Calculation Of Correlation Functions Research Articles

Correlation functions of three-dimensional Yang-Mills theory from the FRG

We compute correlation functions of three-dimensional Landau-gauge Yang-Mills theory with the Functional Renormalisation Group. Starting from the classical action as only input, we calculate the non-perturbative ghost and gluon propagators as well as the momentum-dependent ghost-gluon, three-gluon, and four-gluon vertices in a comprehensive truncation scheme. Compared to the physical case of four spacetime dimensions, we need more sophisticated truncations due to significant contributions from non-classical tensor structures. In particular, we apply a special technique to compute the tadpole diagrams of the propagator equations, which captures also all perturbative two-loop effects, and compare our correlators with lattice and Dyson-Schwinger results.

Handling Handles: Nonplanar Integrability in N=4 Supersymmetric Yang-Mills Theory.

We propose an integrability setup for the computation of correlation functions of gauge-invariant operators in N=4 supersymmetric Yang-Mills theory at higher orders in the large N_{c} genus expansion and at any order in the 't Hooft coupling g_{YM}^{2}N_{c}. In this multistep proposal, one polygonizes the string world sheet in all possible ways, hexagonalizes all resulting polygons, and sprinkles mirror particles over all hexagon junctions to obtain the full correlator. We test our integrability-based conjecture against a nonplanar four-point correlator of large 1/2 Bogomol'nyi-Prasad-Sommerfield operators at one and two loops.

Mass calculations of light quarkonium, exotic JPC=0+− hybrid mesons from Gaussian sum rules

We extend previous calculations of leading-order correlation functions of spin-0 and spin-1 light quarkonium hybrids to include QCD condensates of dimensions five and six, with a view to improving the stability of QCD sum-rules analyses in previously unstable channels. Based on these calculations, prior analyses in the literature, and its phenomenological importance, we identify the exotic $J^{PC}=0^{+-}$ channel as the most promising for detailed study. Using Gaussian sum-rules constrained by the H\"older inequality, we calculate masses of light (nonstrange and strange) quarkonium hybrid mesons with $J^{PC}=0^{+-}$. We consider single narrow, single wide, and double narrow resonance models, and find that the double narrow resonance model yields the best agreement between QCD and phenomenology. In both non-strange and strange cases, we find hybrid masses of $2.60$ GeV and $3.57$ GeV.

The geometry of Casimir W-algebras

Let \mathfrak{g}𝔤 be a simply laced Lie algebra, \widehat{\mathfrak{g}}_1𝔤̂1 the corresponding affine Lie algebra at level one, and \mathcal{W}(\mathfrak{g})𝒲(𝔤) the corresponding Casimir W-algebra. We consider \mathcal{W}(\mathfrak{g})𝒲(𝔤)-symmetric conformal field theory on the Riemann sphere. To a number of \mathcal{W}(\mathfrak{g})𝒲(𝔤)-primary fields, we associate a Fuchsian differential system. We compute correlation functions of \widehat{\mathfrak{g}}_1𝔤̂1-currents in terms of solutions of that system, and construct the bundle where these objects live. We argue that cycles on that bundle correspond to parameters of the conformal blocks of the W-algebra, equivalently to moduli of the Fuchsian system.

АНАЛІЗ МЕТОДИКИ ЗАСТОСУВАННЯ ПОПРАВКИ НА ТОНАЛЬНІСТЬ ПРИ СТЕНДОВИХ ВИПРОБУВАННЯХ ГТД НА ВІДПОВІДНІСТЬ ЕКОЛОГІЧНИМ ВИМОГАМ ПО ШУМУ

The important and actual task of the modern engine engineering is an objective estimation of gas-turbine engine noise levels during its development tests, which will allows to estimate the expected noise levels as part of aircraft. The problem is under review, whose content consists in the analysis of application methods of the tonality amendment during gas-turbine development tests for correspondence with environmental requirements.Classification of tonal noise is contained in many sources. Unfortunately, the determinations and criteria, provided there, are not always consistent with one another that indicate uncomplete determination processes of influence of tonal noise component on its sanitary-hygienic evaluation. The ecological properties of the signal are affected by the modulation law of its tonal (frequency) components. Tone signals of a constant frequency with a unit amplitude modulation index are recognized by the central nervous system as a pure tone and cannot be defined as adverse. These signals, during gas-turbine development tests, include all components parts of the engine that rotate with the constant circular frequency.It is shown that the application of the method of spectral analysis for signals with not determined parameters of stability, leads to undefined methodical error which is not taken into consideration in traditional methods. Determining the value of the tonality parameter, which defines the amendment of the deterioration of object noise assessment, is not strictly validated and is random. In accordance with the foregoing analysis, in our opinion, it is necessary to adjust traditional methods of environmental certification of aircraft on noise level. The methodology should involve the identification of neutral (the summary parameter is not adjusted), unfavorable (the summary parameter is adjusted to the downside) and favorable (the summary parameter is adjusted in the direction of improvement) noises.The ranking algorithm, in connection with the application of the result to biological objects, can be intellectual and identical to the function of Wernicke's area of the central nervous system, i.e. the calculation of mutual correlation function or the correlation coefficient of the signal noise of the aircraft with the database of "favorable" or "unfavorable" signals.

Semiclassical calculation of spectral correlation functions of chaotic systems

We present a semiclassical approach to n-point spectral correlation functions of quantum systems whose classical dynamics is chaotic, for arbitrary n. The basic ingredients are sets of periodic orbits that have nearly the same action and therefore provide constructive interference. We calculate explicitly the first correlation functions, to leading orders in their energy arguments, for both unitary and orthogonal symmetry classes. The results agree with corresponding predictions from random matrix theory, thereby giving solid support to the conjecture of universality.

Full perturbative calculation of spectral correlation functions for chaotic systems in the unitary symmetry class

Starting from a semiclassical approach recently developed for spectral correlation functions of quantum systems whose classical dynamics is chaotic, we focus on the case of broken time-reversal symmetry, the so-called unitary class. We obtain to all orders in perturbation theory the non-oscillatory parts of all correlation functions, showing that the off-diagonal contributions to these correlation functions cancel and the conjectured universailty holds. The innovation that allows this calculation to be performed is the introduction of an auxiliary matrix model which is governed by the same diagrammatic rules as the semiclassical approach and which can be exactly solved.

Lattice study of $J/\Psi$J/Ψ form factors with twisted boundary conditions

We present a lattice calculation for the electromagnetic form factors of $J/\Psi$ by using $N_{f}=2$ twisted mass gauge field configurations. We apply twisted boundary conditions to compute correlation functions at small values of momentum transfer that are difficult to access with periodic boundary conditions. The electromagnetic form factors with more small four-momentum transfer are determined, and further the charge radius and the quadrupole moment for $J/\Psi$ are fitted, respectively.

Revisiting nonfactorizable charm-loop effects in exclusive FCNC B-decays

We revisit the calculation of nonfactorizable corrections induced by charm-quark loops in exclusive FCNC B-decays. For the sake of clarity, we make use of a field theory with scalar particles: this allows us to focus on the conceptual issues and to avoid technical complications related to particle spins in QCD. We perform a straightforward calculation of the appropriate correlation function and show that it requires the knowledge of the full generic three-particle distribution amplitude with non-aligned arguments, 〈0|s¯(y)Gμν(x)b(0)|B(p)〉. Moreover, the dependence of this quantity on the variable (x−y)2 is essential for a proper account of the (ΛQCDmb/mc2)n terms in the amplitudes of FCNC B-decays.

Towards Reconstructing the Quantum Effective Action of Gravity.

Starting from a parametrization of the quantum effective action for gravity, we calculate correlation functions for observable quantities. The resulting templates allow us to reverse engineer the couplings describing the effective dynamics from the correlation functions. Applying this new formalism to the autocorrelation function of spatial volume fluctuations measured within the causal dynamical triangulations program suggests that the corresponding quantum effective action consists of the Einstein-Hilbert action supplemented by a nonlocal interaction term. We expect that our matching-template formalism can be adapted to a wide range of quantum gravity programs allowing us to bridge the gap between the fundamental formulation and observable low-energy physics.

Correlcalc: A ‘generic’ recipe for calculation of two-point correlation function

Abstract This article presents a recipe for computation of galaxy two-point correlation function (2pCF) from redshift surveys using python . One of the salient features of this approach is that it can be used for calculating galaxy clustering for any arbitrary geometry (or Cosmology) model. Being efficient enough to run on a low-spec desktop computer for small datasets, this ‘recipe’ can be used for quick validation of alternative models and for pedagogical purposes.

Correlation Functions of the Quantum Sine-Gordon Model in and out of Equilibrium.

Complete information on the equilibrium behavior and dynamics of quantum field theory (QFT) is provided by multipoint correlation functions. However, their theoretical calculation is a challenging problem, even for exactly solvable models. This has recently become an experimentally relevant problem, due to progress in cold-atom experiments simulating QFT models and directly measuring higher order correlations. Here we compute correlation functions of the quantum sine-Gordon model, a prototype integrable model of central interest from both theoretical and experimental points of view. Building upon the so-called truncated conformal space approach, we numerically construct higher order correlations in a system of finite size in various physical states of experimental relevance, both in and out of equilibrium. We measure deviations from Gaussianity due to the presence of interaction and analyze their dependence on temperature, explaining the experimentally observed crossover between Gaussian and non-Gaussian regimes. We find that correlations of excited states are markedly different from the thermal case, which can be explained by the integrability of the system. We also study dynamics after a quench, observing the effects of the interaction on the time evolution of correlation functions, their spatial dependence, and their non-Gaussianity as measured by the kurtosis.

New compact construction of eigenstates for supersymmetric spin chains

The problem of separation of variables (SoV) in supersymmetric spin chains is closely related to the calculation of correlation functions in mathcal{N}=4 SYM theory which is integrable in the planar limit. To address this question we find a compact formula for the spin chain eigenstates, which does not have any sums over auxiliary roots one usually gets in the widely adopted nested Bethe ansatz. Our construction only involves one application of a simple Bg(uk) operator to the reference state for each of the magnons, in complete analogy with the mathfrak{s}mathfrak{u}(2) algebraic Bethe ansatz. This generalizes our SoV based construction for mathfrak{s}mathfrak{u}(n) to the supersymmetric mathfrak{s}mathfrak{u}left(1Big|2right) case.

Nonperturbative method to compute thermal correlations in one-dimensional systems

We develop a highly efficient method to numerically simulate thermal fluctuations and correlations in non-relativistic continuous bosonic one-dimensional systems. The method is suitable for arbitrary local interactions as long as the system remains dynamically stable. We start by proving the equivalence of describing the systems through the transfer matrix formalism and a Fokker-Planck equation for a distribution evolving in space. The Fokker-Planck equation is known to be equivalent to a stochastic differential (It\={o}) equation. The latter is very suitable for computer simulations, allowing the calculation of any desired correlation function. As an illustration, we apply our method to the case of two tunnel-coupled quasi-condensates of bosonic atoms. The results are compared to the predictions of the sine-Gordon model for which we develop analytic expressions directly from the transfer matrix formalism.

Light-front and conformal field theories in two dimensions

Light-front (LF) quantization of massless fields in two spacetime dimensions is a long-standing and much debated problem. Even though the classical wave-equation is well-documented for almost two centuries, either as problems with initial values in spacetime variables or with initial data on characteristics in light-cone variables, the way to a consistent quantization in both types of frames is still a puzzle in many respects. This is in contrast to the most successful Conformal Field Theoretic (CFT) approach in terms of complex variables [Formula: see text], [Formula: see text] pioneered by Belavin, Polyakov and Zamolodchikov in the ’80s. It is shown here that the 2D-massless canonical quantization in both reference frames is completely consistent provided that quantum fields are treated as Operator-Valued Distributions (OPVD) with Partition of Unity (PU) test functions. We recall first that classical fields have to be considered as distributions (e.g. generalized functions in the Russian literature). Then, a necessary condition on the PU test function follows from the required matching of the classical solutions of the massless differential equations in both types of reference frame. Next we use a mathematical formulation for OPVD, developed in the recent past. Specifically, smooth [Formula: see text] fields are introduced through the convolution operation in the distributional context. Due to the specific behavior of the Fourier-transform of the initial test function, this convolution transform has a well-defined integral in the dual space, whatever the initial choice of the reference frame. The relation to the conformal fields method follows immediately from the transition to Euclidean time and leads directly to explicit calculations of a few correlation functions of the scalar field and its energy–momentum tensor. The LF derivation of the Virasoro algebra is then obtained from the [Formula: see text] and [Formula: see text] expansions of the canonical fields as distributional Laplace-transform in these variables. Finally, the popular and problematic Discretized Light Cone Quantization (DLCQ) method is scrutinized with respect to its zero mode and ultraviolet content as encompassed in the continuum OPVD formulation.

\u21242 boundary twist fields and the moduli space of D-branes

We revisit the boundary conformal field theory of twist fields. Based on the equivalence between twisted bosons on a circle and the orbifold theory at the critical radius, we provide a bosonized representation of boundary twist fields and thus a free field representation of the latter. One advantage of this formulation is that it considerably simplifies the calculation of correlation functions involving twist fields. At the same time this also gives access to higher order terms in the operator product expansions of the latter which, in turn, allows to explore the moduli space of marginal deformation of bound states of D-branes. In the process we also generalize some results on correlation functions with excited twist fields.

Comments on the SN orbifold CFT in the large N-limit

We elaborate on various aspects of the conformal field theory of the symmetric orbifold. We collect various results that have appeared in the literature, and we present a coherent picture of the operator content of this CFT, relying on the orbifold extension of the Virasoro algebra. We then focus on the large N-limit of this theory, discuss the OPE of two twist operators, and find various selection rules. We review how to calculate four-point functions of twist operators, and we write down the most general four-point function in the covering space for large N.We show that it depends on some functions that obey a set of algebraic equations, that resemble the scattering equations. Finally, we provide a recipe on how to calculate correlation functions with insertions of the orbifold Virasoro generators.

Взаємна кореляція компонентів завад роботі тональних рейкових кіл

Tonal rail circuits work in the conditions of simultaneous influence of interferences of different type. These interferences in some cases lead to failures in operation of traveling receivers. For increase in their noise stability it is reasonable to use methodology of optimum reception of signals. Basic operation of processing of entrance additive mix of signal and interferences at such methodology is calculation of mutual correlation function of this mix and basic signal. However in this case there are cross-correlation components of interferences influencing final estimates of parameters of useful signal and these interferences. The purpose of this work is the research of conditions under which the specified cross-correlation components have negligible influence on the specified final estimates. It is shown that in the conditions of regular operation of rail circuits such influence really is negligible. Need of consideration of ways of simplification of means of processing of information signals taking into account the opportunities given by the elicited fact is noted.

Holographic calculation of two-point correlation functions of CFT stress tensor in the BMS gauge and flat-space holography

In this paper, we use the holographic renormalization method to calculate the two-point correlation functions of the CFT stress tensor. In the gravity side, we write the asymptotically AdS spacetimes in the BMS gauge and apply the standard holographic renormalization method for these space-times. The significance of using multi-point functions in this gauge is that its flat-space limit is well-defined. We discuss this point in the last section of the paper.

Influence of super-horizon modes on correlation functions during inflation

Coupling between sub- and super-Hubble modes can affect the locally observed statistics of our universe. In the context of Quasi-Single Field Inflation, we can compute correlation functions and derive the influence of those unobservable modes on observed correlation functions as well as on the inferred cosmological parameters. We study how different classes of diagrams affect the bispectrum in the squeezed limit; in particular, while contact-like diagrams leave the scaling between the long and short modes unchanged, exchange-like diagrams do modify the shape of the bispectrum. We show that the mass of the hidden sector field can hence be biased by an unavoidable cosmic variance that can reach a 1-σ uncertainty of \U0001d4aa(10%) for a weakly non-Gaussian universe. Finally, we go beyond the bispectrum and show how couplings between unobservable and observable modes can affect generic correlation functions with arbitrary order non-derivative self-interactions.