arXiv subjects
Publications and source records attributed to M. I. Polikarpov.
We discuss some properties of abelian monopoles in the Maximal Abelian projection of the SU(2) lattice gluodynamics. We show that in the maximal abelian projection abelian monopoles carry fluctuating electric charge and that the monopole currents are correlated with the magnetic and the electric parts of the SU(2) action density.
The monopole confinement mechanism in the abelian projection of lattice gluodynamics is reviewed. The main topics are: the abelian projection on the lattice and in the continuum, a numerical study of the abelian monopoles in the lattice gauge theory. Additionally, we briefly review the notation of differential forms, duality, and the BKT transformation in the lattice gauge theories.
We study a field-theoretical analogue of the Aharonov-Bohm effect in two-, three- and four-dimensional Abelian Higgs models; the corresponding topological interaction is proportional to the linking number of the Abrikosov vortex and the particle world trajectories. We show that the Aharonov-Bohm effect gives rise to a nontrivial interaction of charged test particles. The numerical calculations in the three-dimensional model confirm this fact.
By numerical calculations we show that the abelian monopole currents are locally correlated with the density of SU(2) lattice action. The correlations are larger by the order of magnitude in the maximal abelian projection than in the projections which correspond to the diagonalization of Polyakov line and to the diagonalization of the plaquette. These facts show that (at least) in the maximal abelian projection the monopoles are the physical objects, they carry the SU(2) action. The larger value of β, the larger the relative action carried by monopole. Calculations on the asymmetric lattice show that this correlation exists also in the deconfinement phase of gluodynamics.
We study various representations of the infrared effective theory of SU(2) gluodynamics starting from the monopole action derived recently. We determine the coupling constants in the abelian-Higgs model directly from lattice QCD and evaluate the type of the QCD vacuum. The string action is derived using the BKT transformation on the lattice. At the classical level this action reproduces the physical string tension with a good accuracy.
By numerical calculations we show that the abelian monopole currents are locally correlated with the density of SU(2) lattice action. This fact is established for the maximal abelian projection. Thus, in the maximal abelian projection the monopoles are physical objects, they carry SU(2) action. Calculations on the asymmetric lattice show that the correlation between monopole currents and the density of SU(2) lattice action also exists in the deconfinement phase of gluodynamics.
The correlations of the topological charge (Q), the electric (Je) and the magnetic (Jm) currents in the SU(2) lattice gauge theory in the Maximal Abelian projection are investigated. A nonzero value of the correlator is obtained for a wide range of values of the bare charge, as well as under the cooling.
The general properties of the abelian projection are reviewed. We derive the explicit expression for the abelian functional integral for U(1) abelian theory which corresponds to the abelian projection of the SU(2) gluodynamics. The numerical results for the temperature dependence of the monopole condensate are presented.
We describe numerical calculation results for the probability distribution of the value of the monopole creation operator in the SU(2) lattice gluodynamics. We work in the maximal abelian projection. It occurs that at low temperatures, below the deconfinement phase transition, the maximum of the distribution is shifted from zero, which means that the effective constraint potential is of the Higgs type. Above the phase transition the minimum of the potential (the maximum of the monopole field distribution) is at the zero value of the monopole field. This fact confirms the existence of the abelian monopole condensate in the confinement phase of lattice gluodynamics, and agrees with the dual superconductor model of the confining vacuum.
Different aspects of bozonization algorithm proposed by Slavnov are tested by numerical simulations of a one dimensional toy model.
The abelian projection of lattice gluodynamics is reviewed. The main topics are: abelian and monopole dominance, monopole condensate as the disorder parameter, effective abelian Lagrangian, monopoles in the instanton field, Aharonov -- Bohm effect on the lattice.
We study a field--theoretical analogue of the Aharonov--Bohm effect in the 3D Abelian Higgs Model: the corresponding topological interaction is proportional to the linking number of the vortex and the particle world trajectories. We show that the Aharonov--Bohm effect gives rise to a nontrivial interaction of tested charged particles.
We discuss the Aharonov--Bohm effect in three and four dimensional non--compact lattice Abelian Higgs model. We show analytically that this effect leads to the long--range Coulomb interaction of the charged particles, which is confining in three dimensions. The Aharonov--Bohm effect is found in numerical calculations in 3D Abelian Higgs model.
We present the results of the numerical calculation of the probability distribution of the value of the monopole creation operator in $SU(2)$ lattice gluodynamics. We work in the maximal abelian projection. It occurs that at the low temperature, below the deconfinement phase transition the maximum of the distribution is shifted from zero, which means that the effective constraint potential is of the Higgs type. Above the phase transition the minimum of the potential (the maximum of the monopole field distribution) is at the zero value of the monopole field. This is the direct proof of the existence of the abelian monopole condensate in the confinement phase of the gluodynamics, which confirms the dual superconductor model of the confining vacuum.
We show that the monopole confinement mechanism in lattice gluodynamics may be a particular feature of the maximal abelian projection. We give an explicit example of the $SU(2) \rightarrow U(1)$ projection (the minimal abelian projection), in which the confinement is due to topological objects other than monopoles. We also discuss the string representation of the abelian projected $SU(2)$ gluodynamics.
The time evolution of a many-fermion system can be described by a Green's function corresponding to an effective potential, which takes anti-symmetrization of the wave function into account, called the Pauli-potential. We show that this idea can be combined with the Green's Function Monte Carlo method to accurately simulate a system of many non-relativistic fermions. The method is illustrated by the example of systems of several (2-9) fermions in a square well.
We study a field--theoretical analogue of the Aharonov--Bohm effect in the Abelian Higgs Model: the corresponding topological interaction is proportional to the linking number of the Abrikosov--Nielsen--Olesen string world sheets and the particle world trajectory. The creation operators of the strings are explicitly constructed in the path integral and in the Hamiltonian formulation of the theory. We show that the Aharonov--Bohm effect gives rise to several nontrivial commutation relations. We also study the Aharonov--Bohm effect in the lattice formulation of the Abelian Higgs Model. It occurs that this effect gives rise to a nontrivial interaction of tested charged particles.
Starting from the Abelian Higgs field theory, we construct the theory of quantum Abrikosov--Nielsen--Olesen strings. It is shown that in four space -- time dimensions in the limit of infinitely thin strings, the conformal anomaly is absent, and the quantum theory exists. We also study an analogue of the Aharonov--Bohm effect: the corresponding topological interaction is proportional to the linking number of the string world sheet and the particle world trajectory. The creation operators of the strings are explicitly constructed in the path integral and in the Hamiltonian formulation of the theory. We show that the Aharonov--Bohm effect gives rise to several nontrivial commutation relations.