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Quantum non-demolition measurements facilitate various quantum technologies, including quantum communication. Notably, their operational structure can be replicated by a classical model--referred to as a noncontextual model--making it…
The Hilbert space structure of classical field theory is proposed as a general theoretical framework to model human cognitive processes which do not often follow classical (Bayesian) probability principles. This leads to an extension of the…
The two-category with three-manifolds as objects, h-cobordisms as morphisms, and diffeomorphisms of these as two-morphisms, is extremely rich; from the point of view of classical physics it defines a nontrivial topological model for general…
In an effort to provide an alternative method to represent a quantum spin, a precise nonlinear dynamics semi-classical model is used to show that standard quantum spin analysis can be obtained. The model includes a multi-body,…
In this thesis we use the language of sheaf theory in order to develop a deeper understanding of some of the fundamental differences - such as entanglement, contextuality and non-locality - between quantum and classical physics. We first…
We show how quantum mechanics can be understood as a space-time theory provided that its spatial continuum is modelled by a variable real number (qrumber) continuum. Such a continuum can be constructed using only standard Hilbert space…
The concept of complementarity in combination with a non-Boolean calculus of propositions refers to a pivotal feature of quantum systems which has long been regarded as a key to their distinction from classical systems. But a non-Boolean…
A structural similarity between Classical Mechanics (CM) and Quantum Mechanics (QM) was revealed by P.A.M. Dirac in terms of Lie Algebras: while in CM the dynamics is determined by the Lie algebra of Poisson brackets on the manifold of…
The nongeneric six- and eightdimensional orbits of SO(4,2) are described in explicitly covariant way. The relevant Hamiltonian dynamical systems are constructed and canonically quantized. It is shown that the resulting unitary…
Quantum Chern-Simons invariants of differentiable manifolds are analyzed from the point of view of homological algebra. Given a manifold M and a Lie (or, more generally, an L-infinity) algebra g, the vector space H^*(M) \otimes g has the…
There are several indications (from different approaches) that Spacetime at the Plank Scale could be discrete. One approach to Quantum Gravity that takes this most seriously is the Causal Sets Approach. In this approach spacetime is…
Topos theory has been suggested by D\"oring and Isham as an alternative mathematical structure with which to formulate physical theories. In particular, the topos approach suggests a radical new way of thinking about what a theory of…
The causal structure of space-time offers a natural notion of an opposite or orthogonal in the logical sense, where the opposite of a set is formed by all points non time-like related with it. We show that for a general space-time the…
In quantum geometry, we consider a set of loops, a compact orientable surface and a solid compact spatial region, all inside $\mathbb{R} \times \mathbb{R}^3 \equiv \mathbb{R}^4$, which forms a triple. We want to define an ambient isotopic…
A non-associative algebra of observables cannot be represented as operators on a Hilbert space, but it may appear in certain physical situations. This article employs algebraic methods in order to derive uncertainty relations and…
A general algebraic approach, incorporating both invariance groups and dynamic symmetry algebras, is developed to reveal hidden coherent structures (closed complexes and configurations) in quantum many-body physics models due to symmetries…
Quantum field planes furnish a noncommutative differential algebra $\Omega$ which substitutes for the commutative algebra of functions and forms on a contractible manifold. The data required in their construction come from a quantum field…
We explore a possible link between the structure of space at short length scales and the emergence of classical phenomena at macroscopic scales. To this end we adopt the paradigm of non-commutative space at short length scales and…
By relating and ordering events, causality constitutes a pivotal feature of our world. On the one hand, there are information-theoretic notions of causality defined in terms of the information processing ability of agents and on the other…
Exotic spinors arise in non-simply connected base manifolds due to the nonequivalent spinor structure. The dynamics of exotic spinors are endowed with an additional differential factor. In this work, we merge the exotic spinor scenario with…