Related papers: Introduction to {\it Quantum Matter}
In recent years, the notion of Quantum Materials has emerged as a powerful unifying concept across diverse fields of science and engineering, from condensed-matter and cold atom physics to materials science and quantum computing. Beyond…
Quantum geometry, i.e., the quantum theory of intrinsic and extrinsic spatial geometry, is a cornerstone of loop quantum gravity. Recently, there have been many new ideas in this field, and I will review some of them. In particular, after a…
Geometrical aspects of quantum computing are reviewed elementarily for non-experts and/or graduate students who are interested in both Geometry and Quantum Computation. In the first half we show how to treat Grassmann manifolds which are…
These are the lecture notes for a course that I am teaching at Zhiyuan College of Shanghai Jiao Tong University (available at https://www.youtube.com/derekkorg), though the first draft was created for a previous course I taught at the…
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.
Ideas from quantum field theory and topology have proved remarkably fertile in suggesting new phenomena in the quantum physics of condensed matter. Here I'll supply some broad, unifying context, both conceptual and historical, for the…
These notes are an elaboration on: (i) a short course that I gave at the IPhT-Saclay in May-June 2012; (ii) a previous letter on reversibility in quantum mechanics. They present an introductory, but hopefully coherent, view of the main…
An introduction is given to discussions on the possiblity of fabricating spacetime geometries allowing time-travel scenarios with the help of matter possessing typically quantum features. Those scenarios are considered in the framework of…
This is a written version of the review talk given at the meeting on "Interface of Gravitational and Quantum Realms" at IUCAA, Pune during December 2001. The talk reviewed the recent work of Martin Bojowald on Loop Quantum Cosmology.
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…
`How do our ideas about quantum mechanics affect our understanding of spacetime?' This familiar question leads to quantum gravity. The complementary question is also important: `How do our ideas about spacetime affect our understanding of…
In this paper we present a survey of the use of differential geometric formalisms to describe Quantum Mechanics. We analyze Schroedinger and Heisenberg frameworks from this perspective and discuss how the momentum map associated to 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…
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…
We gather material from many sources about the quantum potential and its geometric nature. The presentation is primarily expository but some new observations relating Q, V, and psi are indicated.
We present an introduction to the canonical quantization of gravity performed in loop quantum gravity, based on lectures held at the 3rd quantum geometry and quantum gravity school in Zakopane in 2011. A special feature of this introduction…
These lecture notes (from the Second Autumn School in High Energy Physics and Quantum Field Theory, Yerevan 2014) cover a number of topics related to geometric quantization. Most of the material is presented from a physicist's point of…
This is a transcript of the round table that took place during the conference Quantum Theory: Reconsideration of Foundations - 3, June 2005, Vaxjo, Sweden. There are presented opinions of leading experts in quantum foundations on such…
The theory of quantum computation is presented in a self contained way from a computer science perspective. The basics of classical computation and quantum mechanics is reviewed. The circuit model of quantum computation is presented in…
We formulate quantum theory taking as a starting point the cone of states.