Search results for "CONTINUA"
showing 10 items of 362 documents
Euclidean correlators at imaginary spatial momentum and their relation to the thermal photon emission rate
2018
The photon emission rate of a thermally equilibrated system is determined by the imaginary part of the in-medium retarded correlator of the electromagnetic current transverse to the spatial momentum of the photon. In a Lorentz-covariant theory, this correlator can be parametrized by a scalar function ${\cal G}_R(u\cdot {\cal K},{\cal K}^2)$, where $u$ is the fluid four-velocity and ${\cal K}$ corresponds to the momentum of the photon. We propose to compute the analytic continuation of ${\cal G}_R(u\cdot {\cal K},{\cal K}^2)$ at fixed, vanishing virtuality ${\cal K}^2$, to imaginary values of the first argument, $u\cdot {\cal K}= i\omega_n$. At these kinematics, the retarded correlator is eq…
Lattice QCD and the timelike pion form factor.
2011
We present a formula that allows one to calculate the pion form factor in the timelike region 2mpi <= sqrt{s} <= 4mpi in lattice QCD. The form factor quantifies the contribution of two-pion states to the vacuum polarization. It must be known very accurately in order to reduce the theoretical uncertainty on the anomalous magnetic moment of the muon. At the same time, the formula constitutes a rare example where, in a restricted kinematic regime, the spectral function of a conserved current can be determined from Euclidean observables without an explicit analytic continuation.
Corner contribution to cluster numbers in the Potts model
2013
For the two-dimensional Q-state Potts model at criticality, we consider Fortuin-Kasteleyn and spin clusters and study the average number N_Gamma of clusters that intersect a given contour Gamma. To leading order, N_Gamma is proportional to the length of the curve. Additionally, however, there occur logarithmic contributions related to the corners of Gamma. These are found to be universal and their size can be calculated employing techniques from conformal field theory. For the Fortuin-Kasteleyn clusters relevant to the thermal phase transition we find agreement with these predictions from large-scale numerical simulations. For the spin clusters, on the other hand, the cluster numbers are no…
Data-driven dispersive analysis of the ππ and πK scattering
2021
We present a data-driven analysis of the resonant $S$-wave $\ensuremath{\pi}\ensuremath{\pi}\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\pi}$ and $\ensuremath{\pi}K\ensuremath{\rightarrow}\ensuremath{\pi}K$ reactions using the partial-wave dispersion relation. The contributions from the left-hand cuts are accounted for using the Taylor expansion in a suitably constructed conformal variable. The fits are performed to experimental and lattice data as well as Roy analyses. For the $\ensuremath{\pi}\ensuremath{\pi}$ scattering we present both a single- and a coupled-channel analysis by including additionally the $K\overline{K}$ channel. For the latter the central result is the Omn\`es m…
Resurgent Deformation Quantisation
2013
We construct a version of the complex Heisenberg algebra based on the idea of endless analytic continuation. In particular, we exhibit an integral formula for the product of resurgent operators with algebraic singularities. This algebra would be large enough to capture quantum effects that escape ordinary formal deformation quantisation.
Light quark condensates from QCD sum rules
1985
The light quark condensates have been determined by two different methods: By Laplace transformed QCD sum rules together with an improved hadronic continuum from extended PCAC and by analytic continuation by duality (ACD) of the asymptotic QCD amplitude. Both methods yield compatible results. The PCAC corrections are considerably large: for theu, d quarks near 8% and for theu, s quarks of order 60%.
Surface tension and interfacial fluctuations in d-dimensional Ising model
2005
The surface tension of rough interfaces between coexisting phases in 2D and 3D Ising models are discussed in view of the known results and some original calculations presented in this paper. The results are summarised in a formula, which allows to interpolate the corrections to finite-size scaling between two and three dimensions. The physical meaning of an analytic continuation to noninteger values of the spatial dimensionality d is discussed. Lattices and interfaces with properly defined fractal dimensions should fulfil certain requirements to possibly have properties of an analytic continuation from d-dimensional hypercubes. Here 2 appears as the marginal value of d below which the (d-1)…
A Study on the Propagation of Plane Stress Waves across the Thickness of a Plate by the Method of Analytic Continuation in Time
2004
The interaction of plane tension/compression waves propagating within a plate perpendicularly to its surface is considered. The analytic solution is obtained by a modified method of characteristics for the one-dimensional wave equation used in problems on an impact of a rigid body on the surface of a plate. The displacements, velocities, and stresses in the plate are determined by the edge disturbance caused by the initial velocity and the stationary force field of masses of the striker and the plate. The method of analytic continuation in time put forward allows a stress analysis for an arbitrary time interval by using finite expressions. Contrary to a stress analysis in the frequency doma…
Analytic Continuation of the Kite Family
2019
We consider results for the master integrals of the kite family, given in terms of ELi-functions which are power series in the nome q of an elliptic curve. The analytic continuation of these results beyond the Euclidean region is reduced to the analytic continuation of the two period integrals which define q. We discuss the solution to the latter problem from the perspective of the Picard–Lefschetz formula.
The role of negative and positive forms of power in supporting CSR alignment and commitment between large firms and SMEs
2018
Do large firms exert power to shape the CSR behavior of their SME partners?” We answer this question by proposing a model built on the stakeholder theory and the shareholder theory, and go on to explain how this impact influences the commitment of the SME towards their large partner. The model highlights the central role that different forms of power exercised by the large firm play in the process. A survey of 291 SMEs confirms the key hypotheses, including the mediating role of reward power. The effects of coercive power are noteworthy and they illustrate the complex and competing forces at play in influencing CSR behavioral change in SMEs. The research makes a novel contribution to practi…