Why is helicity a good quantum number if it's not Lorentz invariant?

[touqra]

If an operator commutes with the Hamiltonian, then, the eigenvalues are said to be good quantum numbers. For example, the helicity. But then, helicity is not an invariant for a massive particle. I can always go to another Lorentz frame such that the helicity is now reversed. How then, can it be a good quantum number?

 

[Parlyne]

And, if you did that, the eigenvalue of the Hamiltonian, in general, would also be different; but, this doesn't seem to trouble you.

The point of thinking about "good quantum numbers" isn't that they're the same in all frames. The point is that you can measure them without changing the particle's energy.

 

[DeepQ]

Hi touqra, I am curious where you read that helicity commutes in the quantum Hamiltonian? (Dirac warns us about that.)