75 research outputs found

### 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

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