Differential Equations for Definition and Evaluation of Feynman Integrals

It is shown that every Feynman integral can be interpreted as Green function of some linear differential operator with constant coefficients. This definition is equivalent to usual one but needs no regularization and application of $R$-operation. It is argued that presented formalism is convenient for practical calculations of Feynman integrals.Comment: pages, LaTEX, MSU-PHYS-HEP-Lu2/9

Explicit results for all orders of the epsilon-expansion of certain massive and massless diagrams

An arbitrary term of the epsilon-expansion of dimensionally regulated off-shell massless one-loop three-point Feynman diagram is expressed in terms of log-sine integrals related to the polylogarithms. Using magic connection between these diagrams and two-loop massive vacuum diagrams, the epsilon-expansion of the latter is also obtained, for arbitrary values of the masses. The problem of analytic continuation is also discussed.Comment: 8 pages, late

Anomalous Commutator Algebra for Conformal Quantum Mechanics

The structure of the commutator algebra for conformal quantum mechanics is considered. Specifically, it is shown that the emergence of a dimensional scale by renormalization implies the existence of an anomaly or quantum-mechanical symmetry breaking, which is explicitly displayed at the level of the generators of the SO(2,1) conformal group. Correspondingly, the associated breakdown of the conservation of the dilation and special conformal charges is derived.Comment: 23 pages. A few typos corrected in the final version (which agrees with the published Phys. Rev. D article

Renormalized Path Integral for the Two-Dimensional Delta-Function Interaction

A path-integral approach for delta-function potentials is presented. Particular attention is paid to the two-dimensional case, which illustrates the realization of a quantum anomaly for a scale invariant problem in quantum mechanics. Our treatment is based on an infinite summation of perturbation theory that captures the nonperturbative nature of the delta-function bound state. The well-known singular character of the two-dimensional delta-function potential is dealt with by considering the renormalized path integral resulting from a variety of schemes: dimensional, momentum-cutoff, and real-space regularization. Moreover, compatibility of the bound-state and scattering sectors is shown.Comment: 26 pages. The paper was significantly expanded and numerous equations were added for the sake of clarity; the main results and conclusions are unchange

A New Gauge for Computing Effective Potentials in Spontaneously Broken Gauge Theories

A new class of renormalizable gauges is introduced that is particularly well suited to compute effective potentials in spontaneously broken gauge theories. It allows one to keep free gauge parameters when computing the effective potential from vacuum graphs or tadpoles without encountering mixed propagators of would-be-Goldstone bosons and longitudinal modes of the gauge field. As an illustrative example several quantities are computed within the Abelian Higgs model, which is renormalized at the two-loop level. The zero temperature effective potential in the new gauge is compared to that in $R_\xi$ gauge at the one-loop level and found to be not only easier to compute but also to have a more convenient analytical structure. To demonstrate renormalizability of the gauge for the non-Abelian case, the renormalization of an SU(2)-Higgs model with completely broken gauge group and of an SO(3)-Higgs model with an unbroken SO(2) subgroup is outlined and renormalization constants are given at the one-loop level.Comment: 24 pages, figures produced by LaTeX, plain LaTeX, THU-93/16. (Completely revised. Essential changes. New stuff added. To appear in Phys.Rev.D.

Backward pion-nucleon scattering

A global analysis of the world data on differential cross sections and polarization asymmetries of backward pion-nucleon scattering for invariant collision energies above 3 GeV is performed in a Regge model. Including the $N_\alpha$, $N_\gamma$, $\Delta_\delta$ and $\Delta_\beta$ trajectories, we reproduce both angular distributions and polarization data for small values of the Mandelstam variable $u$, in contrast to previous analyses. The model amplitude is used to obtain evidence for baryon resonances with mass below 3 GeV. Our analysis suggests a $G_{39}$ resonance with a mass of 2.83 GeV as member of the $\Delta_{\beta}$ trajectory from the corresponding Chew-Frautschi plot.Comment: 12 pages, 16 figure

Gauss hypergeometric function: reduction, epsilon-expansion for integer/half-integer parameters and Feynman diagrams

The Gauss hypergeometric functions 2F1 with arbitrary values of parameters are reduced to two functions with fixed values of parameters, which differ from the original ones by integers. It is shown that in the case of integer and/or half-integer values of parameters there are only three types of algebraically independent Gauss hypergeometric functions. The epsilon-expansion of functions of one of this type (type F in our classification) demands the introduction of new functions related to generalizations of elliptic functions. For the five other types of functions the higher-order epsilon-expansion up to functions of weight 4 are constructed. The result of the expansion is expressible in terms of Nielsen polylogarithms only. The reductions and epsilon-expansion of q-loop off-shell propagator diagrams with one massive line and q massless lines and q-loop bubble with two-massive lines and q-1 massless lines are considered. The code (Mathematica/FORM) is available via the www at this URL http://theor.jinr.ru/~kalmykov/hypergeom/hyper.htmlComment: 19 pages, LaTeX, 1-eps figure; v5: The code (Mathematica/FORM) is available via the www http://theor.jinr.ru/~kalmykov/hypergeom/hyper.htm

Seasonal water discharge and sediment load changes in the Upper Yangtze, China

Mountain Research and Development23156-6

Factors Influencing Color of Dark Cutting Beef Muscle

Color of dark cutting beef rib muscle was measured as affected by treatment with rotenone or chilling in an oxygen rich atmosphere. Samples homogenized with the mitochondrial inhibitor, rotenone, or pH 5.0 buffer remained red for up to 1 hr. Control samples blended with water remained red when chilled but turned dark when held at room temperature. Thin slices of dark cutting beef muscle would turn red when chilled in air or oxygen to 3°C, or when chilled in oxygen to 14°C, but would turn dark when transferred from oxygen at 3°C to air at room temperature. Thus, dark cutting beef muscle will turn red if mitochondrial respiration is inhibited, allowing myoglobin at muscle surfaces to remain oxygenated