Mathematically, the symmetries can be described by a smooth symmetry group G . Under the action of this group, H 0 is invariant. The explicit symmetry breaking then comes from a second term in the Hamiltonian, H int , which is not invariant under the action of G . This is sometimes interpreted as an interaction of the system with itself or possibly with an externally applied field. It is often chosen to contain a factor of a small interaction parameter.