7,568 research outputs found
Duality for local fields and sheaves on the category of fields
Duality for complete discrete valuation fields with perfect residue field
with coefficients in (possibly p-torsion) finite flat group schemes was
obtained by Begueri, Bester and Kato. In this paper, we give another
formulation and proof of this result. We use the category of fields and a
Grothendieck topology on it. This simplifies the formulation and proof and
reduces the duality to classical results on Galois cohomology. A key point is
that the resulting site correctly captures extension groups between algebraic
groups.Comment: 63 pages. Revision after the second referee repor
Some remarks on the local class field theory of Serre and Hazewinkel
We give a new approach for the local class field theory of Serre and
Hazewinkel. We also discuss two-dimensional local class field theory in this
framework.Comment: 23 pages; final versio
Massless two-loop "master" and three-loop two point function in NDIM
NDIM (Negative Dimensional Integration Method) is a technique for evaluating
Feynman integrals based on the concept of analytic continuation. The method has
been successfully applied to many diagrams in covariant and noncovariant gauge
field interactions and has shown its utility as a powerful technique to handle
Feynman loop integrations in quantum field theories. In principle NDIM can
handle any loop calculation; however, in practical terms, the resulting
multiseries with several variables in general cannot be summed up conveniently
and its analytic properties are generally unknown.
The alternative then is to use order by order (loop by loop) integration in
which the first integral is of the triangle diagram type. However, the
na\"{i}ve momentum integration of this leads to wrong results. Here we use the
shortened version for the triangle in NDIM that is suitable for a loop by loop
calculation and show that it leads (after appropriate analytic continuation to
positive dimension) to agreement with the known result for the two-loop master
diagram. From it, a three-loop is then calculated and shown again its
consistency with the already published result for such a diagram.Comment: 15 pages, 2 figure
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