Related papers: Quanta of Geometry and Unification

The algebras of non-relativistic and of classical mechanics are unstable algebraic structures. Their deformation towards stable structures leads, respectively, to relativity and to quantum mechanics. Likewise, the combined relativistic…

Quantum groups emerged in the latter quarter of the 20th century as, on the one hand, a deep and natural generalisation of symmetry groups for certain integrable systems, and on the other as part of a generalisation of geometry itself…

In a previous effort [arXiv:1708.05492] we have created a framework that explains why topological structures naturally arise within a scientific theory; namely, they capture the requirements of experimental verification. This is…

It is shown uniquely that quantized spaces are realised on four-dimensional compact manifolds. In the case of O(1,5) quantized space this are four independent parameters of O(5) unit vector; in the case of O(2,4) these are parameters of one…

Phase space is the state space of classical mechanics, and this manifold is normally endowed only with a symplectic form. The geometry of quantum mechanics is necessarily more complicated. Arguments will be given to show that augmenting the…

We propose a mathematical model of quantum spacetime as an infinite-dimensional manifold locally homeomorphic to an appropriate Schwartz space. This extends and unifies both the standard function space construction of quantum mechanics and…

Three different representation of the proper Euclidean geometry are considered. They differ in the number of basic elements, from which the geometrical objects are constructed. In E-representation there are three basic elements (point,…

An algebraic quantization procedure for discretized spacetime models is suggested based on the duality between finitary substitutes and their incidence algebras. The provided limiting procedure that yields conventional manifold…

Quantum computing has been a fascinating research field in quantum physics. Recent progresses motivate us to study in depth the universal quantum computing models (UQCM), which lie at the foundation of quantum computing and have tight…

One considers geometry with the intransitive equaivalence relation. Such a geometry is a physical geometry, i.e. it is described completely by the world function, which is a half of the squared distance function. The physical geometry…

We give a survey of our joint ongoing work with Ali Chamseddine, Slava Mukhanov and Walter van Suijlekom. We show how a problem purely motivated by "how geometry emerges from the quantum formalism" gives rise to a slightly noncommutative…

The lack of clear new-physics signals at the LHC searches motivates models that can guide current and future collider searches. The spectral action principle within the noncommutative geometry (NCG) framework yields such models with…

A detailed study is made of the noncommutative geometry of $R^3_q$, the quantum space covariant under the quantum group $SO_q(3)$. For each of its two $SO_q(3)$-covariant differential calculi we find its metric, the corresponding frame and…

There is a U(4')\times U(4)-bundle on four-dimensional square root Lorentz manifold. Then a Pati-Salam model in curved space-time (Lagrangian) and a gravity theory (Lagrangian) are constructed on square root Lorentz manifold based on…

Based on a more careful canonical analysis, we motivate a reduced quantization - in the sense of superspace quantization - of slightly inhomogeneous cosmology in place of the Dirac quantization in the existing literature, and provide it in…

Geometric quantization is an attempt at using the differential-geometric ingredients of classical phase spaces regarded as symplectic manifolds in order to define a corresponding quantum theory. Generally, the process of geometric…

We develop the spectral point of view on geometry based on the formalism of quantum physics. We start from the simple physical question of specifying our position in space and explain how the spectral geometric point of view provides a new…

Quantum mechanics is among the most important and successful mathematical model for describing our physical reality. The traditional formulation of quantum mechanics is linear and algebraic. In contrast classical mechanics is a geometrical…

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…

The traditional formalism of non-relativistic quantum theory allows the state of a quantum system to extend across space, but only restricts it to a single instant in time, leading to distinction between theoretical treatments of spatial…