On Essential Incompleteness of Hertz's Experiments on Propagation of Electromagnetic Interactions

The historical background of the 19th century electromagnetic theory is revisited from the standpoint of the opposition between alternative approaches in respect to the problem of interactions. The 19th century electrodynamics became the battle-field of a paramount importance to test existing conceptions of interactions. Hertz's experiments were designed to bring a solid experimental evidence in favor of one of them. The modern scientific method applied to analyze Hertz's experimental approach as well as the analysis of his laboratory notes, dairy and private letters show that Hertz's "\textit{crucial}" experiments cannot be considered as conclusive at many points as it is generally implied. We found that alternative Helmholtz's electrodynamics did not contradict any of Hertz's experimental observations of transverse components as Maxwell's theory predicted. Moreover, as we now know from recently published Hertz's dairy and private notes, his first experimental results indicated clearly on infinite rate of propagation. Nevertheless, Hertz's experiments provided no further explicit information on non-local longitudinal components which were such an essential feature of Helmholtz's theory. Necessary and sufficient conditions for a decisive choice on the adequate account of electromagnetic interactions are discussed from the position of modern scientific method

Geometric approach to asymptotic expansion of Feynman integrals

We present an algorithm that reveals relevant contributions in non-threshold-type asymptotic expansion of Feynman integrals about a small parameter. It is shown that the problem reduces to finding a convex hull of a set of points in a multidimensional vector space.Comment: 6 pages, 2 figure

Baxter equations and Deformation of Abelian Differentials

In this paper the proofs are given of important properties of deformed Abelian differentials introduced earlier in connection with quantum integrable systems. The starting point of the construction is Baxter equation. In particular, we prove Riemann bilinear relation. Duality plays important role in our consideration. Classical limit is considered in details.Comment: 28 pages, 1 figur

Solar wind and temperature field of the troposphere

Relationship between solar wind velocities and temperature field of lower troposphere derived from satellite measurement

The Four-Loop Dressing Phase of N=4 SYM

We compute the dilatation generator in the su(2) sector of planar N=4 super Yang-Mills theory at four-loops. We use the known world-sheet scattering matrix to constrain the structure of the generator. The remaining few coefficients can be computed directly from Feynman diagrams. This allows us to confirm previous conjectures for the leading contribution to the dressing phase which is proportional to zeta(3).Comment: 19 pages, v2: referenced adde

The Tails of the Crossing Probability

The scaling of the tails of the probability of a system to percolate only in the horizontal direction $\pi_{hs}$ was investigated numerically for correlated site-bond percolation model for $q=1,2,3,4$.We have to demonstrate that the tails of the crossing probability far from the critical point have shape $\pi_{hs}(p) \simeq D \exp(c L[p-p_{c}]^{\nu})$ where $\nu$ is the correlation length index, $p=1-\exp(-\beta)$ is the probability of a bond to be closed. At criticality we observe crossover to another scaling $\pi_{hs}(p) \simeq A \exp (-b {L [p-p_{c}]^{\nu}}^{z})$. Here $z$ is a scaling index describing the central part of the crossing probability.Comment: 20 pages, 7 figures, v3:one fitting procedure is changed, grammatical change

Analytic Results for Massless Three-Loop Form Factors

We evaluate, exactly in d, the master integrals contributing to massless three-loop QCD form factors. The calculation is based on a combination of a method recently suggested by one of the authors (R.L.) with other techniques: sector decomposition implemented in FIESTA, the method of Mellin--Barnes representation, and the PSLQ algorithm. Using our results for the master integrals we obtain analytical expressions for two missing constants in the ep-expansion of the two most complicated master integrals and present the form factors in a completely analytic form.Comment: minor revisions, to appear in JHE