Calculus Revisited

By: R.W. Carroll

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Hardcover | 31 December 2002

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528 Pages

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24.13 x 16.51 x 2.54

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In this book the details of many calculations are provided for access to work in quantum groups, algebraic differential calculus, noncommutative geometry, fuzzy physics, discrete geometry, gauge theory, quantum integrable systems, braiding, finite topological spaces, some aspects of geometry and quantum mechanics and gravity. Audience: Graduate students and researchers in mathematical physics and technology.

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Preface
Basics for Quantum Groups
Preliminary Ideas
Braiding
Calculus and Algebra
Integration and Fourier Transform
Differential Calculi
Differential Calculi I
Differential Calculi II
Differential Calculi III
Further Remarks on Differential Calculi
More on Q-Analysis
Quantum Planes
Remarks on Quantum Planes
Further Details on Q-Analysis
The Heisenberg Algebra
Remarks on Quantum Transmutation
Introduction
Some Quantum Transmutations
Classical Transmutation
Some Q-Calculus
Fourier Transforms and Distributions
Some Preliminary Calculations
Quantum Intertwining
Discretization and Quantum Mechanics
Preliminary Remarks
Discretization and Moyal
Q-Discretization
Calculations
Connections to Integrability
KP and DKP
Remarks on Q-KP
Remarks on Star Products
Discrete Calculus
Differential Calculus on Finite Sets
Finite Quantum Physics
Fuzzy Physics and Matrix Geometry
The Fuzzy Sphere
Aspects of Noncommutative Geometry
WZW
Coherent States
Further Aspects of FQM
Spectral Triples and Distance
Discrete Riemannian Geometry
Remarks on Lattice Gauge Theory
Connections to Gravity
Knots and the KZ Equation
Integrable Systems
Generalized Sigma Models
Bicomplexes
Aspects of Gauge Theory
Some Background
Gauge Theory on NC Spaces
Summary and Recapitulation
Pointless Spaces and Quantum Gravity
Introduction
Pointless Spaces
Singularities
Bibliography
Index
Table of Contents provided by Blackwell. All Rights Reserved.

Calculus Revisited

At a Glance

Hardcover

Shipping

How to return your order

Defective items

You Can Find This Book In

Other Editions and Formats

Paperback

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