# Particle Spin, Isospin, weak Isospin

1. May 11, 2010

### billbray

I'm losing my mind trying to differentiate spin, isospin, weak isospin; then there's chirality, helicity - i must be dyslexic and quantumly challenged.

Since it would be a monumental undetaking to do this online, does anyone know of a reliable source i can access online (other than wikipedia, etc) that describes the differences between these types of spin? I think once i get it, i'll be ok..

thanks

2. May 11, 2010

### ansgar

Spin = intrinsic angular momentum in minkowski space

isospin = nuclear isospin, the up and down quark are up and down states in an abstract space due to their (almost) degenerate (=equal)mass. Thus except for their electric charge, they are the same particle in this space. The spin-up state of this particle is then the up quark and the spin-down state is then the down quark. This leads to the neutron and the proton are the same particle as well: the nucleon. The neutron is the then the spin down state and the proton the spin up state.

Weak isospin = spin in another abstract space, you assign SU(2) symmetry (the same symmetry but another space than the space for to the SU(2) symmetry for the up and down quarks)

but what is wrong with the wikipedia anyway?

the difference in these are just in the space they symmetry "acts" upon.

now helicity is the projection of spin on the momentum vector.

chirality is how particles transform under the Lorentz group, i.e. if they transform under the Left or the Right handed SU(2) subgroup of SO(1,3)

for massless particles, helicty and chirality is the same.

3. May 11, 2010

### haael

Chirality - the property of particles (or anything else) so that they are not symmetric under space inversions.
Helicity - the sign of chirality, to distinguish the two versions of a particle; based on convention.
Spin - intrinsic angular momentum; all massless particles with nonzero spin are chiral.
Weak isospin - conserved "charge" that is represented as a vector (unlike electric charge, which is a scalar). Isospin has nothing to do with spin, except the name.
(Strong) isospin - non-conserved quantity. For first-generation fermions it is somehow similar to weak isospin, however it is just a random consequence of small quark masses, not a fundamental symmetry or such.