In this work the determination of low-energy bound states in quantum chromodynamics is recast so that it is linked to a weak-coupling problem. This allows one to approach the solution with the same techniques which solve electrodynamics: namely, a combination of weak-coupling diagrams and many-body quantum mechanics. The key to eliminating necessarily nonperturbative effects is the use of a bare Hamiltonian in which quarks and gluons have nonzero constituent masses rather than the zero rriasses of the current picture. The use of constituent masses cuts off the growth of the running coupling constant and makes it possible that the running coupling never leaves the perturbative domain. For stabilization purposes an artificial potential is added to the Hamiltonian, hut with a coefficient that vanishes a t the physical value of the coupling constant. The weak-coupling approach potentially reconciles the simplicity of the constituent quark model with tlie conlplexities of quantum chromodynamics. The penalty for achieving this perturbative picture is the necessity of formulating the dynamics of QCD in light-front coordinates and of dealing with the complexities of renormalization which such a fornlulation entails. We describe the reriormalization process first using a qualitative phase space cell analysis. and we then set up a precise similarity renormalization scheme with cutoffs on constituent mornenta and exhibit calculations to second order. We outline further computations that remain to be carried out. There is an initial nonperturbative but nonrelativistic calculation of the hadronic masses that deterirlines the artificial potential, with binding energies required to be fourth order in the coupling as in CJED. Next there is a calculation of the leading radiative corrections to these masses which requires our renornialization program. Then the real struggle of finding the right extensions to perturbation theorv to study the strong-coupling behavior of bound states can begin.PACS number(s): 11.1O.Ef. ll.lO.Gh, 1 2 . 3 8 . B~ I. I N T R O D U C T I O NT h e only truly successful approach t o bound states in field theory has been q u a n t u m electrodynamics ( Q E D ) . with its combination of nonrelativistic q u a n t u m mechanics t o handle b o u n d states a n d perturbation theory t o handle relativistic effects. Lattice gauge theory is nlaturing b u t has yet t o rival Q E D ' s comprehensive success. There are four barriers which prohibit a n approach t o q u a n t u m chromodynamics ( Q C D ) t h a t is analogous t o Q E D . T h e barriers a r e (1) t h e unlimited growth of t h e running coupling constant g in t h e infrared region.which invalidates perturbation theory, (2) confinement. which requires potentials t h a t diverge a t long distances as opposed t o t h e Coulombic potentials of perturbation theory. ( 3 ) spontaneous chiral symmetry breaking, which does not occur in perturbation theory. a n d (4) t h e nonperturbative structure of t h e Q C D vacuum. Contrasting t h e gloomy picture of t h e str...

Abstract. A matrix model of an asymptotically free theory with a bound state is solved using a perturbative similarity renormalization group for hamiltonians. An effective hamiltonian with a small width, calculated including the first three terms in the perturbative expansion, is projected on a small set of effective basis states. The resulting small hamiltonian matrix is diagonalized and the exact bound state energy is obtained with accuracy of order 10%. Then, a brief description and an elementary illustration are given for a related light-front Fock space operator method which aims at carrying out analogous steps for hamiltonians of QCD and other theories.

We present new renormalization group equations for effective Hamiltonians in quantum field theory. PACS number(s): 11.1O.Hi

We observe that the linear potential used as a leading approximation for describing color confinement in the instant form of dynamics corresponds to a quadratic confining potential in the front form of dynamics. In particular, the instant-form potentials obtained from lattice gauge theory and string models of hadrons agree with the potentials determined from models using front-form dynamics and light-front holography, not only in their shape, but also in their numerical strength.

Renormalization group limit cycles may be a commonplace for quantum Hamiltonians requiring renormalization, in contrast to experience to date with classical models of critical points, where fixed points are far more common. We discuss the simplest model Hamiltonian identified to date that exhibits a renormalization group limit cycle. The model is a discrete Hamiltonian with two coupling constants and a non-perturbative renormalization group that involves changes in only one of these couplings and is soluble analytically. The Hamiltonian is the discrete analog to a continuum Hamiltonian previously proposed by us.