Spin Statistics and CPT for Solitons

Conditions are analysed under which the statistics of soliton sectors of massive two-dimensional field theories can be properly defined. A soliton field algebra is defined as a crossed product with the group of soliton sectors. In this algebra, the nonlocal commutation relations are determined and weak locality, spin statistics and CPT theorems are proven. These theorems depart from their usual appearance due to the broken symmetry connecting the inequivalent vacua. An interpretation of these results in terms of modular theory is given. For the neutral subalgebra of the soliton algebra, the theorems hold in a familiar form, and twisted duality is derived.