251 research outputs found
Non-perturbative Landau gauge and infrared critical exponents in QCD
We discuss Faddeev-Popov quantization at the non-perturbative level and show
that Gribov's prescription of cutting off the functional integral at the Gribov
horizon does not change the Schwinger-Dyson equations, but rather resolves an
ambiguity in the solution of these equations. We note that Gribov's
prescription is not exact, and we therefore turn to the method of stochastic
quantization in its time-independent formulation, and recall the proof that it
is correct at the non-perturbative level. The non-perturbative Landau gauge is
derived as a limiting case, and it is found that it yields the Faddeev-Popov
method in Landau gauge with a cut-off at the Gribov horizon, plus a novel term
that corrects for over-counting of Gribov copies inside the Gribov horizon.
Non-perturbative but truncated coupled Schwinger-Dyson equations for the gluon
and ghost propagators and in Landau gauge are solved
asymptotically in the infrared region. The infrared critical exponents or
anomalous dimensions, defined by and are obtained in space-time dimensions . Two
possible solutions are obtained with the values, in dimensions, , or .Comment: 26 pages. Modified 2.25.02 to update references and to clarify
Introduction and Conclusio
Realization of an Inductance Scale Traceable to the Quantum Hall Effect Using an Automated Synchronous Sampling System
In this paper, the realization of an inductance scale from 1~H to 10~H
for frequencies ranging between 50~Hz to 20~kHz is presented. The scale is
realized directly from a series of resistance standards using a fully automated
synchronous sampling system. A careful systematic characterization of the
system shows that the lowest uncertainties, around 12~H/H, are obtained
for inductances in the range from 10~mH to 100~mH at frequencies in the kHz
range. This new measurement system which was successfully evaluated during an
international comparison, provides a primary realization of the henry, directly
traceable to the quantum Hall effect. An additional key feature of this system
is its versatility. In addition to resistance-inductance (R-L) comparison, any
kind of impedances can be compared: R-R, R-C, L-L or C-C, giving this sampling
system a great potential of use in many laboratories around the world
Equivariant Poincar\'e series of filtrations and topology
Earlier, for an action of a finite group on a germ of an analytic
variety, an equivariant -Poincar\'e series of a multi-index filtration in
the ring of germs of functions on the variety was defined as an element of the
Grothendieck ring of -sets with an additional structure. We discuss to which
extend the -Poincar\'e series of a filtration defined by a set of curve or
divisorial valuations on the ring of germs of analytic functions in two
variables determines the (equivariant) topology of the curve or of the set of
divisors
A consistent derivation of the quark--antiquark and three quark potentials in a Wilson loop context
In this paper we give a new derivation of the quark-antiquark potential in
the Wilson loop context. This makes more explicit the approximations involved
and enables an immediate extension to the three-quark case. In the
case we find the same semirelativistic potential obtained in
preceding papers but for a question of ordering. In the case we find a
spin dependent potential identical to that already derived in the literature
from the ad hoc and non correct assumption of scalar confinement. Furthermore
we obtain the correct form of the spin independent potential up to the
order.Comment: 30 pages, Revtex (3 figures available as hard copies only), IFUM
452/F
Finite temperature amplitudes and reaction rates in Thermofield dynamics
We propose a method for calculating the reaction rates and transition
amplitudes of generic process taking place in a many body system in
equilibrium. The relationship of the scattering and decay amplitudes as
calculated in Thermo Field Dynamics the conventional techniques is established.
It is shown that in many cases the calculations are relatively easy in TFD.Comment: 32 pages, RevTex, 2 PS figures, to appear in Phys. Rev.
Analytic properties of the scattering amplitude and resonances parameters in a meson exchange model
The analytic properties of scattering amplitudes provide important
information. Besides the cuts, the poles and zeros on the different Riemann
sheets determine the global behavior of the amplitude on the physical axis.
Pole positions and residues allow for a parameterization of resonances in a
well-defined way, free of assumptions for the background and energy dependence
of the resonance part. This is a necessary condition to relate resonance
contributions in different reactions. In the present study, we determine the
pole structure of pion-nucleon scattering in an analytic model based on meson
exchange. For this, the sheet structure of the amplitude is determined. To show
the precision of the resonance extraction and discuss phenomena such as
resonance interference, we discuss the S11 amplitude in greater detail.Comment: 22 pages, 22 figure
Form factors in RQM approaches: constraints from space-time translations
Different relativistic quantum mechanics approaches have recently been used
to calculate properties of various systems, form factors in particular. It is
known that predictions, which most often rely on a single-particle current
approximation, can lead to predictions with a very large range. It was shown
that accounting for constraints related to space-time translations could
considerably reduce this range. It is shown here that predictions can be made
identical for a large range of cases. These ones include the following
approaches: instant form, front form, and "point-form" in arbitrary momentum
configurations and a dispersion-relation approach which can be considered as
the approach which the other ones should converge to. This important result
supposes both an implementation of the above constraints and an appropriate
single-particle-like current. The change of variables that allows one to
establish the equivalence of the approaches is given. Some points are
illustrated with numerical results for the ground state of a system consisting
of scalar particles.Comment: 37 pages, 7 figures; further comments in ps 16 and 19; further
references; modified presentation of some formulas; corrected misprint
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