Conservation laws

The conservation of momentum is caused by the Hamiltonian being unchanged under small translations of the coordinate system:

The conservation of angular momentum is caused by the Hamiltonian being unchanged under a small rotation of the coordinate system:

H() = H(+d)

The application of periodic boundary conditions causes a break-down of the symmetry under small rotations and thus a break-down of the conservation of angular momentum:

Usually there are 7 constants: E, p_x, p_y, p_z, L_x, L_y, L_z
E has a unique role in thermodynamics which is caused by the conventional choice of coordinate-system.