For 10 points, name this concept from physics whereby certain features of physical systems are preserved during transformations.
Potential energy curves corresponding to electronic states of the same this cannot cross. In quantum mechanics, Wigner showed that this type of operation is always represented by a unitary or antiunitary transformation. Also in QM, operations of this type must be a norm-preserving bijection from a Hilbert space of states to itself. When this concept is applied to an action of a system, a corresponding conservation law is produced according to Noether's theorem. Nambu-Goldstone bosons are characteristics of one type of it being spontaneously broken, which is how the Higgs mechanism imparts mass. It can be applied to charge, parity and time. For 10 points, name this concept from physics whereby certain features of physical systems are preserved during transformations.
Potential energy curves corresponding to electronic states of the same this cannot cross.
symmetry transformation [or symmetry operation; or continuous symmetry]