In physics, the C parity or charge parity is a multiplicative quantum number of some particles that describes their behavior under the symmetry operation of charge conjugation.
Contents
- Formalism
- Eigenvalues
- Eigenstates
- Multiparticle systems
- Experimental tests of C parity conservation
- References
Charge conjugation changes the sign of all quantum charges (that is, additive quantum numbers), including the electrical charge, baryon number and lepton number, and the flavor charges strangeness, charm, bottomness, topness and Isospin (I3). In contrast, it doesn't affect the mass, linear momentum or spin of a particle.
Formalism
Consider an operation
Both states must be normalizable, so that
which implies that
By acting on the particle twice with the
we see that
meaning that the charge conjugation operator is Hermitian and therefore a physically observable quantity.
Eigenvalues
For the eigenstates of charge conjugation,
As with parity transformations, applying
allowing only eigenvalues of
Eigenstates
The above implies that
Multiparticle systems
For a system of free particles, the C parity is the product of C parities for each particle.
In a pair of bound bosons there is an additional component due to the orbital angular momentum. For example, in a bound state of two pions, π+ π− with an orbital angular momentum L, exchanging π+ and π− inverts the relative position vector, which is identical to a parity operation. Under this operation, the angular part of the spatial wave function contributes a phase factor of (−1)L, where L is the angular momentum quantum number associated with L.
With a two-fermion system, two extra factors appear: one comes from the spin part of the wave function, and the second from the exchange of a fermion by its antifermion.
Bound states can be described with the spectroscopic notation 2S+1LJ (see term symbol), where S is the total spin quantum number, L the total orbital momentum quantum number and J the total angular momentum quantum number. Example: the positronium is a bound state electron-positron similar to an hydrogen atom. The parapositronium and ortopositronium correspond to the states 1S0 and 3S1.