41 research outputs found
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 -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 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
, , and trajectories, we
reproduce both angular distributions and polarization data for small values of
the Mandelstam variable , 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 resonance with a mass of 2.83 GeV as
member of the 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