scholarly journals ANALYTIC INVARIANT CHARGE IN QCD

2003 ◽  
Vol 18 (30) ◽  
pp. 5475-5519 ◽  
Author(s):  
A. V. NESTERENKO
Keyword(s):  
Perturbative Expansion ◽  
Quantum Field ◽  
Perturbative Approach ◽  
Interaction Processes ◽  
Running Coupling ◽  
Wide Range ◽  
Local Quantum ◽  
Concrete Realization ◽  
Β Function ◽  
Analytic Invariant

This paper gives an overview of recently developed model for the QCD analytic invariant charge. Its underlying idea is to bring the analyticity condition, which follows from the general principles of local Quantum Field Theory, in perturbative approach to renormalization group (RG) method. The concrete realization of the latter consists in explicit imposition of analyticity requirement on the perturbative expansion of β function for the strong running coupling, with subsequent solution of the corresponding RG equation. In turn, this allows one to avoid the known difficulties originated in perturbative approximation of the RG functions. Ultimately, the proposed approach results in qualitatively new properties of the QCD invariant charge. The latter enables one to describe a wide range of the strong interaction processes both of perturbative and intrinsically nonperturbative nature.

scholarly journals Perturbative QCD in acceptable schemes with holomorphic coupling

2015 ◽  
Vol 30 (15) ◽  
pp. 1550082 ◽  
Author(s):  
Carlos Contreras ◽  
Gorazd Cvetič ◽  
Reinhart Kögerler ◽  
Pawel Kröger ◽  
Oscar Orellana
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Perturbative Qcd ◽  
Perturbation Series ◽  
Quantum Field ◽  
Sum Rule ◽  
Running Coupling ◽  
Local Quantum ◽  
Rule Analysis ◽  
Physical Quantities

Perturbative QCD in mass independent schemes leads in general to running coupling a(Q2) which is nonanalytic (nonholomorphic) in the regime of low spacelike momenta |Q2|≲1 GeV 2. Such (Landau) singularities are inconvenient in the following sense: evaluations of spacelike physical quantities 𝒟(Q2) with such a running coupling a(κQ2)(κ~1) give us expressions with the same kind of singularities, while the general principles of local quantum field theory require that the mentioned physical quantities have no such singularities. In a previous work, certain classes of perturbative mass independent beta functions were found such that the resulting coupling was holomorphic. However, the resulting perturbation series showed explosive increase of coefficients already at N 4 LO order, as a consequence of the requirement that the theory reproduce the correct value of the τ lepton semihadronic strangeless decay ratio rτ. In this paper, we successfully extend the construction to specific classes of perturbative beta functions such that the perturbation series do not show explosive increase of coefficients, the perturbative coupling is holomorphic, and the correct value of rτ is reproduced. In addition, we extract, with Borel sum rule analysis of the V+A channel of the semihadronic strangeless decays of τ lepton, reasonable values of the corresponding D = 4 and D = 6 condensates.

scholarly journals A thermodynamic origin for the Cohen-Kaplan-Nelson bound

2021 ◽  
Author(s):  
Satish Ramakrishna
Keyword(s):  
General Relativity ◽  
Free Energy ◽  
Equation Of State ◽  
Density Of States ◽  
Canonical Ensemble ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Local Quantum ◽  
The Universe

Abstract The Cohen-Kaplan-Nelson bound is imposed on the grounds of logical consistency (with classical General Relativity) upon local quantum field theories. This paper puts the bound into the context of a thermodynamic principle applicable to a field with a particular equation of state in an expanding universe. This is achieved without overtly appealing to either a decreasing density of states or a minimum coupling requirement, though they might still be consistent with the results described. The paper establishes that the holographic principle applied to cosmology is consistent with minimizing the free energy of the universe in the canonical ensemble, upon the assumption that the ultraviolet cutoff is a function of the causal horizon scale.

scholarly journals Different Quantum Field Constructions in the (1/2,0) ⊕ (0,1/2) Representation

1997 ◽  
Vol 12 (36) ◽  
pp. 2741-2748 ◽  
Author(s):  
Valeri V. Dvoeglazov
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Neutrino Physics ◽  
Present Situation ◽  
Quantum Field ◽  
Concrete Realization ◽  
Intrinsic Parity ◽  
Special Case

We present another concrete realization of a quantum field theory, envisaged many years ago by Bargmann, Wightman and Wigner. Considering the special case of the (1/2,0)⊕ (0,1/2) field and developing the Majorana–McLennan–Case–Ahluwalia construction for neutrino, we show that fermion and its antifermion can have the same intrinsic parity. The construction can be applied to explain the present situation in neutrino physics.

Hyper-asymptotic expansions and instantons

2019 ◽  
pp. 471-492
Author(s):  
Jean Zinn-Justin
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Mechanics ◽  
Asymptotic Expansions ◽  
Perturbative Expansion ◽  
Quantum Field ◽  
Wkb Method ◽  
Additional Information ◽  
Spectral Equation ◽  
Double Well Potential

Chapter 24 examines the topic of hyper–asymptotic expansions and instantons. A number of quantum mechanics and quantum field theory (QFT) examples exhibit degenerate classical minima connected by quantum barrier penetration effects. The analysis of the large order behaviour, based on instanton calculus, shows that the perturbative expansion is not Borel summable, and does not define unique functions. An important issue is then what kind of additional information is required to determine the exact expanded functions. While the QFT examples are complicated, and their study is still at the preliminary stage, in quantum mechanics, in the case of some analytic potentials that have degenerate minima (like the quartic double–well potential), the problem has been completely solved. Some examples are described in Chapter 24. There, the perturbative, complete, hyper–asymptotic expansion exhibits the resurgence property. The perturbative expansion can be related to the calculation of the spectral equation via the complex WKB method.

Manifest non-locality in quantum mechanics, quantum field theory and quantum gravity

2019 ◽  
Vol 34 (28) ◽  
pp. 1941004
Author(s):  
Laurent Freidel ◽  
Robert G. Leigh ◽  
Djordje Minic
Keyword(s):  
Quantum Theory ◽  
String Theory ◽  
Quantum Gravity ◽  
Closed String ◽  
Covariant Formulation ◽  
Quantum Field ◽  
Quantum Geometry ◽  
Local Quantum ◽  
Generic Representation ◽  
Non Locality

We summarize our recent work on the foundational aspects of string theory as a quantum theory of gravity. We emphasize the hidden quantum geometry (modular spacetime) behind the generic representation of quantum theory and then stress that the same geometric structure underlies a manifestly T-duality covariant formulation of string theory, that we call metastring theory. We also discuss an effective non-commutative description of closed strings implied by intrinsic non-commutativity of closed string theory. This fundamental non-commutativity is explicit in the metastring formulation of quantum gravity. Finally we comment on the new concept of metaparticles inherent to such an effective non-commutative description in terms of bi-local quantum fields.

RAINBOW STATISTICS

2009 ◽  
Vol 24 (25n26) ◽  
pp. 4623-4641 ◽  
Author(s):  
MICHELE ARZANO ◽  
DARIO BENEDETTI
Keyword(s):  
Quantum Group ◽  
Hilbert Spaces ◽  
Group Symmetry ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Additional Structure ◽  
Local Quantum ◽  
Group Symmetries ◽  
Noncommutative Quantum

Noncommutative quantum field theories and their global quantum group symmetries provide an intriguing attempt to go beyond the realm of standard local quantum field theory. A common feature of these models is that the quantum group symmetry of their Hilbert spaces induces additional structure in the multiparticle states which reflects a nontrivial momentum-dependent statistics. We investigate the properties of this "rainbow statistics" in the particular context of κ-quantum fields and discuss the analogies/differences with models with twisted statistics.

scholarly journals NEW ANALYTIC RUNNING COUPLING IN QCD: HIGHER LOOP LEVELS

2001 ◽  
Vol 16 (39) ◽  
pp. 2517-2528 ◽  
Author(s):  
A. V. NESTERENKO ◽  
I. L. SOLOVTSOV
Keyword(s):  
General Definition ◽  
Asymptotic Freedom ◽  
Loop Level ◽  
Running Coupling ◽  
Β Function ◽  
Definition Of

The properties of the new analytic running coupling are investigated at the higher loop levels. The expression for this invariant charge, independent of the normalization point, is obtained by invoking the asymptotic freedom condition. It is shown that at any loop level the relevant β-function has the universal behaviors at small and large values of the invariant charge. Due to this feature the new analytic running coupling possesses the universal asymptotics in both the ultraviolet and infrared regions irrespective of the loop level. The consistency of the model considered with the general definition of the QCD invariant charge is shown.

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