Related papers: Quantum Geometric Origin of Orbital Magnetization
In this chapter we take up the quantum Riemannian geometry of a spatial slice of spacetime. While researchers are still facing the challenge of observing quantum gravity, there is a geometrical core to loop quantum gravity that does much to…
The geometry of the symplectic structures and Fubini-Study metric is discussed. Discussion in the paper addresses geometry of Quantum Mechanics in the classical phase space. Also, geometry of Quantum Mechanics in the projective Hilbert…
Quantum geometry governs a wide range of transport and optical phenomena in quantum materials. Recent works have explored analogue electromagnetism and gravity in terms of the quantum geometric tensor, whose real and imaginary parts…
Quantum geometry, which describes the geometry of Bloch wavefunctions in solids, has become a cornerstone of modern quantum condensed matter physics. The quantum geometrical tensor encodes this geometry through two fundamental components:…
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…
Exactly soluble models can serve as excellent tools to explore conceptual issues in non-perturbative quantum gravity. In perturbative approaches, it is only the two radiative modes of the linearized gravitational field that are quantized.…
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…
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…
The unsatisfactory status of the search for a consistent and predictive quantization of gravity is taken as motivation to study the question whether geometrical laws could be more fundamental than quantization procedures. In such an…
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…
Over the past six years, a detailed framework has been constructed to unravel the quantum nature of the Riemannian geometry of physical space. A review of these developments is presented at a level which should be accessible to graduate…
In this article the geometry of quantum gravity is quantized in the sense of being noncommutative (first quantization) but it is also quantized in the sense of being emergent (second quantization). A new mechanism for quantum geometry is…
General Relativity describes gravity in geometrical terms. This suggests that quantizing such theory is the same as quantizing geometry. The subject can therefore be called quantum geometry and one may think that mathematicians are…
Geometric Quantum Mechanics is a novel and prospecting approach motivated by the belief that our world is ultimately geometrical. At the heart of that is a quantity called Quantum Geometric Tensor (or Fubini-Study metric), which is a…
In the last decade, the development of new ideas in quantum theory, including geometric and deformation quantization, the non-Abelian Berry factor, super- and BRST symmetries, non-commutativity, has called into play the geometric techniques…
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…
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…
The application of geometry to physics has provided us with new insightful information about many physical theories such as classical mechanics, general relativity, and quantum geometry (quantum gravity). The geometry also plays an…
After a brief introduction, basic ideas of the quantum Riemannian geometry underlying loop quantum gravity are summarized. To illustrate physical ramifications of quantum geometry, the framework is then applied to homogeneous isotropic…
In any attempt to build a quantum theory of gravity, a central issue is to unravel the structure of space-time at the smallest scale. Of particular relevance is the possible definition of coordinate functions within the theory and the study…