Microlocal Geometry and Valued Fields

Microlocal spectrum condition and Hadamard form for vector-valued quantum fields in curved spacetime

The characterization of Hadamard states in terms of a specific form of the wavefront set of their two-point functions has been developed some years ago by Radzikowski for scalar fields on a four-dimensional globally hyperbolic spacetime, and initiated a major progress in the understanding of Hadamard states and the further development of quantum field theory in curved spacetime. In the present ...

Donaldson-Thomas Type Invariants via Microlocal Geometry

We prove that Donaldson-Thomas type invariants are equal to weighted Euler characteristics of their moduli spaces. In particular, such invariants depend only on the scheme structure of the moduli space, not the symmetric obstruction theory used to define them. We also introduce new invariants generalizing Donaldson-Thomas type invariants to moduli problems with open moduli space. These are usef...

FUZZY HYPERVECTOR SPACES OVER VALUED FIELDS

In this note we first redefine the notion of a fuzzy hypervectorspace (see [1]) and then introduce some further concepts of fuzzy hypervectorspaces, such as fuzzy convex and balance fuzzy subsets in fuzzy hypervectorspaces over valued fields. Finally, we briefly discuss on the convex (balanced)hull of a given fuzzy set of a hypervector space.

Valued Difference Fields and Ntp

We show that the theory of the non-standard Frobenius automorphism, acting on an algebraically closed valued field of equal characteristic 0, is NTP2. More generally, in the contractive as well as in the isometric case, we prove that a σ-Henselian valued difference field of equicharacteristic 0 is NTP2, provided both the residue difference field and the value group (as an ordered difference gro...

Amalgamating valued fields