Properties of Antiparticles
Quantum states of a particle and an antiparticle can be interchanged by applying the charge conjugation (C), parity (P), and time reversal (T) operators. If denotes the quantum state of a particle (n) with momentum p, spin J whose component in the z-direction is σ, then one has
where nc denotes the charge conjugate state, i.e., the antiparticle. This behaviour under CPT is the same as the statement that the particle and its antiparticle lie in the same irreducible representation of the Poincaré group. Properties of antiparticles can be related to those of particles through this. If T is a good symmetry of the dynamics, then
where the proportionality sign indicates that there might be a phase on the right hand side. In other words, particle and antiparticle must have
- the same mass m
- the same spin state J
- opposite electric charges q and -q.
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“A drop of water has the properties of the sea, but cannot exhibit a storm. There is beauty of a concert, as well as of a flute; strength of a host, as well as of a hero.”
—Ralph Waldo Emerson (1803–1882)