Abstract:
QCD is constructed as a lattice gauge theory in which the
elements of the link matrices are represented by
non-commuting operators acting in a Hilbert space. The
resulting quantum link model for QCD is formulated with a
fifth Euclidean dimension, whose extent resembles the
inverse gauge coupling of the resulting four-dimensional
theory after dimensional reduction. The inclusion of quarks
is natural in Shamir's variant of Kaplan's fermion method,
which does not require fine-tuning to approach the chiral
limit. A rishon representation in terms of fermionic
constituents of the gluons is derived and the quantum link
Hamiltonian for QCD with a U(N) gauge symmetry is expressed
in terms of glueball, meson and constituent quark operators.
The new formulation of QCD is promising both from an
analytic and from a computational point of view.