What Does It Mean When a Particle Has a Parity of +1?

[Higgy]

I have a simple question about parity and semantics. (And it's coursework/textbook related, so I assume it goes here.)

When someone says, "Such-and-such particle has parity of +1," does this mean that if we operate on the state representing that particle, we get back that same state times +1? That is, for any particle $p$ (not only the proton, which p sometimes stands for),

$$P |p \rangle = \lambda |p \rangle$$

so that, if "the parity of $p$" is, say, -1, then what we mean in saying this is that $\lambda = -1$ for the particle $p$, and

$$P |p \rangle = - |p \rangle$$?

(Analogously, if we say "the particle $p$ has spin of 1/2", what we really mean is that $S_{z} |p \rangle = m_{s} |p \rangle = \pm \frac{1}{2} |p \rangle$, right?)

It's easy to find resources on how to do the math for this stuff, but finding out how to speak about it properly is not as easy. So thanks for any insight!

 

[NateD]

Yes, that is correct. If a particle has a parity of +1, then operating on the state representing the particle with the parity operator will give you back the same state multiplied by +1. Similarly, if the particle has a spin of 1/2, then operating on the state representing the particle with the spin operator in the z-direction will give you back the same state multiplied by +1/2 (or -1/2).