Related papers: Shape Quantities for Relational Quadrilateralland
We define a "quantum relation" on a von Neumann algebra M \subset B(H) to be a weak* closed operator bimodule over its commutant M'. Although this definition is framed in terms of a particular representation of M, it is effectively…
While real Hamiltonian mechanics and Hermitian quantum mechanics can both be cast in the framework of complex canonical equations, their complex generalisations have hitherto been remained tangential. In this paper quaternionic and…
The mathematical formalism of quantum mechanics has been successfully employed in the last years to model situations in which the use of classical structures gives rise to problematical situations, and where typically quantum effects, such…
We analyze classical and quantum dynamics of a particle in 2d spacetimes with constant curvature which are locally isometric but globally different. We show that global symmetries of spacetime specify the symmetries of physical phase-space…
General non-commutative supersymmetric quantum mechanics models in two and three dimensions are constructed and some two and three dimensional examples are explicitly studied. The structure of the theory studied suggest other possible…
Semiclassical methods are essential in analyzing quantum mechanical systems. Although they generally produce approximate results, relatively rare potentials exist for which these methods are exact. Such intriguing potentials serve as…
This paper proposes an intrinsic or background-independent quantum framework based on entangled state rather than absolute quantum state, it describes a quantum relative state between the under-study quantum system and the quantum measuring…
This paper is the first of two papers devoted to formulation of quantum mechanics of a particle in a normal geodesic frame of reference in the general Riemannian space-time. Here canonical quantization of geodesic motion in the…
The quantum mechanical motion of a relativistic particle in a non-continuous spacetime is investigated. The spacetime model is a dense, rationale subset of two-dimensional Minkowski spacetime. Solutions of the Dirac equation are calculated…
The study of general two dimensional models of gravity allows to tackle basic questions of quantum gravity, bypassing important technical complications which make the treatment in higher dimensions difficult. As the physically important…
We propose that large quantum fluctuations of the conformal factor drastically modify classical general relativity at cosmological distance scales, resulting in a scale invariant phase of quantum gravity in the far infrared. We derive…
Kendall's Shape Theory covers shapes formed by $N$ points in $\mathbb{R}^d$ upon quotienting out the similarity transformations. This theory is based on the geometry and topology of the corresponding configuration space: shape space.…
We discuss the deformation quantization approach for the teaching of quantum mechanics. This approach has certain conceptual advantages which make its consideration worthwhile. In particular, it sheds new light on the relation between…
In the absence of an external frame of reference physical degrees of freedom must describe relations between systems. Using a simple model, we investigate how such a relational quantum theory naturally arises by promoting reference systems…
The relational interpretation (or RQM, for Relational Quantum Mechanics) solves the measurement problem by considering an ontology of sparse relative events, or "facts". Facts are realized in interactions between any two physical systems…
We show that, in spite of a rather common opinion, quantum mechanics can be represented as an approximation of classical statistical mechanics. The approximation under consideration is based on the ordinary Taylor expansion of physical…
Quantum theory is applicable, in principle, to both the microscopic and macroscopic realms. It is therefore worthwhile to investigate whether it is possible to evolve a quantum-compatible view of the properties and states of macroscopic…
No theory of four-dimensional quantum gravity exists as yet. In this situation the two-dimensional theory, which can be analyzed by conventional field-theoretical methods, can serve as a toy model for studying some aspects of quantum…
Quantum theory can be understood as pointing to an ontology of relations. I observe that this reading of quantum mechanics is supported by the ubiquity of relationality in contemporary fundamental physics, including in classical mechanics,…
We discuss the relational strategy to solve the problem of time in quantum gravity and different ways in which it could be implemented, pointing out in particular the fundamentally new dimension that the problem takes in a quantum gravity…