Gluon condensates from the Hamiltonian formalism

We derive recently obtained relations connecting the logarithmic gauge coupling derivative of the hadron mass and the cosmological constant to the matter and vacuum gluon condensates, within a Hamiltonian framework. The key idea is a canonical transformation which brings the relevant part of the Hamiltonian into a suitable form. We have checked that the transformation is free from rescaling anomalies. The Hamiltonian framework allows one to extend these connections to the case of direct product gauge groups relevant to the Standard Model for example. Furthermore, we illustrate the relations within the Schwinger model and N=2 super Yang–Mills theory (Seiberg–Witten theory). (paper)