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...

Light-front theory may provide a promising avenue of research for nuclear and particle physics, but a Tamm-Dancoff truncation of field theory is required for practical computations. Such a truncation limits the number of virtual mesons allowed in hadronic field theories, or the number of quarks and gluons allowed in bound states described by quantum chromodynamics. Past Tamm-Dancoff renormalization problems are analyzed and a solution is proposed.Despite years of effort, strongly interacting relativistic systems are not understood. We are able to compute the properties of strongly interacting nonrelativistic systems using traditional methods from many-body quantum mechanics. Bound and scattering states of weakly interacting particles are well described by perturbative field theory. The major unsolved problem is that of the highly relativistic bound state. The main difficulties are far better understood now than they were in the 1940s when the effort to use field theory in the study of strong interactions began, but no practical tool has been developed for circumventing these difficulties. In this Letter we propose a path that leads around some of these problems and hopefully through the remainder, lightfront Tamm-Dancoff (LFTD). LFTD is simply the original Tamm-Dancoff approach 1,2 applied to light-front field theory. 3 The most closely related work is that of Brodsky, Lepage, Pauli, and collaborators. 4 Two key areas where the relativistic bound-state problem is central are nuclear physics and quantum chromodynamics (QCD). Consider first the problem of understanding the structure of light nuclei. At low energy and low resolution we can eliminate intermediate-and highenergy degrees of freedom, and describe nuclei using nonrelativistic nucleons interacting via potentials. As energy and resolution are increased we believe a limit is approached in which nuclei are systems of many highly correlated quarks and gluons, but there are many ways that this limit might be reached. In particular, there might be an intermediate regime where nonrelativistic models prove inadequate, but where relatively few hadronic degrees of freedom can be utilized to accurately describe both nuclear structure and response. 5 To determine if this is the case, one must have sufficiently accurate descriptions of strongly interacting hadronic systems. One-pion exchange is usually considered to be adequately described by potentials, so one really wants to push the description at least to the range of two-pion exchange. In this range it is not reasonable to consider pion exchange without including the fact that pions dress nucleons; nor does it make any sense to ignore the fact that pions interact with one another strongly. All strongly interacting degrees of freedom included in any problem should be allowed to fully interact with one another.Hamiltonian methods are extremely effective in describing systems of a few strongly interacting particles, and are immediately suggested by this problem.The second example is the problem of bound states of li...

Hamiltonian light-front quantum field theory constitutes a framework for the non-perturbative solution of invariant masses and correlated parton amplitudes of self-bound systems. By choosing the light-front gauge and adopting a basis function representation, we obtain a large, sparse, Hamiltonian matrix for mass eigenstates of gauge theories that is solvable by adapting the ab initio no-core methods of nuclear many-body theory. Full covariance is recovered in the continuum limit, the infinite matrix limit. There is considerable freedom in the choice of the orthonormal and complete set of basis functions with convenience and convergence rates providing key considerations. Here, we use a two-dimensional harmonic oscillator basis for transverse modes that corresponds with eigensolutions of the soft-wall AdS/QCD model obtained from light-front holography. We outline our approach and present illustrative features of some non-interacting systems in a cavity. We illustrate the first steps towards solving QED by obtaining the mass eigenstates of an electron in a cavity in small basis spaces and discuss the computational challenges.Comment: 35 pages, 15 figures, Revised to correct Fig. 7 and add new Fig. 15 with spectral results for electron in a transverse cavit

In this work we address several issues associated with orbital angular momentum relevant for leading twist polarized deep inelastic scattering. We present a detailed analysis of the light-front helicity operator (generator of rotations in the transverse plane) in QCD. We explicitly show that, the operator constructed from the manifestly gauge invariant, symmetric energy momentum tensor in QCD, in the gauge A + = 0, after the elimination of constraint variables, is equal to the naive canonical form of the light-front helicity operator plus surface terms. Restricting to topologically trivial sector, we eliminate the residual gauge degrees of freedom and surface terms. Having constructed the gauge fixed light-front helicity operator, we introduce quark and gluon orbital helicity distribution functions relevant for polarized deep inelastic scattering as Fourier transform of the forward hadron matrix elements of appropriate bilocal operators. The utility of these definitions is illustrated with the calculation of anomalous dimensions in perturbation theory. We explicitly verify the helicity sum rule for dressed quark and gluon targets in light-front perturbation theory. We also consider internal orbital helicity of a composite system in an arbitrary reference frame and contrast the results in the non-relativistic situation versus the light-front (relativistic) case.

The light-front gauge A; = 0 is known to be a convenient gauge in practical QCD calculations for short-distance behavior, but there are persistent concerns about its use because of its "singular" nature. The study of nonperturbative field theory quantizing on a light-front plane for hadronic bound states requires one to gain a priori systematic control of such gauge singularities. In the second paper of this series we study the two-component old-fashioned perturbation theory and various severe infrared divergences occurring in old-fashioned light-front Hamiltonian calculations for QCD. We also analyze the ultraviolet divergences associated with a large transverse momentum and examine three currently used regulators: an explicit transverse cutoff, transverse dimensional regularization, and a global cutoff. We discuss possible difficulties caused by the light-front gauge singularity in the applications of light-front QCD to both old-fashioned perturbative calculations for short-distance physics and upcoming nonperturbative investigations for hadronic bound states.