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Consistent Interactions in terms of the Generalized Fields Method
The interactions which preserve the structure of the gauge interactions of
the free theory are introduced in terms of the generalized fields method of
solving the Batalin-Vilkovisky master equation. It is shown that by virtue of
this method the solution of the descent equations resulting from the
cohomological analysis is provided straightforwardly. The general scheme is
illustrated by applying it to spin-1 gauge field in 3 and 4 dimensions, to free
BF theory in 2-d and to the antisymmetric tensor field in any dimension. It is
shown that it reproduces the results obtained by cohomological techniques.Comment: to appear in IJMPA, extended and some refs. adde
Norms as products of linear polynomials
Let F be a number field, and let F\subset K be a field extension of degree n.
Suppose that we are given 2r sufficiently general linear polynomials in r
variables over F. Let X be the variety over F such that the F-points of X
bijectively correspond to the representations of the product of these
polynomials by a norm from K to F. Combining the circle method with descent we
prove that the Brauer-Manin obstruction is the only obstruction to the Hasse
principle and weak approximation on any smooth and projective model of X.Comment: 25 page
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