Gluon field strength correlation functions within a constrained instanton model

We suggest a constrained instanton (CI) solution in the physical QCD vacuum which is described by large-scale vacuum field fluctuations. This solution decays exponentially at large distances. It is stable only if the interaction of the instanton with the background vacuum field is small and additional constraints are introduced. The CI solution is explicitly constructed in the ansatz form, and the two-point vacuum correlator of the gluon field strengths is calculated in the framework of the effective instanton vacuum model. At small distances the results are qualitatively similar to the single instanton case; in particular, the invariant structure is small, which is in agreement with the lattice calculations. Received: 18 June 1999 / Revised version: 21 July 1999 / Published online: 17 February 2000     

On the statistical mechanics of dense instanton gases

Instanton gases of two-dimensional?P ^n?1 and four-dimensionalSU(n) Yang-Mills theories are considered. The presumable denseness of instanton gases in these models and the corresponding statistics of instantons lead to a theormodynamic limit in which the coupling constant dependence of non-perturbative quantities is modified by a factor proportional to 1/n compared to the case of a dilute gas. As a consequence the largen limit and the infinite volume limit do not appear to commute. We present a naive droplet model for dense instanton gases which exhibits these features. Possible consequences for the large order behaviour of perturbation series are discussed.     

Nonperturbative contribution to the quark form factor within the instanton model

The nonperturbative effects in the quark form factor are considered in the Wilson loop formalism, within the framework of the instanton liquid model. For the integration path corresponding to this form factor, the explicit expression for the vacuum expectation value of the Wilson operator is found to the leading order. It is shown that the instantons produce the power-like corrections to the perturbative result, which are comparable in magnitude with the perturbative part at the scale of order of the inverse average instanton size. It is demonstrated that the instanton contributions to the quark form factor are exponentiated to high orders in the small instanton density parameter.Received: 30 September 2002, Published online: 22 October 2003PACS: 12.38.-t Quantum chromodynamics - 11.15.Tk Other nonperturbative techniques     

The generalized Fubini instanton

We show that (1+2) nonlinear Klein-Gordon equation with negative coupling admits an exact solution which appears to be the linear superposition of the plane wave and the nonsingular rational soliton. We show that the same approach allows to construct the solution of similar properties for the Euclidean ?⁴ model with broken symmetry. Interestingly, this regular solution will be of instanton type only in the D?5 Euclidean space. Thus one can use the generalized Fubini instantons (in quantum cosmology for example) only for the case of the single infinite extra dimension.     

Constrained instanton and black hole creation

It is generally accepted that the Einstein theory of general relativity governs the evolution of the universe. However, the singularity theorem of Hawking and Penrose[1] shows that under the most reasonable physical conditions, a spacetime singularity, where physics laws and even causality are broken down, is unavoidable. One has to impose the boundary or initial conditions at the edge of spacetime for the evolution of the universe. This is the so-called first cause problem. The no-boundary …     

Instantons and fermions in the field of instanton

The number of instantons and the number of zero fermion modes in the field of instanton are calculated. The quantum fluctuations of instantons are studied.     

A new AF gravitational instanton

It has long been conjectured that the Euclidean Schwarzschild and Euclidean Kerr instantons are the only non-trivial asymptotically flat (AF) gravitational instantons. In this Letter, we show that this conjecture is false by explicitly constructing a new two-parameter AF gravitational instanton with a U(1)×U(1) isometry group, using the inverse-scattering method. It has Euler number χ=3 and Hirzebruch signature τ=1, and its global topology is CP² with a circle S¹ removed appropriately. Various other properties of this gravitational instanton are also discussed.     

Weak charge quantization as an instanton of the interacting sigma model

Coulomb blockade in a quantum dot attached to a diffusive conductor is considered in the framework of the nonlinear sigma model. It is shown that the weak charge quantization on the dot is associated with instanton configurations of the Q field in the conductor. The instantons have a finite action and are replica nonsymmetric. It is argued that such instantons may play a role in the transition regime to the interacting insulator.     

Self-dual fields harbored by a Kerr–Taub-bolt instanton

We present a new exact solution for self-dual Abelian gauge fields living on the space of the Kerr–Taub-bolt instanton, which is a generalized example of asymptotically flat instantons with non-self-dual curvature, by constructing the corresponding square integrable harmonic form on this space.     

Effect of hadronization on the form of correlation moments for instanton processes and possibility of discovering them experimentally

The possibility of discovering QCD instantons in deep-inelastic scattering by analyzing correlations in final states is studied. The correlation moments F _q and H _q for instanton processes are calculated at the parton and at the hadron level. Hadronization is taken into account by the Monte Carlo method. The moments for instanton and for usual processes are found to behave differently, which can be used to identify experimentally instantons.     

Flat space as a gravitational instanton

Gravitational instantons may influence elementary particle phenomena, even when space-time is flat. To illustrate this point, we employ instanton techniques to rederive a result first obtained by totally different methods; an observer accelerating uniformly in flat Minkowski space experiences a heat bath whose temperature is proportional to his acceleration.     

The “instanton liquid”

We review the theory of interacting topological fluctuations in the ground state of quantum gauge theories, the so called “instanton liquid”. First we outline some known phenomenological facts, both coming from “real” experiments (for QCD) and from the lattice data. Then we describe interaction of instantons and the statistical mechanics of their ensemble for theSU(2) gauge theory. The very essential role of the light quarks is considered using numerical experiments. One of the main conclusions is that instantons induce chiral symmetry breaking in vacuum, but as they are suppressed (e.g. by the nonzero temperature) this symmetry is restored. Phase transition is found to be very strong and of the first order.     

Bose-Einstein condensation beyond perturbation theory: Goldstone singularities and instanton solution

Temperature Green functions are applied to the analysis of Bose-condensation of weaklyinteracting gas. The character of Goldstone singularities of correlation functions isestablished to all orders in perturbation theory. These singularities are regularized bythe system volume. An anomalous volume dependence of the correlation functions isrevealed. Quantum-field perturbation series are studied in the framework of the instantonapproach. It is shown that there are no time-dependent instantons and that thetime-independent instanton solutions exhibit factorial growth in large orders of thequantum-field perturbation expansion.     

The Dyson-Schwinger equations in the instanton vacuum of the Schwinger model

Using the exact path integral solution of the Schwinger model — a model where instantons are present — the Dyson-Schwinger equations are shown to hold by explicit computation. It turns out that the Dyson-Schwinger equations separately hold for every instanton sector. This is due to the invariance of the Schwinger model.Supported by Fonds zur Förderung der wissenschaftlichen Forschung in Österreich, Projekt Nr.P8444-TEC.     

瞬子效应在0++胶球的QCD求和规则中的作用

利用包含瞬子效应的QCD求和规则计算了0⁺⁺胶球的质量上限,结果为1.3GeV.还探讨了变动瞬子参量时对QCD求和规则的影响,发现包含瞬子修正的QCD求和规则在瞬子大小为1/3fm时变得很稳定     

The instanton vacuum of generalized CP models

It has recently been pointed out that the existence of massless chiral edge excitations has important strong coupling consequences for the topological concept of an instanton vacuum. In the first part of this paper we elaborate on the effective action for “edge excitations” in the Grassmannian U (m + n)/U (m) × U (n) non-linear sigma model in the presence of the θ term. This effective action contains complete information on the low energy dynamics of the system and defines the renormalization of the theory in an unambiguous manner. In the second part of this paper we revisit the instanton methodology and embark on the non-perturbative aspects of the renormalization group including the anomalous dimension of mass terms. The non-perturbative corrections to both the β and γ functions are obtained while avoiding the technical difficulties associated with the idea of constrained instantons. In the final part of this paper we present the detailed consequences of our computations for the quantum critical behavior at θ = π. In the range 0 ? m, n ? 1 we find quantum critical behavior with exponents that vary continuously with varying values of m and n. Our results display a smooth interpolation between the physically very different theories with m = n = 0 (disordered electron gas, quantum Hall effect) and m = n = 1 (O (3) non-linear sigma model, quantum spin chains) respectively, in which cases the critical indices are known from other sources. We conclude that instantons provide not only a qualitative assessment of the singularity structure of the theory as a whole, but also remarkably accurate numerical estimates of the quantum critical details (critical indices) at θ = π for varying values of m and n.     

New instanton and meron solutions of a generally covariant four-dimensional sigma model

We construct new solutions of the fourdimensional sigma model coupled to the metric tensor field and having an internalO invariance. Our solutions interpolate continuously between the known instanton and meron solutions depending upon a parameterf. We find that the typical domain for the instantons is 2<f≦3 while for the merons is 0≦f≦2.     

Off-diagonal quark distributions in pions in the effective single-instanton approximation

Nonperturbative functions that parametrize off-diagonal hadronic matrix elements of the light-cone leading-twist quark operators are considered. These functions are calculated within the proposed relativistic quark model allowing for the nontrivial structure of the QCD vacuum, special attention being given to gauge invariance. Hadrons are treated as bound states of quarks; strong-interaction quark-pion vertices are described by effective interaction Lagrangians generated by instantons. The parameters of the instanton vacuum, such as the effective radius of the instanton and the quark mass, are related to the vacuum expectation values of the quark-gluon operators of the lowest dimension and to low-energy pion observables.