Theory of a Fusion Field Composed of Free Massless Spinor Fields in Two Dimensions
Abstract
A theory of a free massless fusion field composed of free massless spinor fields are investigated in the framework of the indefinitemetric quantum field theory. It is found that the free theory already interesting features characteristic of twodimensional massless models. On the basis of finitevolume considerations, a massless ``scalar'' fusion theory is constructed consistently in the infinitevolume limit. Two different sets of charge operators are found to exist. Subsidiary conditions in terms of the charges define the positivedefinite physical Hilbert space H_{phys}. However the conditions are not unique and lead us to different structures of the Hilbert space. Some cases have the unique vacuum in H_{phys}, whereas other cases have vacuum degeneracy, i.e., the vacua characterized in terms of one or two parameters (θvacua). Which realization of the symmetries generated by the charges shows up depends on the vacuum chosen. Various cases are possible. Poincaré transformations are discussed. The fusion fields are not Lorentz scalars in a strict sense, but they behave as scalars in H_{phys}.
 Publication:

Progress of Theoretical Physics
 Pub Date:
 March 1982
 DOI:
 10.1143/PTP.67.935
 Bibcode:
 1982PThPh..67..935S