_{L}} : (2,\frac{1}{3})\\ u_{R}:(1,\frac{4}{3})\\ d_{R}:(1,-\frac{2}{3})\\ \psi_{L}=\binom{\nu_{eL}}{e_{L}} : (2,-1)\\ e_{R}:(1,-2)\\ \tag{2.10} $$ I don't understand where the terms:  $(2,\frac{1}{3}),(1,\frac{4}{3}),(1,-\frac{2}{3}),(2,-1),(1,-2)$ come from and what they represent. Also, it would be nice if anyone can tell me why left handed particles form doublets and right handed particles are singlets.

I'm reading the book "massive neutrinos in physics and astrophysics", and have a question about its notation. The Equation 2.10, it says: $$ q_{L}=\binom{u_{L}}{d_{L}} : (2,\frac{1}{3})\\ u_{R}:(1,\frac{4}{3})\\ d_{R}:(1,-\frac{2}{3})\\ \psi_{L}=\binom{\nu_{eL}}{e_{L}} : (2,-1)\\ e_{R}:(1,-2)\\ \tag{2.10} $$ I don't understand where the terms:$(2,\frac{1}{3}),(1,\frac{4}{3}),(1,-\frac{2}{3}),(2,-1),(1,-2)$ come from and what they represent. Also, it would be nice if anyone can tell me why left handed particles form doublets and right handed particles are singlets.

I'm reading the book "Massive neutrinos in physics and astrophysics" by R. N. Mohapatra and P. B. Pal, and have a question about its notation. The Equation 2.10, it says: $$ q_{L}=\binom{u_{L}}{d_{L}} : (2,\frac{1}{3})\\ u_{R}:(1,\frac{4}{3})\\ d_{R}:(1,-\frac{2}{3})\\ \psi_{L}=\binom{\nu_{eL}}{e_{L}} : (2,-1)\\ e_{R}:(1,-2)\\ \tag{2.10} $$ I don't understand where the terms  $(2,\frac{1}{3}),(1,\frac{4}{3}),(1,-\frac{2}{3}),(2,-1),(1,-2)$ come from and what they represent. Also, it would be nice if anyone can tell me why left handed particles form doublets and right handed particles are singlets.

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Quantumania
Quantumania
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Representation in $SU(2)_{L}\times U(1)_{Y}$

I'm reading the book "massive neutrinos in physics and astrophysics", and have a question about its notation. The Equation 2.10, it says: $$ q_{L}=\binom{u_{L}}{d_{L}} : (2,\frac{1}{3})\\ u_{R}:(1,\frac{4}{3})\\ d_{R}:(1,-\frac{2}{3})\\ \psi_{L}=\binom{\nu_{eL}}{e_{L}} : (2,-1)\\ e_{R}:(1,-2)\\ \tag{2.10} $$ I don't understand where the terms:$(2,\frac{1}{3}),(1,\frac{4}{3}),(1,-\frac{2}{3}),(2,-1),(1,-2)$ come from and what they represent. Also, it would be nice if anyone can tell me why left handed particles form doublets and right handed particles are singlets.