Conjugate variables in quantum field theory and a refinement of Paulis theorem

Abstract

For the case of spin zero we construct conjugate pairs of operators on Fock space. On states multiplied by polarization vectors coordinate operators Q conjugate to the momentum operator P exist. The massive case is derived from a geometrical quantity, the massless case is realized by taking the limit mass going to zero on the one hand, on the other from conformal transformations. Crucial is the norm problem of the states on which the Q's act: they determine eventually how many independent conjugate pairs exist. It is intriguing that light wedge variables and hence the wedge-local case seems to be preferred.