Instantons in Large Order of the Perturbative Series

Behavior of the Euclidean path integral at large orders of the perturbation series is studied. When the model allows tunneling, the path-integral functional in the zero instanton sector is known to be dominated by bounce-like configurations at large order of the perturbative series, which causes non-convergence of the series. We find that in addition to this bounce the perturbative functional has a subleading peak at the instanton and anti-instanton pair, and its sum reproduces the non-perturbative valley.Comment: 9 pages (without figures), KUCP-6

Path-Integral for Quantum Tunneling

Path-integral for theories with degenerate vacua is investigated. The origin of the non Borel-summability of the perturbation theory is studied. A new prescription to deal with small coupling is proposed. It leads to a series, which at low orders and small coupling differs from the ordinary perturbative series by nonperturbative amount, but is Borel-summable.Comment: 25 pages + 12 figures (not included, but available upon request) [No changed in content in this version. Problem with line length fixed.

Forward Jet Production at small x in Next-to-Leading Order QCD

The production of forward jets of transverse energy E_T\simeq Q and large momentum fraction x_jet >> x is calculated in next-to-leading order including consistently direct and resolved virtual photon contributions. The predictions are compared to recent ZEUS and H1 data. Good agreement with the data is found.Comment: 11 pages, 3 eps figues; text in 2.1 clearified, figure 2 slightly changed; version to appear in Phys. Lett.

Recent Developments in the Theory of Tunneling

Path-integral approach in imaginary and complex time has been proven successful in treating the tunneling phenomena in quantum mechanics and quantum field theories. Latest developments in this field, the proper valley method in imaginary time, its application to various quantum systems, complex time formalism, asympton theory for the large order analysis of the perturbation theory, are reviewed in a self-contained manner.Comment: 100 pages, LaTeX, PTPTeX.sty, 36 eps figures, To be published in Progress of Theoretical Physics Supplimen

Reggeized Gluons with a Running Coupling Constant

The equation for two reggeized gluons in the vacuum channel is generalized to take into account the running QCD coupling constant on the basis of the bootstrap condition for gluon reggeization. Both the gluon trajectory as a function of momentum and the interaction as a function of distance grow like $\log\log$ in the ultraviolet. The resulting equation depends on the confinement region. With a simple parametrization of its influence by an effective gluon mass the pomeron intercept turns out much smaller than for a fixed coupling constant (the BFKL pomeron).Comment: 9 pages, LaTeX, US-FT/12-9

High-colour pomerons with a running coupling constant in the Hartree-Fock approximation

The Hartree-Fock approximation is applied to study the "high-colour pomerons" in the system of many reggeized gluons with a running QCD coupling constant. It is shown that, contrary to the fixed coupling case, the high-colour pomerons result supercritical, although with a smaller intercept than the multipomeron states.Comment: 8 pages, LaTeX, no figure

On the Evolution Kernels of Twist 2 Light-Ray Operators for Unpolarized and Polarized Deep Inelastic Scattering

The non-singlet and singlet evolution kernels of the twist--2 light-ray operators for unpolarized and polarized deep inelastic scattering are calculated in $O(\alpha_s)$ for the general case of virtualities $q^2, q'^2 \neq 0$. Special cases as the kernels for the general single-variable evolution equation and the Altarelli-Parisi and Brodsky-Lepage limits are derived from these results.Comment: 10 pages latex, including 1 ps-figure, typos correcte