Threshold value expansion and dimensionally adjusted
dynamics
Non RelativisticquantenChromo
Single dump
A Lagrangeschees and a set guidelines Feynman are represented
for nonrelativistic quantenfeldtheorien with the obvious energy, which
counts in the heavy particle rate V. A regime is indicated, in that
energy and Momentum of the order Mv is. It is identical neither to
ultrasoftregime, radiation processes to energy and Momentum of the
order Mv^2 corresponds, still to the possible regime also on heavy
particles of the Shells and coulomb operation difficulty. In this soft
regime are massless particles on Shell, and heavy particle-widen become
static. Examples show that it contributes and Zweischleifenzu the
corrections of the Zerstreuen and production scopes a close threshold
value. Therefore nonrelativistic quantenfeldtheorie corresponds with
the results of the threshold value expansion. A simple example shows
also the energy of the measure adjustment in the nonrelativistic
quantenfeldtheorie.
Introduction
The rate energy, which count in the Non Relativisticquantenfeldtheorien
(Caswell and Lepage, Braaten et aluminium), particularly in the
nonrelativistic Quantenelectrodynamics
and in the nonrelativistic quantity Chromodynamics (NRQCD) and the flag
of the relevant energy and Momentumregime checked more difficult than
beforehand believed. In a new article Beneke and Smirnov that rescaling
the guidelines of the rate, which are suggested by hatch and
Manohar and Grinstein and Rothstein reproduce and from hatch and Savage
are united, did not underline the correct behavior of the exchange
contribution with two gluon to the coulomb, those, between
nonrelativistic particle close threshold value absent-minded. This
threw something doubts whether NRQCD, in its dimensionally adjusted
version after hatch and Savage, can be particularly formulated with an
independent low Lagrangescheen energy. The target of this character is
to show that a rate energy counting Lagrangescheen of manufacturing
express existierent, and to show that this Lagrangeschee reproduces the
results, which are achieved by Beneke and Smirnov.
This character for outlining the ideas to recover the puzzle
play limited and shifts more formal arguments, calculations and
derivatives on a future, longer publication, which employs also
teaching theories and exemplary calculations. It is organized, as
follows: In chapter 2, the relevant regime by NRQFT are indicated. A
simple example shows the usableness of the measure adjustment, if it
activates the express rate energy counting. Chapter 3 suggests
rescaling the guidelines, which are necessary for a Lagrangeschees with
the obvious rate energy counting. The guidelines Feynman are given.
Simple examples in chapter 4 manufacture the far necessity for
the new, soft regime, which is introduced to chapter 3. Summary and
prospect conclude the character.
Summaries and prospect
The training aim of this character was a simple representation of the
ideas behind the express energy, which counts in
dimensionally adjusted NRQFT. The flag of three different Regimen of
the scale for Aufshellpartikel in NRQFT leads in a natural way to the
existence of a new quark field and the new gluon field in the soft
regimeregime regime. None of the five fields in the three Regimen
should be regarded as physical particles. Rather they represent the
applicable quark and the gluon in the respective Regimen. A
Lagrangeschees for nonrelativistic quantenfeldtheorie was suggested,
which leads to the correct behavior of the Zerstreuen and production
scopes. It manufactures the express rate energy counting, which is
conserved to all orders in the disturbance theory. The reason for the
existence of such a Lagrangescheem, as soon as measure adjustment is
decided, in order to execute the theory, was ausgearbeitt on in a
simple example: non commutativity the expansion in the small parameters
with dimensionally adjusted integrals.
Because of the similarity between the calculation of the
examples in the work, those is explained here and in the paper by
Beneke and Smirnov, one can the impression receive that the
Lagrangeschee is represented only a simple new formulation of the
threshold value expansion. Partly this is applicable, and a future
publication points indeed the equivalence of the two approximations to
all orders in the threshold value and coupling expansion. A list of
other topics turning there contains: the direct verallgemeinerung to
NRQCD; a proof, whether particle contents, which are outlined above
are, not only completely continuously however executes, i.e.. that no
new fields (e.g. ultrasoftquark) or unusual regime develop; an
investigation of the influence of the soft quarks and that of gluon on
blocked status calculations in NRQED and in NRQCD; a full list of the
different couplings between the different Regimen and a utilization of
their meaning for physical processes. The formal reason, why double
counting between different Regimen particularly does not occur and
between switch and ultrasoftgluons, a derivative of the soft pairs of
quarks of the way to the external sources and the role of the soft
gluon, with the Comptonzerstreuen earn further attention, also.
I would like to stress that the graphic threshold
value
expansion, which is calculated here permits a more automatic and more
intuitive approximation and it more simply to determine inside the
order forms too, which a certain diagram contributes. On the other hand
the Lagrangeschee box NRQFT is applied easily at blocked status
problems. While the threshold value expansion Beneke and Smirnov in a
relativistic adjustment begins, it can be harder formal to treat
blocked statuses there. Indeed I that, even if one does not know
position SE IN possibly in that believe, to check the assumptions of
which drives off from the other one, both approximations from each
other in the wedding from NRQFT and from threshold value expansion to
profit.***
TRANSLATION ENDS HERE ***