Related papers: A Non-Classical Linear Xenomorph as a Model for Qu…
We present a categorical construction for modelling causal structures within a general class of process theories that include the theory of classical probabilistic processes as well as quantum theory. Unlike prior constructions within…
The Lie and module (Rinehart) algebraic structure of vector fields of compact support over C infinity functions on a (connected) manifold M define a unique universal non-commutative Poisson * algebra. For a compact manifold, a…
In the framework of semiclassical theory the universal properties of quantum systems with classically chaotic dynamics can be accounted for through correlations between partner periodic orbits with small action differences. So far, however,…
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…
A locally finite, causal and quantal substitute for a locally Minkowskian principal fiber bundle $\cal{P}$ of modules of Cartan differential forms $\omg$ over a bounded region $X$ of a curved $C^{\infty}$-smooth differential manifold…
The structure and properties of possible $q$-Minkowski spaces is discussed, and the corresponding non-commutative differential calculi are developed in detail and compared with already existing proposals. This is done by stressing its…
A possible causal solution to the problem of providing a spacetime description of the transmission of signals in quantum entangled states is described using a `bimetric' spacetime structure, in which the quantum entanglement measurements…
We address the quantum-classical correspondence for chaotic systems with a crossover between symmetry classes. We consider the energy level statistics of a classically chaotic system in a weak magnetic field. The generating function of…
Quantum nonseparability is a central feature of quantum mechanics, and raises important philosophical questions. Interestingly, a particular theoretical development of quantum mechanics, called the process matrix formalism (PMF), features…
This article presents a precise description of the interplay between the symmetries of a quantum or classical theory with spacetime interpretation, and some of its physical properties relating to causality, horizons and positive energy. Our…
Causal reasoning is essential to science, yet quantum theory challenges it. Quantum correlations violating Bell inequalities defy satisfactory causal explanations within the framework of classical causal models. What is more, a theory…
These lecture notes cover 13 sessions and are presented as an e-print, intended to evolve over time. Quantum invariants do more than distinguish topological objects; they build bridges between topology, algebra, number theory and quantum…
An enumerative invariant theory in Algebraic Geometry, Differential Geometry, or Representation Theory, is the study of invariants which 'count' $\tau$-(semi)stable objects $E$ with fixed topological invariants $[E]=\alpha$ in some…
A deformation of the canonical algebra for kinematical observables of the quantum field theory in Minkowski space-time has been considered under the condition of Lorentz invariance. A relativistic invariant algebra obtained depends on…
When compared to quantum mechanics, classical mechanics is often depicted in a specific metaphysical flavour: spatio-temporal realism or a Newtonian "background" is presented as an intrinsic fundamental classical presumption. However, the…
This is intended as an analysis of the global properties of static and stationary spacetimes with complete (timelike) Killing field, with particular attention to quotients by group actions. This is presented in terms of algebraic structures…
This paper provides the quantum treatment of the relational quadrilateral. The underlying reduced configuration spaces are $\mathbb{CP}^2$ and the cone over this, C($\mathbb{CP}^2$). We consider exact free and isotropic HO potential cases…
We show that the notion of generalized Berry phase i.e., non-abelian holonomy, can be used for enabling quantum computation. The computational space is realized by a $n$-fold degenerate eigenspace of a family of Hamiltonians parametrized by…
Because of the non-locality of quantum entanglement, realist approaches to completing quantum mechanics have implications for our conception of space. Quantum gravity also is expected to predict phenomena in which the locality of classical…
We explain why and how the Hilbert space comes about in quantum theory. The axiomatic structures of vector space, of scalar product, of orthogonality, and of the linear functional are derivable from the statistical description of quantum…