Suppose there is a particle present on a circle, that is in a spatial dimension which is periodic with radius $R$. Thus it's momentum is quantised. It's momentum takes integer values upto a multiplicative constant ($\frac{n}{R}$). Since there is no spatial symmetry anymore, the momentum won't be transformed by Lorentz transformations between two different observers. So my question is:
- How would we transform the momentum values between two different frames of reference?
- Would a governing rule for finding answer 1 be that in any frame, the momentum must be same in structure (integer valued upto a multiplicative constant)?
