Formulating Light Cone QCD on the Lattice

We present the near light cone Hamiltonian $H$ in lattice QCD depending on the parameter $\eta$, which gives the distance to the light cone. Since the vacuum has zero momentum we can derive an effective Hamiltonian $H_{eff}$ from $H$ which is only quadratic in the momenta and therefore solvable by standard methods. An approximate ground state wave functional is determined variationally in the limit $\eta \to 0$.Comment: 48 pages, 8 figure

Calculation of the Mass Spectrum of QED-2 in Light-Front Coordinates

With the aim of a further investigation of the nonperturbative Hamiltonian approach in gauge field theories, the mass spectrum of QED-2 is calculated numerically by using the corrected Hamiltonian that was constructed previously for this theory on the light front. The calculations are performed for a wide range of the ratio of the fermion mass to the fermion charge at all values of the parameter \hat\theta related to the vacuum angle \theta. The results obtained in this way are compared with the results of known numerical calculations on a lattice in Lorentz coordinates. A method is proposed for extrapolating the values obtained within the infrared-regularized theory to the limit where the regularization is removed. The resulting spectrum agrees well with the known results in the case of \theta=0; in the case of \theta=\pi, there is agreement at small values of the fermion mass (below the phase-transition point).Comment: LaTex 2.09, 20 pages, 7 figures. New improved expression for the effective LF Hamiltonian was adde

Gauge Invariant Regularization of Quantum Field Theory on the Light-Front

Gauge invariant regularization of quantum field theory in the framework of Light-Front (LF) Hamiltonian formalism via introducing a lattice in transverse coordinates and imposing boundary conditions in LF coordinate $x^-$ for gauge fields on the interval $|x^-|\le L$ is considered. The remaining ultraviolet divergences in the longitudinal momentum $p_-$ are removed by gauge invariant finite mode regularization. We find that LF canonical formalism for the introduced regularization does not contain usual most complicated second class constraints connecting zero and nonzero modes of gauge fields. The described scheme can be used either for the regularization of conventional gauge theory or for gauge invariant formulation of effective low-energy models on the LF. The lack of explicit Lorentz invariance in our approach leads to difficulty with defining the vacuum state. We discuss this difficulty, particulary, in the connection with the problem of taking the limit of continuous space.Comment: LaTeX 2.09, 15 pages, Proceedings of "12th V.Fock School of Physics", St-Petersburg 200

Quantum Fields on the Light Front, Formulation in Coordinates close to the Light Front, Lattice Approximation

We review the fundamental ideas of quantizing a theory on a Light Front including the Hamiltonian approach to the problem of bound states on the Light Front and the limiting transition from formulating a theory in Lorentzian coordinates (where the quantization occurs on spacelike hyperplanes) to the theory on the Light Front, which demonstrates the equivalence of these variants of the theory. We describe attempts to find such a form of the limiting transition for gauge theories on the Wilson lattice.Comment: LaTeX 2e, 14 page