Construction of a perturbatively correct light-front Hamiltonian for a (2+1)-dimensional gauge theory

We discuss a perturbation theory on the light front regularized by a method analogous to Pauli–Villars regularization for the (2+1)-dimensional SU(N)-symmetric gauge theory. This allows constructing a correct renormalized light-front Hamiltonian.     

On the light-cone quantization of non-abelian gauge theory

The implications of periodic boundary conditions in the light-cone quantization of non-abelian fields are studied. Formulation of the theory in the singularity-free case is presented. Some consequences of field singularities are discussed.     

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 θ. 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 θ = 0; in the case of θ = π, there is agreement at small values of the fermionmass (below the phase-transition point).     

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

We briefly describe problems of the Hamiltonian approach for quantizing gauge fields on the light front for space–time bounded by the inequality |x ^–|L with periodic boundary conditions in the variable x ^– imposed on all fields (the DLCQ method). With these restrictions, we consider the gauge-invariant ultraviolet regularization by passing to a lattice in transverse coordinates. We remove the remaining ultraviolet divergences in the longitudinal momentum p _– by imposing a gauge-invariant finite-mode regularization. It turns out that the canonical formalism on the light front with such a regularization imposed does not contain the usual most complicated second-class constraints between zero and nonzero modes of fields. The described scheme can be used both to regularize the standard gauge theory and to provide a gauge-invariant formulation of effective low-energy models on the light front. Because the manifest Lorentz invariance is broken in our formalism, the vacuum state is poorly defined. We discuss this problem, in particular, in relation to the problem of passing to the continuous space limit.     

Constructing the light-front QCD Hamiltonian

We propose the light-front Lagrangian and the corresponding Hamiltonian that produce a theory perturbatively equivalent to the conventional QCD in the Lorentz coordinates after the regularization is removed. The regularization used is nonstandard and breaks the gauge invariance.But after the regularization is removed, this invariance is restored by the introduction of a finite number of counterterms with coefficients dependent on the regularization parameters. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 120, No. 3, pp. 417–437, September, 1999.     

Model of quark–antiquark interaction in quantum chromodynamics on the light front

We formulate a model of quark–antiquark interaction related to the limit transition to the light-front Hamiltonian in quantum chromodynamics. As ultraviolet regularization, we use a lattice in the space of transverse coordinates, and we additionally introduce a longitudinal light-front coordinate cutoff and also corresponding periodic boundary conditions. We regard the zero mode with respect to this coordinate as an independent dynamical variable. The state space of the model is limited to a quark and an antiquark that interact only via the zero mode of the gluon field on the light front. In this framework, we obtain a discrete mass spectrum of bound states. This spectrum is determined by an equation that with respect to the longitudinal coordinate turns out to be analogous to the’ t Hooft equation in two-dimensional quantum chromodynamics. The equation also contains a quark–antiquark potential that ensures confinement in the transverse space.     

Structure and thermal conduction in solid O2 with nonmagnetic impurities

Thermal conductivities of solid oxygen doped with nonmagnetic impurities of nitrogen and argon were measured in the 1–35 K. The antiferromagnetic α-O₂ doped with this impurities exhibits a strong thermal conductivity anomaly, which is assumed to be a result of supperpression of the magnon contribution to the heat transport by impurities. At the same time, the jump in the thermal conductivity at the α-β transition and th thermal conductivity in the β-O₂ are insensitive to the doping effect, which we ascribe to strong magnetostriction effects. The halfwidth of the x-ray reflexes indicates that doping with Ar and Kr enhanced magnetostriction effects while doping with N₂ weakens. This research was made possible by the financial support of the International Science Foundation Grants No U9R000 and U9R200.