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Calculus Revisited Book

Calculus Revisited
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  • Calculus Revisited
  • Written by author Robert W. Carroll
  • Published by Springer-Verlag New York, LLC, December 2002
  • Written for graduate students and researchers in mathematical physics and technology, this book begins with the basics of quantum groups and proceeds to address topics of increasing complexity, including differential calculi, Q-analysis, quantum transmuta
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Preface
Ch. 1Basics for Quantum Groups
1Preliminary Ideas
2Braiding
Ch. 2Calculus and Algebra
1Integration and Fourier Transform
Ch. 3Differential Calculi
1Differential Calculi I
2Differential Calculi II
3Differential Calculi III
4Further Remarks on Differential Calculi
Ch. 4More on Q-Analysis
1Quantum Planes
2Remarks on Quantum Planes
3Further Details on Q-Analysis
4The Heisenberg Algebra
Ch. 5Remarks on Quantum Transmutation
1Introduction
2Some Quantum Transmutations
3Classical Transmutation
4Some Q-Calculus
5Fourier Transforms and Distributions
6Some Preliminary Calculations
7Quantum Intertwining
Ch. 6Discretization and Quantum Mechanics
1Preliminary Remarks
2Discretization and Moyal
3Q-Discretization
4Calculations
5Connections to Integrability
6KP and DKP
7Remarks on Q-KP
8Remarks on Star Products
Ch. 7Discrete Calculus
1Differential Calculus on Finite Sets
2Finite Quantum Physics
Ch. 8Fuzzy Physics and Matrix Geometry
1The Fuzzy Sphere
2Aspects of Noncommutative Geometry
3WZW
4Coherent States
Ch. 9Further Aspects of FQM
1Spectral Triples and Distance
2Discrete Riemannian Geometry
3Remarks on Lattice Gauge Theory
4Connections to Gravity
5Knots and the KZ Equation
Ch. 10Integrable Systems
1Generalized Sigma Models
2Bicomplexes
Ch. 11Aspects of Gauge Theory
1Some Background
2Gauge Theory on NC Spaces
3Summary and Recapitulation
Ch. 12Pointless Spaces and Quantum Gravity
1Introduction
2Pointless Spaces
3Singularities
Bibliography
Index


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