Quantum chromadynamics at low energies

The author proposes a new description of the salient, non-perturbative features of Quantum Chromodynamics. Starting from a canonically quantized, temporal-gauge, hamiltonian formalism, this thesis shows that invariance under time-independent gauge transformations requires the path integral for SU(N) Yang-Mills theory to include an integration over a compact field defined on the SU(N) manifold at each spacetime point. The author shows that this new path integral reduces to the traditional one only if it is assumed that the fluctuations of the compact field are infinitesimal on the scale of the cutoff. Under this assumption, the compact field decompactifies and behaves like the lost time-component of the gauge-field. It is found, however, that due to a open-quotes centerclose quotes symmetry the compact field has singular fluctations on the scale of the cutoff which the traditional, Yang-Mills path integral is inadequate to describe the strong interaction at low energies. The author suggests instead a simple sine-Gordon effective action to incorporate, in the infrared, the effects of the new non-polynomial terms generated by the non-trival jacobian factor associated with the integration over the gauge group. The thesis then shows, in a large-Ncolor approximation, that this sine-Gordon action confines color charges and produces pairwise, linear interactions between constituents in mesons and in baryons. The author further shows, in a pairing approximation, that this action dynamically breaks chiral symmetry. The thesis ends with a discussion of the renormalization of the full, compact Yang-Mills theory. After describing this theory's perturbative renormalization, the author suggests a procedure for deriving the proposed sine-Gordon action from our bare, compact Yang-Mills theory defined at an energy scale where asymptotic freedom prevails