Related papers: A (possibly new) structure without the canonical b…
A general theory based upon 7 postulates is introduced. The basical notions are theoretical variables that are associated with an observer or with a group of communicating observers. These variables may be accessible or inaccessible. From…
We introduce the bicategory of bialgebras with coverings (which can be thought of as coalgebra-indexed families of morphisms), and provide a motivating application to the transfer of formulas for primitives and antipode. Additionally, we…
This paper aims to build a new understanding of the nonstandard mathematical analysis. The main contribution of this paper is the construction of a new set of numbers, $\mathbb{R}^{\mathbb{Z}_< }$, which includes infinities and…
The subject of this thesis are various properties of quantum states that make them "non-classical" and their behaviour under unitary operations. In chapter 2 some basic concepts of quantum mechanics and quantum information are reviewed. In…
We argue that the conventional construction for quantum fields in curved spacetime has a grave drawback: It involves an uncountable set of physical field systems which are nonequivalent with respect to the Bogolubov transformations, and…
The present survey results from the will to reconcile two approaches to quantum probabilities: one rather physical and coming directly from quantum mechanics, the other more algebraic. The second leading idea is to provide a unified picture…
We propose a notion of a generalized order, which can be used for the notion of a strict partial order. We introduce a weak order to replace the usual weak order defined from a strict partial order. In a constructive setting, that usual…
We consider non-local properties of quanternionic quantum mechanics, in which the complex numbers are replaced by the quaternions as the underlying algebra. Specifically, we show that it is possible to construct a non-local box. This allows…
We investigate the associativity property for functions of indefinite arities and introduce and discuss the more general property of preassociativity, a generalization of associativity which does not involve any composition of functions.
We give a brief overview of the properties of a higher dimensional generalization of matrix model which arises naturally in the context of a background independent approach to quantum gravity, the so called group field theory. We show that…
In this paper we build a set of parametric quotient Lie group structures on the probabilistic simplex that can be extended to real vector space structures. In particular, we rediscover the main mathematical objects generally used when…
We develop an extension of institution theory that accommodates implicitly the partiality of the signature morphisms and its syntactic and semantic effects. This is driven primarily by applications to conceptual blending, but other…
Recent works of the authors have demonstrated the usefulness of considering moduli spaces of Artinian reductions of a given ring when studying standard graded rings and their Lefschetz properties. This paper illuminates a key aspect of…
The canonical dimension is an invariant attached to admissible representations of p-adic reductive groups, which has only received significant attention in the case of mod-p representations. In the case of complex representations, the…
A new construction to associate an internal category to an enriched one is presented. The key concept is that of extensive ambient category, and the construction follows the one that associates a category whose idempotents split to a given…
In this work, we introduce a new generalized integral transform involving many potentially known or new transforms as special cases. Basic properties of the new integral transform, that investigated in this work, include the existence…
Classical limits of quantum systems are shown to lead to different conceptions of spaces different from the classical one underlying the process of quantization of such systems. The accent is put in situations where traces of…
We first elaborate on the theory of relative internality in stable theories, focusing on the notion of uniform relative internality (called collapse of the groupoid in an earlier work of the second author), and relating it to orthogonality,…
A method of constructing a canonical gauge invariant quantum formulation for a non-gauge classical theory depending on a set of parameters is advanced and then applied to the theory of closed bosonic string interacting with massive…
We explain the quantum structure as due to the presence of two effects, (a) a real change of state of the entity under influence of the measurement and, (b) a lack of knowledge about a deeper deterministic reality of the measurement…