Related papers: Geometric and Algebraic Topological Methods in Qua…

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…

In this scientific preface to the first issue of International Journal of Geometric Methods in Modern Physics, we briefly survey some peculiarities of geometric techniques in quantum models.

Geometrization of physical theories have always played an important role in their analysis and development. In this contribution we discuss various aspects concerning the geometrization of physical theories: from classical mechanics to…

In this paper we will present an ongoing project which aims to use model theory as a suitable mathematical setting for studying the formalism of quantum mechanics. We will argue that this approach provides a geometric semantics for such…

For many materials, a precise knowledge of their dispersion spectra is insufficient to predict their ordered phases and physical responses. Instead, these materials are classified by the geometrical and topological properties of their…

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…

Many basis sets for electronic structure calculations evolve with varying external parameters, such as moving atoms in dynamic simulations, giving rise to extra derivative terms in the dynamical equations. Here we revisit these derivatives…

We develop a unified quantum geometric framework to understand reactive quantum dynamics. The critical roles of the quantum geometry of adiabatic electronic states in both adiabatic and non-adiabatic quantum dynamics are unveiled. A…

This note, in a rather expository manner, serves as a conceptional introduction to the certain underlying mathematical structures encoding the geometric quantization formalism and the construction of Witten's quantum invariants, which is in…

The earlier approach is used for description of qubits and geometric phase parameters, the things critical in the area of topological quantum computing. The used tool, Geometric (Clifford) Algebra is the most convenient formalism for that…

One of the most celebrated accomplishments of modern physics is the description of fundamental principles of nature in the language of geometry. As the motion of celestial bodies is governed by the geometry of spacetime, the motion of…

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 exploration of the Riemannian structure of the Hilbert space has led to the concept of quantum geometry, comprising geometric quantities exemplified by Berry curvature and quantum metric. While this framework has profoundly advanced the…

States of a quantum mechanical system are represented by rays in a complex Hilbert space. The space of rays has, naturally, the structure of a K\"ahler manifold. This leads to a geometrical formulation of the postulates of quantum mechanics…

The use of geometric and symmetry techniques in quantum and classical information processing has a long tradition across the physical sciences as a means of theoretical discovery and applied problem solving. In the modern era, the emergent…

Geometrical methods in quantum information are very promising for both providing technical tools and intuition into difficult control or optimization problems. Moreover, they are of fundamental importance in connecting pure geometrical…

In the first part of this review we introduce the basics theory behind geometric phases and emphasize their importance in quantum theory. The subject is presented in a general way so as to illustrate its wide applicability, but we also…

The purpose of this contribution is to give an introduction to quantum geometry and loop quantum gravity for a wide audience of both physicists and mathematicians. From a physical point of view the emphasis will be on conceptual issues…

Berry curvature-related topological phenomena have been a central topic in condensed matter physics. Yet, until recently other quantum geometric quantities such as the metric and connection received only little attention due to 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…