12 research outputs found
Groups of diffeomorphisms and geometric loops of manifolds over ultra-normed fields
The article is devoted to the investigation of groups of diffeomorphisms and
loops of manifolds over ultra-metric fields of zero and positive
characteristics. Different types of topologies are considered on groups of
loops and diffeomorphisms relative to which they are generalized Lie groups or
topological groups. Among such topologies pairwise incomparable are found as
well. Topological perfectness of the diffeomorphism group relative to certain
topologies is studied. There are proved theorems about projective limit
decompositions of these groups and their compactifications for compact
manifolds. Moreover, an existence of one-parameter local subgroups of
diffeomorphism groups is investigated.Comment: Some corrections excluding misprints in the article were mad
Spectral action, Weyl anomaly and the Higgs-Dilaton potential
We show how the bosonic spectral action emerges from the fermionic action by
the renormalization group flow in the presence of a dilaton and the Weyl
anomaly. The induced action comes out to be basically the Chamseddine-Connes
spectral action introduced in the context of noncommutative geometry. The
entire spectral action describes gauge and Higgs fields coupled with gravity.
We then consider the effective potential and show, that it has the desired
features of a broken and an unbroken phase, with the roll down.Comment: 23 pages, 4 figure