Conjugate variables in quantum field theory: the conformal case

Within standard quantum field theory of one scalar field we devise a scheme of constructing operators conjugate to the energy-momentum operators of the theory. We require them to arise from local operators, to represent charges, to transform as a vector under Lorentz transformations and to have dimension -1. These specifications single out the charges generating special conformal transformations. We solve all relevant eigenvalue problems, relate them to each other and reconstruct ordinary Fock space in terms of the eigenstates. We have a look at Pauli's theorem, point out applications of these conjugate operators and discuss the extension of the construction to other models.