Layperson trying to learn particle physics here. For strong interactions, there are three colors (and corresponding anti-colors) which define the possible states of a particle (i.e. quark) for the strong force. Gluons change these quarks from one state to another. For weak interactions, it seems like there should be two possible properties (and anti-properties) which act similarly, and the weak bosons change between these states. I can make this work by saying +1/2 weak isospin (up-type quarks and neutrinos) and -1/2 weak isospin (down-type quarks and charged leptons) are these two different states instead of simply opposites like red and anti-red. Does that thought process work/make sense? Or in other words, is the upness/downness of a particle the weak version of color in the strong force?
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1$\begingroup$ Does this answer your question? How many kinds of "weak charges" exist? $\endgroup$– John RennieCommented Aug 1, 2023 at 4:25
1 Answer
Yes!
But an explanation for the layperson is not forthcoming.
The particles exist in multiplets that transform as representations of the underlying symmetry group...so $SU(3)$ has the color triplet, while $SU(2)$ has a doublet.
If $SU(2)$ is for spin, then the doublet is the spin up/down state of the same particle, and they are connected by angular momentum raising and lowering operators, which appear in a dipole interaction from an external magnetic field.
If it's isospin (strong nuclear force), then the doublet if proton/neutron, connected by $\pi^+$/$\pi^-$ exchange.
In the weak interaction, the doublet is either up/down quarks or electron/neutrino, and $W^{\pm}$ act as raising and lower operators (aka ladder operators), though ladder operators are undergraduate level quantum mechanics...which is as simple as it gets.
Of course, symmetries are broken, so there are all kinds of caveats, but your general idea is entirely correct.
