1,684 research outputs found
Computer package DIZET v. 6.45
The new version of the DIZET electroweak library is described. Changes and
additional code features concerning the previous version are explained. The
software allows one to make state-of-the-art theoretical predictions for
pseudo-observable quantities, including higher-order radiative corrections. The
current version of the DIZET library v. 6.45 incorporates advanced recent
results of theoretical calculations. Numerical comparisons with the results of
the previous version are performed. Estimates of theoretical uncertainties are
discussed.Comment: 14 pages, 3 figures, 8 table
Gravitational potential of a homogeneous circular torus: new approach
The integral expression for gravitational potential of a homogeneous circular
torus composed of infinitely thin rings is obtained. Approximate expressions
for torus potential in the outer and inner regions are found. In the outer
region a torus potential is shown to be approximately equal to that of an
infinitely thin ring of the same mass; it is valid up to the surface of the
torus. It is shown in a first approximation, that the inner potential of the
torus (inside a torus body) is a quadratic function of coordinates. The method
of sewing together the inner and outer potentials is proposed. This method
provided a continuous approximate solution for the potential and its
derivatives, working throughout the region.Comment: 10 pages, 9 figures, 1 table; some misprints in formulae were
correcte
Physics in Riemann's mathematical papers
Riemann's mathematical papers contain many ideas that arise from physics, and
some of them are motivated by problems from physics. In fact, it is not easy to
separate Riemann's ideas in mathematics from those in physics. Furthermore,
Riemann's philosophical ideas are often in the background of his work on
science. The aim of this chapter is to give an overview of Riemann's
mathematical results based on physical reasoning or motivated by physics. We
also elaborate on the relation with philosophy. While we discuss some of
Riemann's philosophical points of view, we review some ideas on the same
subjects emitted by Riemann's predecessors, and in particular Greek
philosophers, mainly the pre-socratics and Aristotle. The final version of this
paper will appear in the book: From Riemann to differential geometry and
relativity (L. Ji, A. Papadopoulos and S. Yamada, ed.) Berlin: Springer, 2017
Quantum Spin Chains and Riemann Zeta Function with Odd Arguments
Riemann zeta function is an important object of number theory. It was also
used for description of disordered systems in statistical mechanics. We show
that Riemann zeta function is also useful for the description of integrable
model. We study XXX Heisenberg spin 1/2 anti-ferromagnet. We evaluate a
probability of formation of a ferromagnetic string in the anti-ferromagnetic
ground state in thermodynamics limit. We prove that for short strings the
probability can be expressed in terms of Riemann zeta function with odd
arguments.Comment: LaTeX, 7 page
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