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We study spontaneous symmetry breaking in (l+l)-dimensional qh4 theory using the light-front formulation of field theory. Since the physical vacuum is always the same as the perturbative vacuum in light-front field theory the fields must develop a vacuum expectation value through the zero-mode components of the field. We solve the nonlinear operator equation for the zero mode in the one-mode approximation. We find that spontaneous symmetry breaking occurs at Xcritical = 47r (3 + 4 p 2 , which is consistent with the value Xc,itic,l = 54.27p2 obtained in the equal-time theory. We calculate the vacuum expectation value as a function of the coupling constant in the broken phase both numerically and analytically using the 6 expansion. We find two equivalent broken phases. Finally we show that the energy levels of the system have the expected behavior for the broken phase. PACS number(s): ll.lO.Ef, 11.30.Q~

We use the light-front Hamiltonian of transverse lattice gauge theory to compute from first principles the glueball spectrum and light-front wave functions in the leading order of the 1͞N c color expansion. We find 0 11 , 2 11 , and 1 12 glueballs having masses consistent with N c 3 data available from Euclidean lattice path integral methods. The wave functions exhibit a light-front constituent gluon structure. [S0031-9007(98) PACS numbers: 12.39. Mk, 11.15.Pg, 12.38.Gc, 12.38.Lg There is growing experimental evidence that glueballs, bound states of gluons in the SU(3) gauge theory quantum chromodynamics (QCD), have been discovered in the mass range 1.5-1.7 GeV [1][2][3]. But the confinement feature of QCD-interactions grow stronger as the energy of a process decreases-complicates any first principles calculation of the bound state problem. Until now, the most successful bound state calculations use a Euclidean spacetime lattice and simulate the path integral by Monte Carlo methods. These difficult calculations are now roughly consistent with the experimental signatures of glueballs [2,4], although much detail remains to be clarified. Therefore, it is important to have some independent method of calculating the properties of glueballs from first principles in gauge theory. In this Letter, we present our first results on this problem using an effective light-front Hamiltonian quantization (canonical quantization on a null plane in spacetime). This is the transverse lattice method, suggested originally by Bardeen and Pearson [5,6], which we have developed to the extent that quantitative calculations are now feasible [7,8].Although this work is ostensibly about glueballs, we have a more general motivation for developing the lightfront Hamiltonian formulation of gauge theory. A lightfront Hamiltonian has Lorentz-frame-independent wave functions. Together with the simplicity of the light-front vacuum, this leads to a field-theoretic realization of the parton model for hadrons on which so much understanding is based. The rich phenomenology in hadronic and nuclear physics that would follow from knowledge of the light-front wave functions is surveyed in the lectures of Brodsky [9]. We will use the glueball problem in QCD, which is especially difficult computationally, as a quantitative test of our light-front formalism.A detailed account of our methods and various quantitative tests that we have performed, mostly in 2 1 1 dimensions, can be found in Refs. [7,8], but we will briefly review the salient points below. We will work in the leading order of the 1͞N c expansion of SU͑N c ͒ gauge theory, which omits the 1͞N 2 c -suppressed glue configurations. It also removes "sea" quarks from our theory, an approximation also used in the Euclidean lattice calculations. We work on a coarse transverse lattice, using an effective potential tuned to minimize discretization errors. The ground state J P C 0 11 glueball mass is M 3.3 6 0.2 p s, where s ഠ 0.1936 GeV 2 is the string tension, and is consistent with SU(2) and SU(3) re...

Accurate non-perturbative calculations of glueballs are performed using light-front quantised SU(N) gauge theory, to leading order of the 1/N expansion. Based on early work of Bardeen and Pearson, disordered gauge-covariant link variables M on a coarse transverse lattice are used to approximate the physical gauge degrees of freedom. Simple energetics imply that, at lattice spacings of order the inverse QCD scale, the effective light-front Hamiltonian can be expanded in gauge-invariant powers of M: a colour-dielectric expansion. This leads to a self-consistent constituent structure of boundstates. We fix the couplings of this expansion by optimising Lorentz covariance of low-energy eigenfunctions. To lowest non-trivial order of the expansion, we have found a one-parameter trajectory of couplings that enhances Lorentz covariance. On this trajectory the masses of nearly-covariant glueball states exhibit approximate scaling, having values consistent with large-N extrapolations of continuum results from other methods. There is very little variation with N in pure Yang-Mills theory: the lightest glueball mass changes by only a few percent between SU(3) and SU(infinity). The corresponding light-front wavefunctions show an unconventional structure. We also examine restoration of rotational invariance in the heavy-source potential.Comment: 24 pages, 21 figure