Renormalization group, causality, and nonpower perturbation expansion in QFT |
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Authors: | D V Shirkov |
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Institution: | (1) Bogoliubov Laboratory for Theoretical Physics, Joint Institute for Nuclear Research, Dubna, Russia |
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Abstract: | The structure of the QFT expansion is studied in the framework of a new “invariant analytic” version of the perturbative QCD.
Here, an invariant coupling constant α(Q
2
/Λ
2
) = β
1
αs(Q
2
)/(4π) becomes a Q
2
-analytic invariant function α
an
(Q2/Λ
2
) ≡A(x), which, by construction, is free of ghost singularities because it incorporates some nonperturbative structures. In the
framework of the “analyticized” perturbation theory, an expansion for an observable F, instead of powers of the analytic invariant
charge A(x), may contain specific functions An(x)=an(x)]
an
, the “nth power of a(x) analyticized as a whole.” Functions A
n>2(x) for small Q2 ≤Λ
2
oscillate, which results in weak loop and scheme dependences. Because of the analyticity requirement, the perturbation series
for F(x) becomes an asymptotic expansion à la Erdélyi using a nonpower set {A
n
(x)}. The probable ambiguities of the invariant analyticization procedure and the possible inconsistency of some of its versions
with the renormalization group structure are also discussed.
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 119, No. 1, pp. 55–66, April, 1999. |
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Keywords: | |
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