Generalized local-frame-transformation theory for excited species in external fields

Generalized Bogoliubov Transformation for Confined Fields: Applications in Casimir Effect

The Bogoliubov transformation in thermofield dynamics, an operator formalism for the finite-temperature quantum-field theory, is generalized to describe a field in arbitrary confined regions of space and time. Starting with the scalar field, the approach is extended to the electromagnetic field and the energy-momentum tensor is written via the Bogoliubov transformation. In this context, the Cas...

Ramification Theory for Higher Dimensional Local Fields

The paper contains a construction of ramification theory for higher dimensional local fields K provided with additional structure given by an increasing sequence of their “subfields of i-dimensional constants”, where 0 i n and n is the dimension of K. It is also announced that a local analogue of the Grothendieck Conjecture still holds: all automorphisms of the absolute Galois group of K, which...

Control Theory for Semigroups over Local Fields

Let G be a 1-connected, almost-simple Lie group over a local field and S a subsemigroup of G with non-empty interior. The action of the regular hyperbolic elements in the interior of S on the flag manifold G/P and on the associated Euclidean building allows us to prove that the invariant control set exists and is unique. We also provide a characterization of the set of transitivity of the contr...

Ramification Theory for Local Fields with Imperfect Residue Fields

Notation 1.1. Let l/k be a finite Galois extension of complete discretely valued fields. Let Ok, Ol, πk, πl, k̄, and l̄ be rings of integers, uniformizers, and residue fields, respectively. For an element a ∈ Ol, we use ā to denote its reduction in l̄. Let G = Gl/k be the Galois group. Use vl(·) to denote the valuation on l so that vl(πl) = 1. We call e = vl(πk) the näıve ramification degree; it i...

Local Functionals and Generalized Random Fields