arXiv subjects
Publications and source records attributed to A. I. Veselov.
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.
Solving numerically the equations of motion for the effective lagrangian describing supersymmetric QCD with the SU(2) gauge group, we find a menagerie of complex domain wall solutions connecting different chirally asymmetric vacua. Some of these solutions are BPS saturated walls; they exist when the mass of the matter fields does not exceed some critical value m < m* < 4.67059... There are also sphaleron branches (saddle points of the ebergy functional). In the range m* < m < m** \approx 4.83, one of these branches becomes a local minimum (which is not a BPS saturated one). At m > m*, the complex walls disappear altogether and only the walls connecting a chirally asymmetric vacuum with the chirally symmetric one survive.
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.
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 show that the monopole confinement mechanism in lattice gluodynamics is 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 perform analytical and numerical study of the loop expansion of the Faddeev--Popov determinant for the maximal and the minimal abelian projections, and discuss the fundamental modular region for these projections.