Related papers: Quantum Mechanics of Geometry
In this paper we present some results obtained in a previous paper about the Cartan's approach to Riemannian normal coordinates and our conformal transformations among pseudo-Riemannian manifolds. We also review the classical and the…
Black holes have often provided profound insights into the nature of gravity and the structure of space-time. The study of the mathematical properties of black objects is a major research theme of contemporary theoretical physics. This…
We study an internal structure of (2+1)-dimensional black hole with the neutral scalar matter in the spherically symmetric geometry by using a quantum theory of gravity which holds in the both vicinities of the singularity and the apparent…
In a recent article we have introduced Friedmann thermodynamics, where certain geometric parameters in Friedmann models are treated like their thermodynamic counterparts (temperature, entropy, Gibbs potential etc.). This model has the…
We propose a geometric setting of the axiomatic mathematical formalism of quantum theory. Guided by the idea that understanding the mathematical structures of these axioms is of similar importance as was historically the process of…
Geometries with horizons offer insights into relationships between general relativity and quantum physics. Quantum mechanics constrains relationships between kinematic parameters and the coordinates describing the dynamics. Example quantum…
We discuss a new approach to the problem of quantum gravity in which the quantum mechanical structures that are traditionally fixed, such as the Fubini-Study metric in the Hilbert space of states, become dynamical and so implement the idea…
On the base of years of experience of working on the problem of the physical foundation of quantum mechanics the author offers principles of solving it. Under certain pressure of mathematical formalism there has raised a hypothesis of…
This is an introduction to some of the analytic (or integrable systems) aspects of quantum cohomology which have attracted much attention during the last few years. The small quantum cohomology algebra, regarded as an example of a Frobenius…
These are expanded lecture notes of a mini-course whose objectives were to introduce the basic concepts, constructions and techniques of noncommutative geometry, as well as their uses as a framework for modelling quantum spacetime. Key…
Quantum geometry is a differential geometry based on quantum mechanics. It is related to various transport and optical properties in condensed matter physics. The Zeeman quantum geometry is a generalization of quantum geometry including the…
Quantum thermodynamics is an emerging research field aiming to extend standard thermodynamics and non-equilibrium statistical physics to ensembles of sizes well below the thermodynamic limit, in non-equilibrium situations, and with the full…
In this paper and a companion paper, we show how the framework of information geometry, a geometry of discrete probability distributions, can form the basis of a derivation of the quantum formalism. The derivation rests upon a few…
We reveal strong and weak inequalities relating two fundamental macroscopic quantum geometric quantities, the quantum distance and Berry phase, for closed paths in the Hilbert space of wavefunctions. We recount the role of quantum geometry…
The past few years have seen a revived interest in quantum geometrical characterizations of band structures due to the rapid development of topological insulators and semi-metals. Although the metric tensor has been connected to many…
We present an overview of recent developments concerning modifications of the geometry of space-time to describe various physical processes of interactions among classical and quantum configurations. We concentrate in two main lines of…
The discovery in the early 1970s that black holes radiate as black bodies has radically affected our understanding of general relativity, and offered us some early hints about the nature of quantum gravity. In this chapter I will review the…
Quantum states defined over a parameter space form a Grassmann manifold. To capture the geometry of the associated gauge structure, gauge-invariant quantities are essential. We employ the projector of a multilevel system to quantify the…
The unification of general relativity with quantum theory will also require a coming together of the two quite different mathematical languages of general relativity and quantum theory, i.e., of differential geometry and functional analysis…
Combination of a construction of unambiguous quantum conditions out of the conventional one and a simultaneous quantization of the positions, momenta, angular momenta and Hamiltonian leads to the geometric potential given by the so-called…