  We present an analytical study of the spin projection operator of the spin
state and the helicity state. It is pointed out emphatically that the former is
Lorentz covariant, while the latter is a nonrelativistic two-component
operator. In the special case of $\bm p=p_z$, the helicity state and the spin
state are formally identical. However, even so their spin projection operators
are still different and so the helicity state is not a special case of the spin
state. This makes the spinor is the degenerate state of the two different spin
projection operators. The calculation on the lifetime of polarized muons shows
that this difference will inevitably lead to the left-right
polarization-dependent lifetime asymmetry.
