Related papers: The geometry of physical observables

This paper addresses the question why quantum mechanics is formulated in a unitary Hilbert space, i.e. in a manifestly complex setting. Investigating the linear dynamics of real quantum theory in a finite-dimensional Euclidean Hilbert space…

Second-order superintegrable systems in dimensions two and three are essentially classified. With increasing dimension, however, the non-linear partial differential equations employed in current methods become unmanageable. Here we propose…

Scalar-Tensor theories of gravity can be formulated in different frames, most notably, the Einstein and the Jordan one. While some debate still persists in the literature on the physical status of the different frames, a frame…

Traditionally, robots are regarded as universal motion generation machines. They are designed mainly by kinematics considerations while the desired dynamics is imposed by strong actuators and high-rate control loops. As an alternative, one…

Real algebraic geometry adapts the methods and ideas from (complex) algebraic geometry to study the real solutions to systems of polynomial equations and polynomial inequalities. As it is the real solutions to such systems modeling…

There were many attempts to geometrize electromagnetic field and find out new interpretation for quantum mechanics formalism. The distinctive feature of this work is that it combines geometrization of electromagnetic field and…

Inhomogeneities are introduced in loop quantum cosmology using regular lattice states, with a kinematical arena similar to that in homogeneous models considered earlier. The framework is intended to encapsulate crucial features of…

In this thesis quadratic and cubic algebras, which are extensions of SU(1,1) and SU(2) are studied in detail, with particular attention being given to their construction, their finite and infinite dimensional irreducible representations and…

We construct an explicit representation of the algebra of local diffeomorphisms of a manifold with realistic dimensions. This is achieved in the setting of a general approach to the (quantum) dynamics of a physical system which is…

We study the conformal groups of Jordan algebras along the lines suggested by Kantor. They provide a natural generalization of the concept of conformal transformations that leave 2-angles invariant to spaces where "p-angles" can be defined.…

A three-dimensional polynomial algebra of order $m$ is defined by the commutation relations $[P_0, P_\pm]$ $=$ $\pm P_\pm$, $[P_+, P_-]$ $=$ $\phi^{(m)}(P_0)$ where $\phi^{(m)}(P_0)$ is an $m$-th order polynomial in $P_0$ with the…

The main purpose of this paper is to present a new approach to logic or what we will call superlogic. This approach constitutes a new way of looking at the connection between quantum mechanics and logic. It is a {\it geometrisation} of the…

In this paper we develop a picture of Quantum Mechanics based on the description of physical observables in terms of expectation value functions, generalizing thus the so called Ehrenfest theorems for quantum dynamics. Our basic technical…

Recently, a geometrical characterization of vector spaces served to generalize them into a new class of algebras. Instead of the algebraic properties of the underlying fields, we generalized the recently discovered property of such spaces…

We describe all degenerations of the variety $\mathfrak{Jord}_3$ of Jordan algebras of dimension three over $\mathbb{C}.$ In particular, we describe all irreducible components in $\mathfrak{Jord}_3.$ For every $n$ we define an…

This is a self-contained introduction to quantum Riemannian geometry based on quantum groups as frame groups, and its proposed role in quantum gravity. Much of the article is about the generalisation of classical Riemannian geometry that…

We introduce a new formalism and a number of new results in the context of geometric computational vision. The classical scope of the research in geometric computer vision is essentially limited to static configurations of points and lines…

We consider a geometrization, i.e., we identify geometrical structures, for the space of density states of a quantum system. We also provide few comments on a possible application of this geometrization for composite systems.

Normed division rings are reviewed in the more general framework of composition algebras that include the split (indefinite metric) case. The Jordan - von Neumann - Wigner classification of finite dimensional Jordan algebras is outlined…

The measure of distinguishability between two neighboring preparations of a physical system by a measurement apparatus naturally defines the line element of the preparation space of the system. We point out that quantum mechanics can be…