String Condensation—An Unification of Light and Fermions

Abstract

This book has three types of theories: boson, fermion, and gauge theories. It asks which theories describe the elementary particles in our universe. Surprisingly, elementary particles are described by the two more complicated and non-local theories: fermion theory and gauge theory. In the last chapter and in this chapter it is demonstrated that fermion and gauge theory are not really needed. Boson theory may be able to explain everything, since both fermion theory and gauge theory can emerge from local bosonic models (or qbit models), if bosons (qbits) are organized to have a string-net condensed order. This chapter studies soluble quantum spin models to explain string-net condensation. It finds that gauge bosons are simply collective excitations associated with string density wave (with the electric field corresponding to the string density). The fermons can appear as the ends of open strings. Thus the string-net order explains the emergence of gauge bosons and fermions. It unifies gauge interaction and Fermi statistics. The chapter shows that non-orientable strings give rise to Z_2 gauge theory while the orientable string give rise to U(1) gauge theory.