Quantum Geometry

this book is a classic on the foundations of quantum theory. It examines the subject from a point of view that goes back to Heisenberg and Dirac, and whose definitive mathematical formulation is due to von Neumann. This view, which is essentially geometric and relies on the concept of symmetry, leads most naturally to the fundamental questions that are the basis of all attempts to understand the world of atomic and subatomic particles. The mathematical treatment of symmetry in quantum theory is based on the theory of group representations, and this book includes a self-contained treatment of the parts of this theory that are most useful in quantum physics.

Quantum information theory is at the frontiers of physics, mathematics and information science, offering a variety of solutions that are impossible using classical theory. This book provides an introduction to the key concepts used in processing quantum information and reveals that quantum mechanics is a generalisation of classical probability theory.

Authors: Goswami, Debashish, Bhowmick, Jyotishman
Presents the research on “quantum isometry group” for the first time in a book form
Highlights the interaction of noncommutative geometry and quantum groups

This book presents the text of most of the lectures which were de­ livered at the Meeting Quantum Theories and Geometry which was held at the Fondation Les Treilles from March 23 to March 27, 1987. The general aim of this meeting was to bring together mathemati­ cians and physicists who have worked in this growing field of contact between the two disciplines, namely this region where geometry and physics interact creatively in both directions. It 1S the strong belief of the organizers that these written con­ tributions will be a useful document for research people workin~ 1n geometry or physics. Three lectures were devoted to the deformation approach to quantum mechanics which involves a modification of both the associative and the Lie structure of the algebra of functions on classical phase space.

Quantum information theory is at the frontiers of physics, mathematics and information science, offering a variety of solutions that are impossible using classical theory.