On Green's functions in generalized axially symmetric potential theory

Generalized Axially Symmetric Potential Theory

On the Domain of Regularity of Generalized Axially Symmetric Potentials

which depends analytically on the two real variables x and y in a domain containing a segment of the singular line y — 0, is uniquely determined by its values on y = 0. In this note we shall consider the following problem: If the function g(z) =u(z, 0) is continued to complex values of z, to what extent does its domain of regularity determine the domain of regularity of u(x, y)? A partial answe...

On Axially Symmetric Solutions in the Electroweak Theory

We present the general ansatz, the energy density and the Chern-Simons charge for static axially symmetric configurations in the bosonic sector of the electroweak theory. Containing the sphaleron, the multisphalerons and the sphaleronantisphaleron pair at finite mixing angle, the ansatz further allows the construction of the sphaleron and multisphaleron barriers and of the bisphalerons at finit...

Generalized symmetric functions

It is well known that over an infinite field the ring of symmetric functions in a finite number of variables is isomorphic to the one of polynomial functions on matrices that are invariants by the action of conjugation by general linear group. We generalize this result showing that the abelianization of the algebra of the symmetric tensors of fixed order over a free associative algebra is isomo...

Axially Symmetric Multisphalerons in Yang-mills-dilaton Theory

We construct sequences of axially symmetric multisphaleron solutions in SU(2) Yang-Mills-dilaton theory. The sequences are labelled by a winding number n > 1. For n = 1 the known sequence of spherically symmetric sphaleron solutions is obtained. The solutions within each sequence are labelled by the number of nodes k of the gauge field functions. The limiting solutions of the sequences correspo...