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The world-line (Fock-Feynman-Schwinger) representation is used for quarks in arbitrary (vacuum and valence gluon) field to construct the relativistic Hamiltonian. After averaging the Green's function of the white $q\bar q$ system over gluon fields one obtains the relativistic Hamiltonian, which is matrix in spin indices and contains both positive and negative quark energies. The role of the latter is studied in the example of the heavy-light meson and the standard einbein technic is extended to the case of the matrix Hamiltonian. Comparison with the Dirac equation shows a good agreement of the results. For arbitrary $q\bar q $ system the nondiagonal matrix Hamiltonian components are calculated through hyperfine interaction terms. A general discussion of the role of negative energy components is given in conclusion., Comment: 29 pages, no figures

Propagation of gluons in the confining vacuum is studied in the framework of the background perturbation theory, where nonperturbative background contains confining correlators. Two settings of the problem are considered. In the first the confined gluon is evolving in time together with static quark and antiquark forming the one-gluon static hybrid. The hybrid spectrum is calculated in terms of string tension and is in agreement with earlier analytic and lattice calculations. In the second setting the confined gluon is exchanged between quarks and the gluon Green's function is calculated, giving rise to the Coulomb potential modified at large distances. The resulting screening radius of 0.5 fm presents a serious problem when confronting with lattice and experimental data. A possible solution of this discrepancy is discussed., Comment: 17 pages, no figures; v2: minor numerical changes in the table

We analyse the structure of current-current correlators in coordinate space in large $N_c$ limit when the corresponding spectral density takes the form of an infinite sum over hadron poles. The latter are computed in the QCD string model with quarks at the ends, including the lowest states, for all channels. The corresponding correlators demonstrate reasonable qualitative agreement with the lattice data without any additional fits. Different issues concerning the structure of the short distance OPE are discussed., Comment: LaTeX, 25 pages, 13 figures

The quark-gluon mixed condensate $g<\bar q \sigma_{\mu\nu} F_{\mu\nu} q>$ is calculated in the Gaussian approximation of the Field Correlator Method. In the large N_c limit and for zero mass quarks one obtains a simple result, $m^2_0 \equiv \frac{g<\bar q \sigma_{\mu\nu} F_{\mu\nu} q>}{<\bar q q>} = \frac{16\sigma}{\pi}$, where $\sigma$ is the string tension. For a standard value $\sigma=0.18 GeV^2$ one obtains $m^2_0=1 GeV^2$ in good agreement with the QCD sum rules estimate $m^2_0 = (0.8\pm 0.2) GeV^2$ and the latest lattice result $m^2_0 \cong 1 GeV^2$., Comment: 10 pages, no figures; discussion of accuracy of the result added and misprints corrected

Building on previous works of the mid 1960's, we construct an integral equation for forward elastic scattering (t=0) at arbitrary virtuality Q^2 and large s=W^2. This equation sums the ladder production of massless intermediate bosons to all orders, and the solution exhibits Regge behavior. The equation is used to study scattering in a simple chi^2 phi scalar theory, where it is solved appoximately and applied to the study of DIS at small x. We find that the model can naturally describe the quark distribution in both the large x region and the small x region dominated by Reggeon exchange., Comment: 13 pages with 5 figures

In this review paper the QCD vacuum properties and the structure of color fields in hadrons are studied using the complete set of gauge-invariant correlators of gluon fields. Confinement in QCD is produced by the correlators of some certain Lorentz structure, which violate abelian Bianchi identities and therefore are absent in the case of QED. These correlators are used to define an effective colorless field, which satisfies Maxwell equation with nonzero effective magnetic current. With the help of the effective field and correlators it is shown that quarks are confined due to effective magnetic currents, squeezing gluonic fields into a string, in agreement with the ``dual Meissner effect''. Distribution of effective gluonic fields are plotted in mesons, baryons and glueballs with static sources., Comment: 36 pages, 19 figures, to appear in UFN, updated version. Few references added, minor differences

The masses of $uudd\bar s $ and $uudd\bar d$ pentaquarks are evaluated in a framework of the Effective Hamiltonian approach to QCD using the Jaffe-Wilczek $[ud]^2\bar q$ approximation. The mass of the $[ud]^2\bar s$ state is found to be $\sim 300-500$ MeV higher than the observed $\Theta^+(1540)$ mass., Comment: 6 pages, 1 figure included, LaTeX2e; several references added; misprints corrected; to appear in Physics Letters B

This paper has been withdrawn by the authors, since it had been the excessive repetition of the part of hep-ph/0310190., Comment: withdrawn

The main features of QCD, e.g. confinement, chiral symmetry breaking, Regge trajectories are naturally and economically explained in the framework of the Field Correlator Method (FCM). The same method correctly predicts the spectrum of hybrids and glueballs. When applied to DIS and high-energy scattering it leads to the important role of higher Fock components in the Fock tower of moving hadron, containing primarily gluonic excitations., Comment: 21 pages; Invited talk at the International Conference dedicated to the 90-th birthday of the late Professor I.Ya.Pomeranchuk

The light hadron spectrum as computed in nonperturbative QCD is reviewed and compared to lattice data and experiment. The mixing of mesons, hybrids and glueballs is calculated in the Field Correlator Method. The strong decay mechanisms are found out in the method and compared to the known phenomenological models. The role of sea quarks (unquenched approximation) is studied analytically using radially excited mesons as an example, and compared to experiment., Comment: 17 pages, invited talk at the NPD-2002 Conference of Russian Academy of Sciences, December 2-6, ITEP, to be published in Phys.Atom.Nucl

Effective Chiral Lagrangian is derived from QCD in the framework of Field Correlator Method. It contains the effects of both confinement and chiral symmetry breaking due to a special structure of the resulting quark mass operator. It is shown that this Lagrangian describes light pseudoscalar mesons, and Gell-Mann-Oakes-Renner relations for pions, eta and K mesons are reproduced. Spectrum of radial excitations of pions and K mesons is found and compared to experimentally known masses., Comment: 6 pages; v3: minor corrections, references added

New spectral representations for f_\pi and chiral condensate are derived in QCD and used for calculations in the large N_c limit. Both quantities are expressed in this limit through string tension \sigma and gluon correlation length T_g without fitting parameters. As a result one obtains <\bar q q> = - N_c\sigma^2 T_g a_1, f_\pi =\sqrt{N_c} \sigma T_g a_2, with a_1=0.0823, a_2=0.30. Taking \sigma=0.18 GeV^2 and T_g=1 GeV^(-1), as known from analytic and lattice calculations, this yields <\bar q q>(\mu=2 GeV)=-(0.225 GeV)^3, f_\pi=0.094 GeV, which is close to the standard values., Comment: 17 pages; v2: minor corrections

Pions and kaons have double nature: the chiral dynamics of Nambu-Goldstone bosons together with the usual string dynamics common to all mesons. To uncover the interplay of both dynamics the effective chiral Lagrangian is derived from the QCD Lagrangian using the Field Correlator Method and the pion self-energy (mass) operator is written explicitly. The latter contains an infinite number of poles, but normalized to zero at zero momentum because of spontaneous chiral symmetry breaking. As a result one obtains the Gell-Mann-Oakes-Renner relation for the ground state pion and (slightly shifted by chiral dynamics) the usual spectrum of radially excited pions starting with $\pi(1300)$., Comment: 20 pages, no figures; v2: minor corrections

The structure of hadrons consisting of three static color sources in fundamental (baryons) or adjoint (three-gluon glueballs) representations is studied. The static potentials of glueballs as well as gluon field distributions in glueballs and baryons are calculated in the framework of field correlator method., Comment: 7 pages, 5 figures, talk at the NPD-2002 Conference, December 2-6, ITEP, Moscow, reference added

Some short history of few-body methods originated from the famous Skornyakov-Ter-Martirosyan equation is given, including latest development of Faddeev formalism and Efimov states. The 3q system is shown to require an alternative, which is provided by the hyperspherical method (K-harmonics) which is highly successful for baryons., Comment: 9 pages, invited talk at the miniconference dedicated to the 80-th year celebration of Professor Karen A.Ter-Martirosyan, 30 September - 1 October, ITEP, Moscow

Three decay mechanisms are derived systematically from the QCD Lagrangian using the field correlator method. Resulting operators contain no arbitrary parameters and depend only on characteristics of field correlators known from lattice and analytic calculations. When compared to existing phenomenological models, parameters are in good agreement with the corresponding fitted values., Comment: 12 pages, latex2e

After a short exposition of field correlators in the QCD vacuum and the recently discovered Casimir scaling phenomenon, the origin of confinement in QCD is discussed and two possible mechanisms are suggested, which can be checked by new lattice measurements. Screening of confinement due to sea quarks is discussed and quantitatively explained. Deconfinement is introduced via the colorelectric field evaporation and the transition temperature Tc is found numerically in good agreement with lattice measurements. The Tc dependence on Nc and nf is also predicted and agrees with the recent lattice data., Comment: 11 pages, latex2e, Invited talk at the 3-rd International Sakharov Conference on Physics, Moscow, Lebedev Institute, June 24-29, to be published in Proceedings

Starting in sixties an active group of physicists under the guidance of Prof. K.A.Ter-Martirosyan was creating the theory of high-energy processes in QCD. From the beginning the key element of this theory is the notion of Regge trajectories and in particular of the pomeron trajectory, which have been introduced phenomenologically. In this talk I review the problem of spectrum and Regge trajectories as it can be derived from the nonperturbative QCD dynamics., Comment: 15 pages, 1 eps figure, Latex2e, Invited Talk at the International Seminar devoted to 80-th birthday of K.A. Ter-Martirosyan, to be published in Proceedings

Basic developments in the analytic study of the QCD vacuum structure and of the QCD spectrum, including glueballs and hybrids are reviewed., Comment: LATEX2e, 10 pages, Invited talk at the conference Q2002, June 2002, Novgorod, Russia

Field-correlator method is used to calculate nonperturbative dynamics of quarks in a baryon. General expression for the 3q Green's function is obtained using Fock-Feynman-Schwinger (world-line) path integral formalism, where all dynamics is contained in the 3q Wilson loop with spin-field insertions. Using lowest cumulant contribution for Wilson loop one obtains an Y-shaped string with a deep hole at the string junction position. Using einbein formalism for the quark kinetic terms one automatically obtains constituent quark masses, calculable through the string tension. Resulting effective action for 3q plus Y-shaped strings is quantized in the path-integral formalism to produce two versions of Hamiltonian,one -in the c.m. and another in the light-cone system. Hyperspherical formalism is used to calculate masses and wave functions. Simple estimates in lowest approximation yield baryon masses in good agreement with experiment without fitting parameters., Comment: 36 pages, journal version

The proper time path integral representation is derived explicitly for Green's functions in QCD. After an introductory analysis of perturbative properties, the total gluonic field is separated in a rigorous way into a nonperturbative background and valence gluon part. For nonperturbative contributions the background perturbation theory is used systematically, yielding two types of expansions,illustrated by direct physical applications. As an application, we discuss the collinear singularities in the Feynman-Schwinger representation formalism. Moreover, the generalization to nonzero temperature is made and expressions for partition functions in perturbation theory and nonperturbative background are explicitly written down., Comment: Latex, 61 pages and 7 figures

Nonperturbative and perturbative interaction mechanisms of Wilson loops in gluodynamics are studied within the background field formalism. The first one operates when distance between minimal surfaces of the loops is small and may be important for sea quark effects and strong decay processes. The second mechanism -- perturbative interaction in nonperturbative confining background is found to be physically dominant for all loop configurations characteristic of scattering process. It reduces to perturbative gluon exchanges at small distances, while at larger distances it corresponds to the t-channel exchange of (reggeized) glueball states. Comparison to other approaches is made and possible physical applications are discussed., Comment: LaTeX, 25 pages, 5 EPS-figures

A new physical mechanism is suggested to explain the universal depletion of high meson excitations. It takes into account the appearance of holes inside the string world sheet due to $q\bar{q}$ pair creation when the length of the string exceeds the critical value $R_1 \simeq 1.4$ fm. It is argued that a delicate balance between large $N_c$ loop suppression and a favorable gain in the action, produced by holes, creates a new metastable (predecay) stage with a renormalized string tension which now depends on the separation r. This results in smaller values of the slope of the radial Regge trajectories, in good agreement with the analysis of experimental data in [Ref.3], Comment: 25 pages, 1 figure

Nonperturbative spin-dependent forces of quarks in a baryon are calculated directly from the QCD Lagrangian in the framework of the Field Correlator Method both for heavy and light quarks. Resulting forces contain terms of 5 different structures, only one being known before in asymptotic form. Perturbative terms obtained by the same method are standard and have different signs and structures with respect to the corresponding nonperturbative ones, implying possible cancellations for some baryonic states., Comment: LATEX2e, 21 pages, no figures

Gauge invariant extended configurations are considered for the three fundamental (quarks) or adjoint (gluons) particles. For quarks it is shown that the Y-shaped configuration is the only possible. For adjoint sources both the Y-shaped and triangular configurations may realize. The corresponding static potentials are calculated in the Method of Field Correlators and in the case of baryon shown to be consistent with the lattice simulations. For adjoint sources the potentials of Y-shaped and Delta-shaped configurations turn out to be close to each other, which leads to almost degenerate masses of 3-- 3g glueballs and odderon trajectories., Comment: 9 pages, 5 eps figures, latex2e, one reference added

An effective Lagrangian for the light quark in the field of a static source is derived systematically using the exact field correlator expansion. The lowest Gaussian term is bosonized using nonlocal colorless bosonic fields and a general structure of effective chiral Lagrangian is obtained containing all set of fields. The new and crucial result is that the condensation of scalar isoscalar field which is a usual onset of chiral symmetry breaking and is constant in space-time, assumes here the form of the confining string and contributes to the confining potential, while the rest bosonic fields describe mesons with the q\bar q quark structure and pseudoscalars play the role of Nambu-Goldstone fields. Using derivative expansion the effective chiral Lagrangian is deduced containing both confinement and chiral effects for heavy-light mesons. The pseudovector quark coupling constant is computed to be exactly unity in the local limit,in agreement with earlier large N_c arguments., Comment: LaTeX2e, 17 pages

The proper time path integral representation is derived explicitly for an arbitrary $n$-point amplitude in QCD. In the standard perturbation theory the formalism allows to sum up the leading subseries, e.g. yielding double-logarithm Sudakov asymptotics for form factors. Correspondence with the standard perturbation theory is established and connection to the Bern-Kosower-Strassler method is illustrated., Comment: 20 pages Latex; to appear in the Michael Marinov Memorial Volume, "Multiple facets of quantization and supersymmetry", Eds. M. Olshanetsky and A. Vainshtein (World Scientific)

An effective quark Lagrangian is derived from first principles through bilocal gluon field correlators. It is used to write down equations for baryons, containing both perturbative and nonperturbative fields. As a result one obtains magnetic moments of octet and decuplet baryons without introduction of constituent quark masses and using only string tension as an input. Magnetic moments come out on average in reasonable agreement with experiment, except for nucleons and $\Sigma^-$. The predictions for the proton and neutron are shown to be in close agreement with the empirical values once we choose the string tension such to yield the proper nucleon mass. Pionic corrections to the nucleon magnetic moments have been estimated. In particular, the total result of the two-body current contributions are found to be small. Inclusion of the anomalous magnetic moment contributions from pion and kaon loops leads to an improvement of the predictions., Comment: 24 pages Revtex

The effective QCD Hamiltonian is constructed with the help of the background perturbation theory, and relativistic Feynman--Schwinger path integrals for Green's functions. The resulting spectrum displays mass gaps of the order of one GeV, when additional valence gluon is added to the bound state. Mixing between meson, hybrid, and glueball states is defined in two ways: through generalized Green's functions and via modified Feynman diagram technic giving similar answers. Results for mixing matrix elements are numerically not large (around 0.1 GeV) and agree with earlier analytic estimates and lattice simulations., Comment: LaTeX2e, 23 pages, 4 Postscript figures

General solution of RG equations in the framework of background perturbation theory is written down in the large N_c limit. A simplified (model) approximation to the general solution is suggested which allows to write beta(alpha) and alpha(beta) to any loop order. The resulting alpha_B(Q^2) coincides asymptotically at large $|Q^2|$ with standard (free) alpha_s, saturates at small Q^2 and has poles at time-like Q^2 in agreement with analytic properties of physical amplitudes in the large N_c limit., Comment: 8 pages, 2 figures, misprints corrected

It is shown that analytic properties of standard QCD perturbation theory contradict known spectral properties,and contain in particular IR generated ghost poles and cuts. As an outcome the rigorous background perturbation theory is developed and its analytic properties are shown to be in agreement with general requirements. In a limiting case of large Nc, when QCD amplitudes contain only pole singularities, the strong coupling constant alpha_s(Q) is shown to be also meromorfic function of external momenta. Some simple models and examples are given when nonperturbative beta function and alpha_s(Q) can be written explicitly. General form of amplitudes at large Nc is given in the framework of background perturbation theory and its correspondence with standard perturbation theory at large momenta is demonstrated in the example of e^+e^- annihilation. For time-like momenta the background coupling constant differs drastically from the standard one but the background series averaged over energy intervals has the same (AF) asymptotics at large momenta as in the standard perturbation theory., Comment: 38 pages, no figures

Operator product expansion technique is analyzed in abelian and nonabelian nonsupersymmetric field theoretical models with confinement. Special attention is paid to the regimes where nonzero virtuality of vacuum fields is felt by external currents. It is stressed that despite physics of confinement is sometimes considered as being caused by "soft" vacuum gluon fields, it can exhibit pronounced "hard" effects in OPE both in coordinate and momentum spaces., Comment: LaTeX, 29 pages

Nonperturbative self-energy of a bound quark is computed gauge-invariantly in the framework of background perturbation theory. The resulting Delta m^2_q is negative and is a universal function of string tension and current quark mass. The shift of hadron mass squared, M^2, due to Delta m^2_q is negative, large for light quarks, and solves the long-standing problem of Regge intercepts in relativistic quark models., Comment: LaTeX2e, 13 pages, minor differences are done

Recent lattice calculations have confirmed that QCD static potential for sources in different representations of the gauge group is proportional to eigenvalue of the corresponding quadratic Casimir operator with an accuracy of a few percents. We review the present theoretical status of the "Casimir scaling" phenomenon and stress its importance for analysis of nonperturbative QCD vacuum models and other field theories. It is argued that Casimir scaling strongly advocates the property of Gaussian dominance and we propose different lattice tests to improve our understanding of these phenomena., Comment: RevTeX, 23 pages

The spectra of light-light and heavy-light mesons are calculated within the framework of the QCD string model, which is derived from QCD in the Wilson loop approach. Special attention is payed to the proper string dynamics that allows us to reproduce the straight-line Regge trajectories with the inverse slope being 2\pi\sigma for light-light and twice as small for heavy-light mesons. We use the model of the rotating QCD string with quarks at the ends to calculate the masses of several light-light mesons lying on the lowest Regge trajectories and compare them with the experimental data as well as with the predictions of other models. The masses of several low-lying orbitally and radially excited heavy--light states in the D, D_s, B, and B_s meson spectra are calculated in the einbein (auxiliary) field approach, which has proven to be rather accurate in various calculations for relativistic systems. The results for the spectra are compared with the experimental and recent lattice data. It is demonstrated that an account of the proper string dynamics encoded in the so-called string correction to the interquark interaction leads to an extra negative contribution to the masses of orbitally excited states that resolves the problem of the identification of the D(2637) state recently claimed by the DELPHI Collaboration. For the heavy-light system we extract the constants \bar\Lambda, \lambda_1, and \lambda_2 used in Heavy Quark Effective Theory (HQET) and find good agreement with the results of other approaches., Comment: RevTeX, 42 pages, 7 tables, 7 EPS figures, uses epsfig.sty, typos corrected, to appear in Phys.Rev.D

Lattice measurements of the Pisa group (A.Di Giacomo et al., hep-lat/9603018) are analyzed numerically and parameters of correlation functions are extracted from the data - both below and above deconfinement temperature Tc. Gluon condensate is found for six temperatures in the interval 0.956 Tc - 1.131 Tc and field distributions in deconfined phase are obtained., Comment: LaTeX2e, 13 pages, 7 Postscript figures, minor modifications made, some misprints removed

Recently developed analytic methods in the framework of the Field Correlator Method are reviewed in this series of four lectures and results of calculations are compared to lattice data and experiment. Recent lattice data demonstrating the Casimir scaling of static quark interaction strongly support the FCM and leave very little space for all other theoretical models, e.g. instanton gas/liquid model. Results of calculations for mesons, baryons, quark-gluon plasma and phase transition temperature demonstrate that new analytic methods are a powerful tool of nonperturbative QCD along with lattice simulations., Comment: LaTeX, 34 pages; Lectures given at the 13th Indian-Summer School "Understanding the Structure of Hadrons", August 28 - September 1, 2000, Prague, Czech Republic

Field distributions generated by static quark-antiquark and QQQ sources are calculated analytically in the framework of Gaussian (bilocal) approximation of Field Correlator Method (FCM). Special attention is paid to the QQQ system and asymmetric configurations are also studied. In both quark-antiquark and QQQ cases the string consists mainly of longitudinal color electric field. Transverse color electric field contribution is shown to be less then 3%. Baryon string has an Y-like shape with a deep well at the string junction position. Field distributions for quark-diquark and for three quarks on one line are considered. The interaction potential for quarks forming an equilateral triangle is calculated. The material of the paper is illustrated by 24 3D colored pictures., Comment: LaTeX2e, 13 pages, 20 GIF images, to appear in Yad.Phys

This review is aimed to demonstrate the basics and use of formalism of gauge-invariant nonlocal correlators in nonabelian gauge theories. Many phenomenologically interesting nonperturbative aspects of gluodynamics and QCD can be described in terms of correlators of the nonabelian field strength tensors. It is explained how the properties of correlator ensemble encode the structure of QCD vacuum and determine different nonperturbative observables. It is argued that in gluodynamics and QCD the dominant role is played by the lowest nontrivial two-point correlator (Gaussian dominance). Lattice measurements of field correlators are discussed. Important for the formalism theoretical tools, such as nonabelian Stokes theorem, background perturbation theory, cluster expansion, as well as phenomenological applications to the heavy quarkonium dynamics and QCD phase transition are reviewed., Comment: LaTeX, 77 pages, 7 eps-figures

Dynamics of a light quark in the field of static source (heavy-light meson) is studied using the nonlinear Dirac equation, derived recently. Special attention is paid to the contribution of magnetic correlators and it is found that it yields a significant increase of string tension at intermediate distances. The spectrum of heavy-light mesons is computed with account of this contribution and compared to experimental and lattice data., Comment: 10 pages Revtex