Abstract
We use the Hamiltonian framework to study massless QCD 1+1, i.e. Yang-Mills gauge theories with massless Dirac fermions on a cylinder ( =(1+1) dimensional spacetime S 1× R ) and make explicit the full, non-perturbative structure of these quantum field theory models. We consider N F fermion flavors and gauge group either U( N C , SU( N C ) or another Lie subgroup of U( N C ). In this approach, anomalies are traced back to kinematical requirements such as positivity of the Hamiltonian, gauge invariance, and the condition that all observables are represented by well-defined operators on a Hilbert space. We also give equal time commutators of the energy-momentum tensor and find a gauge-covariant form of the (affine-) Sugawara construction. This allows us to represent massless QCD 1+1 as a gauge theory of Kac-Moody currents and prove its equivalence to a gauged Wess-Zumino-Witten model with a dynamical Yang-Mills field.
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