Fields definable in the free group

Definable Sets in Valued Fields

Groups Definable in Separably Closed Fields

We consider the groups which are infinitely definable in separably closed fields of finite degree of imperfection. We prove in particular that no new definable groups arise in this way: we show that any group definable in such a field L is definably isomorphic to the group of L-rational points of an algebraic group defined over L.

Group Averaging for de Sitter free fields

Perturbative gravity about global de Sitter space is subject to linearizationstability constraints. Such constraints imply that quantum states of matter fields couple consistently to gravity only if the matter state has vanishing de Sitter charges; i.e., only if the state is invariant under the symmetries of de Sitter space. As noted by Higuchi, the usual Fock spaces for matter fields contain n...

Groups, group actions and fields definable in first-order topological structures

Given a group (G, ·), G ⊆M, definable in a first order structureM = (M, . . .) equipped with a dimension function and a topology satisfying certain natural conditions, we find a large open definable subset V ⊆ G and define a new topology τ on G with which (G, ·) becomes a topological group. Moreover, τ restricted to V coincides with the topology of V inherited from M. Likewise we topologize tra...

..free Quantum Fields on the Poincar E Group

A class of free quantum elds deened on the Poincar e group, is described by means of their two-point vacuum expectation values. They are not equivalent to elds deened on the Minkowski spacetime and they are \elemen-tary" in the sense that they describe particles that transform according to irre-ducible unitary representations of the symmetry group, given by the product of the Poincar e group an...