Related papers: Quivers and path semigroups characterized by local…
Locality semigroups were proposed recently as one of the basic locality algebraic structures, which are studied in mathematics and physics. Path semigroups and partial semigroups were also developed by many authors in the literature. In…
Each quiver corresponds to a path semigroup, and such a path semigroup also corresponds to an associative K-algebra over an algebraically closed field K. Let Q be a quiver and S_Q, KQ be its path semigroup, path algebra, respectively. In…
We analyze the property of locality with respect to the framework for quantum mechanics based on the path integral formalism. As is well known, this framework makes the same experimental predictions as does the one based on a separable…
In this work, the notion of a quantum inverse semigroup is introduced as a linearized generalization of inverse semigroups. Beyond the algebra of an inverse semigroup, which is the natural example of a quantum inverse semigroup, several…
The principle of local covariance which was recently introduced admits a generally covariant formulation of quantum field theory. It allows a discussion of structural properties of quantum field theory as well as the perturbative…
We investigate whether semigroups with a given property which are also locally embeddable into finite semigroups can be locally embedded into finite semigroups with the same property, obtaining a positive answer for completely simple and…
Recently it has been noticed that many interesting combinatorial objects belong to a class of semigroups called left regular bands, and that random walks on these semigroups encode several well-known random walks. For example, the set of…
Variational analysis presents a unified theory encompassing in particular both smoothness and convexity. In a Euclidean space, convex sets and smooth manifolds both have straightforward local geometry. However, in the most basic hybrid case…
In a full theory of quantum gravity, local physics is expected to be approximate rather than innate. It is therefore important to understand how approximate locality emerges in the semiclassical limit. Here we show that any notion of…
Quantum families of maps between quantum spaces are defined and studied. We prove that quantum semigroup (and sometimes quantum group) structures arise naturally on such objects out of more fundamental properties. As particular cases we…
One of the many conceptual difficulties in the development of quantum gravity is the role of a background geometry for the structure of quantum field theory. To some extent the problem can be solved by the principle of local covariance. The…
We apply the theory of localization for tame and wild coalgebras in order to prove the following theorem: "Let Q be an acyclic quiver. Then any tame admissible subcoalgebra of KQ is the path coalgebra of a quiver with relations".
We analyze the recent examples of quantum semigroups defined by M.M. Sadr who also brought up several open problems concerning these objects. These are defined as quantum families of maps from finite sets to a fixed compact quantum…
In a previous paper, we have put forward an interpretation of quantum mechanics based on a non-relativistic, Lagrangian 3+1 formalism of a closed Universe $M$, existing on timeless configuration space $\mathcal{M}$. However, not much was…
The most developed aspect of the theory of finite semigroups is their classification in pseudovarieties. The main motivation for investigating such entities comes from their connection with the classification of regular languages via…
One of the most basic notions in physics is the partitioning of a system into subsystems, and the study of correlations among its parts. In this work, we explore these notions in the context of quantum reference frame (QRF) covariance, in…
Density matrices are the most general descriptions of quantum states, covering both pure and mixed states. Positive semidefiniteness is a physical requirement of density matrices, imposing nonnegative probabilities of measuring physical…
A new approach to the model-independent description of quantum field theories will be introduced in the present work. The main feature of this new approach is to incorporate in a local sense the principle of general covariance of general…
A framework which combines ideas from Connes' noncommutative geometry, or spectral geometry, with recent ideas on generally covariant quantum field theory, is proposed in the present work. A certain type of spectral geometries modelling…
In contrast to classical strongly continuous semigroups, the study of bi-continuous semigroups comes with some freedom in the properties of the associated locally convex topology. This paper aims to give minimal assumptions in order to…