SU(2) isospin

τx,τy, τz

+ τ- τz and τ2)

Pairs u,d quarks (originally, neutron and proton) for the construction and properties of hadrons.

SU(3) favor

U, V, T, T3, Λ8

Combines u,d,s for building hadrons. Extension of SU(2)

SU(3) color

U, V, T, T3, Λ8

Generates QCD related to the color charges (R,G,B)

U(1) charge

Q

Overall phase transformation that requires charge confirmation.

U(1) Baryon #

B

Overall phase transformation that requires Baryon number confirmation.

U(1) Hypercharge

Y

U(1) that leads to Electroweak

Translation

 

 

Rotation

 

 

Boost

 

 

SU(2)L weak isospin

 

 

Parity

 

 

U(1) baryon number

 

 

Charge conjugation

 

 

Time reversal

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Note, all of the tranformations are ultimately some type of phase transformation. This is due to the unitarity requirement for the transforamtions on quantum states. More than one symmetry is required in our complete system. Our representation should be compatible with the symmetries required.