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[en] By use of the threshold expansion we develop an algorithm for analytical evaluation, within dimensional regularization, of arbitrary terms in the expansion of the (two-loop) sunset diagram with general masses m₁, m₂ and m₃ near its threshold, i.e. in any given order in the difference between the external momentum squared and its threshold value, (m₁ + m₂ + m₃)². In particular, this algorithm includes an explicit recurrence procedure to analytically calculate sunset diagrams with arbitrary integer powers of propagators at the threshold

[en] We discuss the origin of the Wilson polygon-MHV amplitude duality at a perturbative level. It is shown that the duality for the MHV amplitudes at the one-loop level can be proven upon a particular change of variables in Feynman parametrization and with the use of the relation between Feynman integrals at different space-time dimensions. Some generalization of the duality which implies the insertion of a particular vertex operator at the Wilson triangle is found for the 3-point function. We discuss the analytical structure of Wilson loop diagrams and present the corresponding Landau equations. The geometrical interpretation of the loop diagram in terms of the hyperbolic geometry is discussed.

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No abstract available

[en] We show how to interpret the scalar Feynman integrals which appear when reducing tensor integrals as scalar Feynman integrals coming from certain nice matroids.

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No abstract available

[en] In the middle of the 20th century David Bohm and Richard Feynman developed two fundamentally different approaches of modern quantum mechanics: Bohm a realistic interpretation by means of hidden parameters and Feynman the path-integral formalism. This is by this more remarakable, because both physicists started from similar conditions and originated from similar connections. By its comparing approach this study presents more than a contribution to the history of the quantum theory. By the question for the social and cultural conditions of the formation of theories it is furthermore of science-sociological and science-theoretical interest. The in the beginning similar and later different binding of both scientists into the scientific community allows furthermore to study, which adapting pressure each group puts on the individual scientist and the fundamental parts of his research, and which new degrees of freedom in the formation of theories arise, when this constraint is cancelled

[en] We study the Fredholm minors associated with a Fredholm equation of the second type. We present a couple of new linear recursion relations involving the nth and (n - 1)th minors, whose solution is a representation of the nth minor as an n x n determinant of resolvents. The latter is given a simple interpretation in terms of a path integral over non-interacting fermions. We also provide an explicit formula for the functional derivative of a Fredholm minor of order n with respect to the kernel. Our formula is a linear combination of the nth and the (n ± 1)th minors