Related papers: Orderings and valuations in hyperfields
In this work we study the problem of first order perturbations of a general hypersurface, i.e. with arbitrary causal character at each point. We extend the framework by Mars (Class. Quantum Grav. 22 3325 (2005)) where this problem was…
Higher order conformal perturbation theory is studied for theories with and without boundaries. We identify systematically the universal quantities in the beta function equations, and we give explicit formulae for the universal coefficients…
We discuss the use of field theory for the exact determination of universal properties in two-dimensional statistical mechanics. After a compact derivation of critical exponents of main universality classes, we turn to the off-critical…
We study links between first-order formulas and arbitrary properties for families of theories, classes of structures and their isomorphism types. Possibilities for ranks and degrees for formulas and theories with respect to given properties…
A quantum scalar field theory with spacetime-dependent coupling is studied. Surprisingly, while translation invariance is explicitly broken in the classical theory, momentum conservation is recovered at the quantum level for some specific…
By using methods of umbral nature, we discuss new rules concerning the operator ordering. We apply the technique of formal power series to take advantage from the wealth of properties of the exponential operators. The usefulness of the…
In this paper we present the following two results: we give an explicit description of the space of orderings of the field Q(x) as an inverse limit of finite spaces of orderings and we provide a new, simple proof of the fact that the class…
We extend the definitions of upper and lower valuations on partially ordered sets, and consider the metrics they induce, in particular the metrics available (or not) based on the logarithms of such valuations. Motivating applications in…
This thesis details a class of partial orders on the space of probability distributions and the space of density operators which capture the idea of information content. Some links to domain theory and computational linguistics are also…
After a short review of the classical Lie theorem, a finite dimensional Lie algebra of vector fields is considered and the most general conditions under which the integral curves of one of the fields can be obtained by quadratures in a…
A quasi-order is a binary, reflexive and transitive relation. In the Journal of Pure and Applied Algebra 45 (1987), S.M. Fakhruddin introduced the notion of (totally) quasi-ordered fields and showed that each such field is either an ordered…
In a previous paper we have introduced a class of multiplications of distributions in one dimension. Here we furnish different generalizations of the original definition and we discuss some applications of these procedures to the…
We provide, explicitly, equivalences and dual equivalences between categories of abstract quadratic forms theories and subcategories of multifields and multirings, that will bring new perspectives and methods to the abstract theories of…
<p>We address the general problem of determining the validity of boolean combinations of equalities and inequalities between real-valued expressions. In particular, we consider methods of establishing such assertions using only restricted…
In this paper, a new criterion is given to determine the $p-$rationality of some complex cubic number fields in terms of $ p-$divisibility of certain terms of a third-order recurrence sequence, several illustrated examples are…
Quantum theory is applicable, in principle, to both the microscopic and macroscopic realms. It is therefore worthwhile to investigate whether it is possible to evolve a quantum-compatible view of the properties and states of macroscopic…
Using supervector fields and graded forms along a morphism, we study the geometry of ordinary differential superequations, extend the formalism of higher order Lagrangian mechanics to the graded context and prove a generalization of…
In the paper, notions of relative separability for hypergraphs of models of a theory are defined. Properties of these notions and applications to ordered theories are studied: characterizations of relative separability both in a general…
We generalize the concept of Borel resummability and renormalons to a quantum field theory with an arbitrary number of fields and couplings, starting from the known notion based on the running coupling constants. An approach to identify the…
Using valuation rings and valued fields as examples, we discuss in which ways the notions of "topological IFS attractor" and "fractal space" can be generalized to cover more general settings.