Conjugate variables in quantum field theory and natural symplectic structures

Within standard quantum field theory we establish relations which operators conjugate to the energy–momentum operator of the theory would have. They thus can be understood as representing the effect of coordinate operators. The non-trivial commutation relations we derive constitute natural symplectic structures in the theory. The example which is based on the energy–momentum tensor of the theory is constructed to all orders of perturbation theory. The reference theory is massless ϕ4ϕ4. The extension to other theories is indicated.