Quantum Chromodynamics on a Lattice

Abstract

The phenomenological description of hadrons in terms of quarks continues to be successful; the most recent advance was the description of the new particles as built from charmed quarks. Mean-while theoretical advances have led to the formulation of a specific field theory of quarks, namely “quantum chromodynamics¹.” In quantum chromodynamics, the standard quarks of the quark model are each xeroxed twice to make three different “colors” of quarks, say red, yellow and blue quarks. The three colors form the basis for an SU(3) group (this group is a second SU(3) group, in addition to the Gell-Mann-Ne’eman SU(3).) The quarks interact with an octet of colored vector mesons called gluons. The theory is renormalizable and in some ways is similar to quantum electrodynamics. There is one very crucial difference however: in quantum chromodynamics the gluons interact with themselves. A consequence of this interaction is “asymptotic freedom².” Asymptotic freedom arises as follows. The fundamental interactions of quarks and gluons are modified by “radiative” corrections of higher order in the quark-gluon coupling constant. These radiative corrections depend on the quark and gluon momenta. A careful analysis shows that the cumulative effect of radiative corrections to all orders can be characterized by a momentum-dependent effective coupling constant. The effective coupling is found to vanish in the limit of large momenta (to be precise, large momentum transfers between the quarks and gluons). This is called asymptotic freedom. As a result of asymptotic freedom the quarks can behave as nearly free particles at short distances; this is required to explain the high energy electron scattering experiments³. Meanwhile the interactions of quarks at long distances can be strong enough to bind the quarks into the observed bound states; protons, mesons, etc.