Instantons In Quantum Chromodynamics Research Articles

Monopole and instanton effects in QCD

We aim to show the effects of the magnetic monopoles and instantons in quantum chromodynamics (QCD) on observables; therefore, we introduce a monopole and anti-monopole pair in the QCD vacuum of a quenched SU(3) by applying the monopole creation operator to the vacuum. We calculate the eigenvalues and eigenvectors of the overlap Dirac operator that preserves the exact chiral symmetry in lattice gauge theory using these QCD vacua. We then investigate the effects of magnetic monopoles and instantons. First, we confirm the monopole effects as follows: (i) the monopole creation operator makes the monopoles and anti-monopoles in the QCD vacuum. (ii) A monopole and anti-monopole pair creates an instanton or anti-instanton without changing the structure of the QCD vacuum. (iii) The monopole and anti-monopole pairs change only the scale of the spectrum distribution without affecting the spectra of the Dirac operator by comparing the spectra with random matrix theory. Next, we find the instanton effects by increasing the number density of the instantons and anti-instantons as follows: (iv) the decay constants of the pseudoscalar increase. (v) The values of the chiral condensate, which are defined as negative numbers, decrease. (vi) The light quarks and the pseudoscalar mesons become heavy. The catalytic effect on the charged pion is estimated using the numerical results of the pion decay constant and the pion mass. (vii) The decay width of the charged pion becomes wider than the experimental result, and the lifetime of the charged pion becomes shorter than the experimental result. These are the effects of the monopoles and instantons in QCD.

Of connections and fields - I

We describe some instances of the appearance of Chern’s mathematical ideas in physics. By means of simple examples, we bring out the geometric and topological ideas which have found application in describing the physical world. These applications range from magnetic monopoles in electrodynamics to instantons in quantum chromodynamics to the geometric phase of quantum mechanics. The first part of this article is elementary and addressed to a general reader. The second part is somewhat more demanding and is addressed to advanced students of mathematics and physics.

Instantons in the nonperturbative QCD vacuum

The influence of nonperturbative fields on instantons in quantum chromodynamics is studied. Nonperturbative vacuum is described in terms of nonlocal gauge invariant vacuum averages of gluon field strength.Effective action for instanton is derived in bilocal approximation and it is demonstrated that stochastic background gluon fields are responsible for infra-red (IR) stabilization of instantons. Dependence of characteristic instanton size on gluon condensate and correlation length in nonperturbative vacuum is found. Comparison of obtained instanton size distribution with lattice data is made.

Instanton IR stabilization in the nonperturbative confining vacuum

The influence of nonperturbative fields on instantons in quantum chromodynamics is studied. Nonperturbative vacuum is described in terms of nonlocal gauge invariant vacuum averages of gluon field strength. Effective action for instanton is derived in bilocal approximation and it is demonstrated that stochastic background gluon fields are responsible for infra-red (IR) stabilization of instantons. Dependence of characteristic instanton size on gluon condensate and correlation length in nonperturbative vacuum is found. It is shown that instanton size in QCD is of order of 0.25 fm. Comparison of obtained instanton size distribution with lattice data is made.

Instantons in QCD

The authors review the theory and phenomenology of instantons in quantum chromodynamics (QCD). After a general overview, they provide a pedagogical introduction to semiclassical methods in quantum mechanics and field theory. The main part of the review summarizes our understanding of the instanton liquid in QCD and the role of instantons in generating the spectrum of light hadrons. The authors also discuss properties of instantons at finite temperature and how instantons can provide a mechanism for the chiral phase transition. They give an overview of the role of instantons in some other models, in particular low-dimensional sigma models, electroweak theory, and supersymmetric QCD.

The role of instantons in quantum chromodynamics: (II). Hadronic structure

The “constituent quark” (or “valon”) substructure of ordinary hadrons is the consequence of small instanton radius ϱ c ⋍ 1 3 fm in the QCD vacuum. The same parameter determines hadronic masses and other parameters, in particular the unusually large mass scale for “exceptional” hadrons with zero spin.

The role of instantons in quantum chromodynamics: (I). Physical vacuum

We argue that the physical QCD vacuum is similar to the “instanton liquid” with density d n/d ϱ = n c( gd( ϱ− ϱ c), where n c ⋍ 8 · 10 −4 GeV 4 and ϱ c ⋍ 1 600 GeV . Instantons occupy only about 1 20 th of space-time, which can be traced to the presence of several light quark flavours. Several predictions of the vacuum properties ( e.g. 〈 ψψ〉 ⋍ − 1 · 10 −2 GeV 3) are in agreement with phenomenology.

ABC of instantons

An attempt is made to present an instanton calculus in a relatively simple form. The physical meaning of instantons is explained by the example of the quantum-mechanical problem of energy levels in a two-humped potential. The nonstandard solution to this problem based on instantons is analyzed, and the reader is acquainted with the main technical elements used in this approach. Instantons in quantum chromodynamics are then considered. The Euclidean formulation of the theory is described. Classical solutions of the field equations (the Belavin–Polyakov–Shvarts–Tyapkin instantons) are obtained explicitly and their properties are studied. The calculation of the instanton density is described and the complete result is given for an arbitrary number of colors. The effects associated with fermion fields are briefly described.

Statistical mechanics of instantons in quantum chromodynamics

We develop a field-theoretic method to investigate the statistical mechanics associated with the instanton-antiinstanton ensemble in Yang-Mills gauge theory. This consists in exact rewriting of the partition function in terms of collective fields and incorporation of short-range forces. In the framework of this effective field theory we clarify the meaning of the continuum medium approximation introduced recently by Callan, Dashen, and Gross. Furthermore, we present a direct treatment of the first-order liquid-gas phase transition which is ultimately responsible for bag creation in quantum chromodynamics.

Analogs of merons and meron pairs in theXYmodel

A path-integral formula for the vacuum wave functional is used to show that merons in quantum chromodynamics produce long-range vacuum fluctuations of the form of Wu-Yang monopoles, whereas meron pairs or instantons produce only short-range fluctuations. The existence of long-range vacuum fluctuations may be related to the problem of quark confinement. The $\mathrm{XY}$ model, which describes classical two-component spins on a two-dimensional lattice, is reviewed. Vortex spin-field configurations, which are responsible for the existence of a disordered phase in the $\mathrm{XY}$ model, are shown to be analogous to merons in that they produce long-range fluctuations of the spins along a given axis. The analogy is emphasized by considering the analog of the vacuum wave functional in the $\mathrm{XY}$ model. It is argued that the vortex-antivortex pairs that occur in the ordered phase of the $\mathrm{XY}$ model are analogous to meron pairs or instantons in quantum chromodynamics.