Isospin Conservation: Calculating I3 and I

[tm33333]

Homework Statement

check for isospin conservation in tau(minus)->muon(minus)+anti electron neutrino

Relevant Equations

I3=Q-Y/2
Y=B+S

I got the I3 values for the tau(minus) to be -1, as charge is -1 and Y=0. For muon(minus) i got I3 to be -1 too using the same equation and the anti electron neutrino to have an isospin of zero (since Q=0, Y=0). This shows I3 to be conserved (which is needed for strong interaction i believe), but what about the overall isospin, I? To calculate this do i add the individual I3's from each side together? or do i take the maximum value from each side (in which case overall isospin wouldn't be conserved)

 

[nrqed]

Homework Statement:: check for isospin conservation in tau(minus)->muon(minus)+anti electron neutrino
Relevant Equations:: I3=Q-Y/2
Y=B+S

I got the I3 values for the tau(minus) to be -1, as charge is -1 and Y=0. For muon(minus) i got I3 to be -1 too using the same equation and the anti electron neutrino to have an isospin of zero (since Q=0, Y=0). This shows I3 to be conserved (which is needed for strong interaction i believe), but what about the overall isospin, I? To calculate this do i add the individual I3's from each side together? or do i take the maximum value from each side (in which case overall isospin wouldn't be conserved)

Isospin is like spin (they are both representations of the group SU(2)), do you recall how to combine two spins. from quantum mechanics?

 

[tm33333]

Isospin is like spin (they are both representations of the group SU(2)), do you recall how to combine two spins. from quantum mechanics?

Sorry can't remember ever doing that? Is it a matter of simply adding them or is it more than that?

 

[nrqed]

It is not adding in the usual sense. You may recall from quantum mechanics that if we combine, say, two spin 1/2, one gets either a total spin of zero or a total spin of 1. In adding two spins $S_1,S_2$, one gets all possible spins going from $S_1 +S_2$ down to $|S_1-S_2|$.