How Does Chirality VS. Helicity | Spin and Lorentz Group Work?

Chirality and helicity are like left-handedness and right-handedness, but for tiny particles that move super fast.

Imagine you're holding a spinning top, if it spins clockwise, we might say it's right-handed; if it spins counter-clockwise, it’s left-handed. That’s kind of what helicity is: how the spin of a particle matches its direction of motion, like a little top on a skateboard.

Now, think about wearing gloves, left and right gloves don’t fit each other. That’s like chirality: it's more about what the particle is, not just how it moves or spins at that moment. A particle can be inherently left-handed or right-handed, even if it looks like it's spinning one way now.

The Lorentz group is like a team of rule-makers who decide how things change when they zoom around in space, kind of like traffic rules for the universe. When particles zoom near light speed, their spin (or handedness) can look different to someone watching from far away.

So chirality is more about what the particle is, while helicity is about how it looks as it moves, like a glove vs. how it spins on a skateboard!