Light-cone Qcd on the Lattice *

A number of physicists have urged the development of a workable light-front (LF) Hamiltonian formulation of QCD [1]. Such a quantisation scheme would yield Lorentz-boost-invariant wavefunctions having a natural constituent structure, providing a power tool in the analysis of hadronic physics. The most obvious applications include inclusive and exclusive hard scattering, and weak and electromagnetic decays, but many new possibilities — yet undreamt of — would be opened up with such a dynamical framework. So why has nobody done it? The same dynamical reasons that lead to simplified wavefunctions, in particular the infamous triviality of the vacuum state in the presence of high-energy cut-offs, also complicate the construction of renormalised LF Hamiltonians. Non-perturbative effects normally associated with the vacuum must appear explicitly in the Hamiltonian. This limits the scope of a traditional perturbative RG analysis (see, for example, Refs. [2] for attempts to formulate weak-coupling LF RG’s). Recently, we have attempted to calculate renormalised LF Hamiltonians in lattice gauge theory, using gauge and Lorentz symmetries of low-energy observables to non-perturbatively fix coupling constant trajectories [3]. So far, this method has been used to study glueballs and the heavy-quark potential in the large-N limit. This talk will review the elements of light-front quantisation of lattice gauge theories, and present some recent results for glueballs.