Related papers: Toy quantum categories
Classical objects have been excluded as subjects of the observed quantum properties, and the related problem of the nature of quantum objects has been suspended since the early days of Quantum Theory. Recent experiments show that the…
In view of classification of the quiver 4d N=2 supersymmetric gauge theories, we discuss the characterization of the quivers with superpotential (Q,W) associated to a N=2 QFT which, in some corner of its parameter space, looks like a gauge…
Categories of relations over a regular category form a family of models of quantum theory. Using regular logic, many properties of relations over sets lift to these models, including the correspondence between Frobenius structures and…
We introduce a notion of total acyclicity associated to a subcategory of an abelian category and consider the Gorenstein objects they define. These Gorenstein objects form a Frobenius category, whose induced stable category is equivalent to…
Quantum theory does not only predict probabilities, but also relative phases for any experiment, that involves measurements of an ensemble of systems at different moments of time. We argue, that any operational formulation of quantum theory…
We present a toy model approach to the canonical non-perturbative quantization of the spatially-flat Robertson-Walker Universes with cosmological constant, based on the fact that such models are exactly solvable within the framework of a…
Quantum Electrodynamics (QED) serves as a useful toy model for classical observables in gravitational two-body systems with reduced complexity due to the linearity of QED. We investigate scattering observables in scalar QED at the sixth…
It is well known that the category of Frolicher spaces and smooth mappings is Cartesian closed. The principal objective in this paper is to show that the full subcategory of Frolicher spaces that believe in fantasy that every Weil functor…
A program was recently initiated to bridge the gap between the Planck scale physics described by loop quantum gravity and the familiar low energy world. We illustrate the conceptual problems and their solutions through a toy model: quantum…
We pursue a model-oriented rather than axiomatic approach to the foundations of Quantum Mechanics, with the idea that new models can often suggest new axioms. This approach has often been fruitful in Logic and Theoretical Computer Science.…
A double category of relations is essentially a cartesian equipment with strong, discrete and functorial tabulators and for which certain local products satisfy a Frobenius Law. A double category of relations is equivalent to a double…
What can we learn about quantum gravity from a simple toy model, without actually quantizing it? The toy model consists of a finite number of point particles, coupled to three dimensional Einstein gravity. It has finitely many physical…
Let Rep(F;K) denote the category of functors from finite dimensional F-vector spaces to K-modules, where F is a field and K is a commutative ring. We prove that, if F is a finite field, and Char F is invertible in K, then the K-linear…
Relying on recent generalizations of the Fra\"iss\'e theory to a broader category-theoretic context, we study the class of abstract finite games played between two players and show the existence of an infinitetly countable game which is…
Motivated by team semantics and existential second-order logic, we develop a model-theoretic framework for studying second-order objects such as sets and relations. We introduce a notion of abstract elementary team categories that…
The role of types in categorical models of meaning is investigated. A general scheme for how typed models of meaning may be used to compare sentences, regardless of their grammatical structure is described, and a toy example is used as an…
Mostly self-contained script on functorial topological quantum field theories. These notes give a slow introduction to the basic notions of category theory which serve a closer investigation of cobordisms and (commutative) Frobenius…
Conceptual difficulties in semiclassical and quantum gravity arise from diffeomorphism invariance of classical general relativity. With a motivation to shed some light on these difficulties, we study a class of toy models for which…
Representation theorems relate seemingly complex objects to concrete, more tractable ones. In this paper, we take advantage of the abstraction power of category theory and provide a general representation theorem for a wide class of…
A modular tensor category provides the appropriate data for the construction of a three-dimensional topological field theory. We describe the following analogue for two-dimensional conformal field theories: a 2-category whose objects are…