Related papers: A Royal Road to Quantum Theory (or Thereabouts), E…

We announce here a number of results concerning representation theory of the algebra $R=k<x,y>/ (xy-yx-y^2)$, known as Jordan plane (or Jordan algebra). We consider the question on 'classification' of finite-dimensional modules over the…

There are 13 equivalence classes of 2D second order quantum and classical superintegrable systems with nontrivial potential, each associated with a quadratic algebra of hidden symmetries. We study the finite and infinite irreducible…

These notes offer a lightening introduction to topological quantum field theory in its functorial axiomatisation, assuming no or little prior exposure. We lay some emphasis on the connection between the path integral motivation and the…

We provide a systematic approach to quantum mechanics from an information-theoretic perspective using the language of tensor networks. Our formulation needs only a single kind of object, so-called positive *-tensors. Physical models…

We continue the study undertaken in \cite{DV} of the exceptional Jordan algebra $J = J_3^8$ as (part of) the finite-dimensional quantum algebra in an almost classical space-time approach to particle physics. Along with reviewing known…

For certain problems involving vector fields, it is possible to find an associated imaginary field that, in conjunction with the first, forms a complex field for which the equation can be solved. This result is generalized to arbitrary…

We establish basic facts about the varieties of homogeneous polynomials divisible by powers of linear forms, and explain consequences for geometric complexity theory. This includes quadratic set-theoretic equations, a description of the…

We consider the space of probabilities {P(x)}, where the x are coordinates of a configuration space. Under the action of the translation group there is a natural metric over the space of parameters of the group given by the Fisher-Rao…

We strengthen the case that the new logical perspective afforded by topos theory is suitable to the task of describing the physical world around us. In exploring some of the aspects of construction of a simple quantum-mechanical system in a…

We show how classical and quantum dualities, as well as duality relations that appear only in a sector of certain theories ("emergent dualities"), can be unveiled, and systematically established. Our method relies on the use of morphisms of…

In this note, we introduce monoidal subcategories of the tensor category of finite-dimensional representations of a simply-laced quantum affine algebra, parametrized by arbitrary Dynkin quivers. For linearly oriented quivers of types A and…

Both statistics and quantum theory deal with prediction using probability. We will show that there can be established a connection between these two areas. This will at the same time suggest a new, less formalistic way of looking upon basic…

It came to the attention of myself and the coauthors of (S., Rozowski, Silva, Rot, 2022) that a number of process calculi can be obtained by algebraically presenting the branching structure of the transition systems they specify. Labelled…

The Jordan algebra structure of the bounded real quantum observables was recognized already in the early days of quantum mechanics. While there are plausible reasons for most parts of this structure, the existence of the distributive…

We study atom canonicity for several varieties of cylindric like algebras that contain properly the variety of representable algebras. The algebras in such varieties have relativized representations, and we thereby obtain many omitting…

In the paper "Is there a Jordan geometry underlying quantum physics?" (Int. J. Theor. Phys., to appear; arXiv:0801.3069 [math-ph]), generalized projective geometries have been proposed as a framework for a geometric formulation of Quantum…

Several finite dimensional quasi-probability representations of quantum states have been proposed to study various problems in quantum information theory and quantum foundations. These representations are often defined only on restricted…

Is quantum mechanics about 'states'? Or is it basically another kind of probability theory? It is argued that the elementary formalism of quantum mechanics operates as a well-justified alternative to 'classical' instantiations of a…

We consider a constructive modification of quantum-mechanical formalism. Replacement of a general unitary group by unitary representations of finite groups makes it possible to reproduce quantum formalism without loss of its empirical…

We develop layered monoidal theories -- a generalisation of monoidal theories combining formal descriptions of a system at different levels of abstraction. Via their representation as string diagrams, monoidal theories provide a graphical…