Symmetry and Conservation laws

Physical systems are governed by a number of conservation laws. These are often constraints placed upon the behaviour of a system by an underlying symmetry (i.e invariance under some transformation). We expect these laws to apply to all systems we study. If they fail, their failure points to the existence of new physics. In quantum mechanics, conservation laws are represented by operators which commute with the Hamiltonian.

Exploitation of the conservation laws is especially important in a subject like nuclear physics, where the objects of study are remote from ordinary experience, and we can only apply our physical intuition to a limited degree.

The following are some of the conservation laws that we will use. Most of these are familiar to you; some will be explained in the course.

Energy

The total energy of a closed system is constant (i.e. does not change in time).

Momentum

The momentum of a closed system is constant.

(These two are often combined in a relativistic formulation.)

Angular momentum

The angular momentum of a closed system is constant.

Charge

The charge of a closed system is constant.

Baryon number

The number of baryons minus the number of antibaryons in a closed system is constant.

Lepton number

The number of leptons minus the number of antileptons in a closed system is constant.

Reflection symmetry

The parity of a closed system is constant, if the hamiltonian is symmetric under reflection.