arXiv subjects
Publications and source records attributed to Yu. A. Simonov.
Stochastic quantization is used to derive exact equations, connecting multilocal field correlators in the phi^3 theory and gluodynamics. Perturbative expansion of the obtained equations in the lowest orders is presented.
Dyonic classical solutions of Yang-Mills theory are considered and the complete set of fermionic zero modes of these solutions are studied. Representing the QCD vacuum as a gas of dyons, one obtains chiral symmetry breaking due to zero modes similarly to the case of instantonic vacuum.
Bound states of heavy quarks are considered. Using the path integral formalism we are able to rederive, in a gauge invariant way, the Leutwyler-Voloshin short distance analysis as well as a long distance linear potential. At all distances we describe the states in terms of nonperturbative field correlators, and we include radiative corrections at short and intermediate distances. For intermediate distance states (particularly $b\bar {b}$ with $n=2$) our results improve, qualitatively and quantitatively, standard analyses, thanks mostly to being able to take into account the finiteness of the correlation time.
Chiral symmetry breaking due to instanton-produced fermion zero modes in the confining vacuum is considered. Zero modes provide 'tHooft-type determinant quark interaction, which is bosonized by introduction of auxiliary fields. For three flavours this procedure becomes nontrivial and a method is suggested which allows to derive effective Lagrangian for massless Nambu--Goldstone modes.
The light-cone Hamiltonian is derived from the general gauge -- and Lorentz -- invariant expression for the $q\bar{q}$ Green's function, containing confinement via the area law for the Wilson loop.The resulting Hamiltonian contains in a nonadditive way contributions from quark and string degrees of freedom. Different limiting dynamical regimes of the system of quarks connected by the string are found. In the limit of no transverse motion one recovers the t'Hooft's 1+1 QCD Hamiltonian. The correspondence with the rest frame Hamiltonian spectrum is established. The important notion of the light-cone string, contributing significantly to the energy--momentum is discussed.
Confining configurations are introduced into the standard instanton vacuum model. This drastically improves theoretical properties of the vacuum: instanton size density $d(ρ)$ stabilizes at $ρ\sim 0.2 fm$, all chiral effects are formulated in a gauge-invariant way and quarks are confined. An interesting interplay of chiral and confining dynamics is observed; for the realistic values of parameters the Georgi-Manohar picture emerges with chiral radius $R_{ch}\sim ρ\sim 0.2 fm$ much less than confining radius $R_c\sim$ hadron radius $\sim 1 fm$. In the limit $R_{ch}\ll R_c$ the chiral mass $M_{ch}(p)$ is unaffected by confinement and can be taken in the local limit $M_{ch}(p=0)$. Different types of effective chiral Lagrangians (ECL) are obtained, containing all or a part of gluon, quark and Nambu--Goldstone--meson fields. The ECL are manifestly gauge--invariant and in the limit of no gluon fields coincide with those found previously. The problem of the double role of the pion -- as a Goldstone meson or as a $q\bar{q}$ system is briefly disscussed using confining ECL with quarks, mesons and gluons.
Starting from the QCD Lagrangian we derive the effective action for massive quark and antiquark at large distances, corresponding to the minimal area low of the Wilson loop. The path integral method is used to quantize the system and the spectrum is obtained with asymptotically linear Regge trajectories. Two dynamical regimes distinguished by the string energy--momentum distribution are found: at large orbital excitations ($l\gg 1$) the system behaves as a string and yields the Regge slope of $\frac{1}{2 πσ}$, while at small $l$ one obtains a potential-like regime for relativistic or nonrelativistic system . The problem of relative time is clarified. It is shown that in the valence quark approximation one can reduce the initial four-dimensional dynamics to the three-dimensional one. The limiting case of a pure string (without quark kinetic terms) is studied and the spectrum of the straight-line string is obtained.
Starting from the QCD Lagrangian and taking into account both perturbative and nonperturbative effects, we use the method of vacuum correlators to derive the Dirac equation (rigorously for the Coulomb interaction and heuristically for the confining potential) for a system consisting of a light quark and heavy antiquark. As a result the confining potential is a Lorentz scalar, and the Coulomb part the fourth component of a 4-vector. The energy spectrum of the Dirac equation is considered for these potentials. Numerical calculations of energy eigenvalues $E=E_{nκ}$ are performed, and some exact solutions of the Dirac equation in the case $E=0$ are found. An effective-potential method convenient for qualitative study of the solutions of the Dirac equation is developed. The connection with experimental spectra of $D$- and $B$-mesons is briefly discussed.
Perturbative expansion in the nonperturbative confining QCD background is formulated. The properly renormalized $α_S(R)$ is shown to be finite at large distances, with the string tension playing the role of an infrared regulator. The infra--red renormalons are shown to be absent in the new perturbation series.
The structure of the hadron spectrum is discussed in connection with the main phenomena of nonperturbative QCD: confinement and chiral symmetry breaking (CSB). For the higher part of the spectrum ($M \ge 2 GeV$) spin and chiral effects are unimportant; spectrum of $q\bar{q}$ system is described by an effective Hamiltonian deduced from QCD. The Hamiltonian reduces to relativistic quark potential model or to the open string model in two opposite limits. Hybrids are shown to appear naturally in theory and enter the multiplets which are compared to experiment and bosonic string theory. The phenomenon of conspiracy of the spectrum of radial excited states producing operator product expansion is discussed. The lower part of the spectrum $(M< 2 GeV)$ is influenced by spin and chiral effects. CSB and the chiral quark mass are deduced for the vacuum containing instantons and confining background. Main points are summarized in conclusion.
The background field formalism is used to implement nonperturbative QCD contributions into diagrammatic technic at $T>0$. The leading terms both in the confining and nonconfining phase are identified at large $N_c$ and the transition temperature is calculated in this limit, which appears to be in good agreement with the Monte Carlo calculations.
In this work the Feynman-Schwinger representation for the two-body Greens function is studied. After having given a brief introduction to the formalism, we report on the first calculations based on this formalism. In order to demonstrate the validity of the method, we consider the static case where the mass of one of the particles becomes very large. We show that the heavy particle follows a classical trajectory and we find a good agreement with the Klein-Gordon result.