Novel quantum numbers in condensed matter physics

The physics understanding novel quantum numbers in condensed matter physics are discussed. Examples are given from the fields of conducting quasi-one-dimensional conductors 3He–A and the fractional quantum Hall effect. A common feature of these systems is a symmetry breaking whose under parameter describes a discrete symmetry breaking. This lead to flow of charge in the vacuum without excitation of carriers above the symmetry breaking induced gap. Fractional statistics is a natural consequence of the symmetry breaking through the Berry phase accumulated as two quasi-particles are interchanged.