Book contents
- Frontmatter
- Contents
- List of Symbols
- Acknowledgments
- 1 A Brief History
- 2 Maxwell's Equations
- 3 Electromagnetic Waves
- 4 Special Relativity
- 5 Mechanics and Maxwell's Equations
- 6 Mechanics, Lagrangians, and the Calculus of Variations
- 7 Potentials
- 8 Lagrangians and Electromagnetic Forces
- 9 Differential Forms
- 10 The Hodge ⋆ Operator
- 11 The Electromagnetic Two-Form
- 12 Some Mathematics Needed for Quantum Mechanics
- 13 Some Quantum Mechanical Thinking
- 14 Quantum Mechanics of Harmonic Oscillators
- 15 Quantizing Maxwell's Equations
- 16 Manifolds
- 17 Vector Bundles
- 18 Connections
- 19 Curvature
- 20 Maxwell via Connections and Curvature
- 21 The Lagrangian Machine, Yang-Mills, and Other Forces
- References
- Index
- Plate Section
- References
References
Published online by Cambridge University Press: 05 February 2015
Book contents
- Frontmatter
- Contents
- List of Symbols
- Acknowledgments
- 1 A Brief History
- 2 Maxwell's Equations
- 3 Electromagnetic Waves
- 4 Special Relativity
- 5 Mechanics and Maxwell's Equations
- 6 Mechanics, Lagrangians, and the Calculus of Variations
- 7 Potentials
- 8 Lagrangians and Electromagnetic Forces
- 9 Differential Forms
- 10 The Hodge ⋆ Operator
- 11 The Electromagnetic Two-Form
- 12 Some Mathematics Needed for Quantum Mechanics
- 13 Some Quantum Mechanical Thinking
- 14 Quantum Mechanics of Harmonic Oscillators
- 15 Quantizing Maxwell's Equations
- 16 Manifolds
- 17 Vector Bundles
- 18 Connections
- 19 Curvature
- 20 Maxwell via Connections and Curvature
- 21 The Lagrangian Machine, Yang-Mills, and Other Forces
- References
- Index
- Plate Section
- References
Summary
A summary is not available for this content so a preview has been provided. Please use the Get access link above for information on how to access this content.
- Type
- Chapter
- Information
- Electricity and Magnetism for MathematiciansA Guided Path from Maxwell's Equations to Yang–Mills, pp. 275 - 278Publisher: Cambridge University PressPrint publication year: 2015
References
[1] , “On the Work of Simon Donaldson,” Proceedings of the International Congress of Mathematicians, Berkeley CA, 1986, American Mathematical Society, pp. 3–6.
[2] , “On the Work of Edward Witten,” Proceedings of the International Congress of Mathematicians, Kyoto, 1990 (Tokyo, 1991), pp. 31–35.
[3] , Collected Works Volume 6, Oxford University Press, 2005.
[4] , Magnetism: A Very Short Introduction, Oxford University Press, 2012.
[5] , Collected Papers of Raoul Bott, Volume 4, edited by , Birkhäuser, 1994.
[6] and , Elementary Differential Equations and Boundary Value Problems, eighth edition, Wiley, 2004.
[7] , Electrodynamics from Thomson and Maxwell to Hertz, Chapter 19 in The Oxford Handbook of the History of Physics (edited by and ), Oxford University Press, 2013.
[8] and (editors), The Oxford Handbook of the History of Physics, Oxford University Press, 2013.
[9] and , Separation of Variables for Partial Differential Equations: An Eigenfunction Approach (Studies in Advanced Mathematics), Chapman & Hall/CRC, 2005.
[10] , and , Lectures in Differential Geometry, World Scientific, 1999.
[11] , Energy, the Subtle Concept: The Discovery of Feynman's Blocks from Leibniz to Einstein, Oxford University Press, 2010.
[12] and , Classical Mechanics, second edition, Dover, 1994.
[13] , Electrodynamics from Ampere to Einstein, Oxford University Press, 2000.
[14] , “An application of gauge theory to 4-dimensional topology,” Journal of Differential Topology, Volume 18, Number 2 (1983), pp. 279–315.
[15] , “Connections, cohomology and the intersection forms of 4-manifolds,” Journal of Differential Geometry, Volume 24, Number 3 (1986), pp. 275–341.
[16] and , The Geometry of Four-Manifolds, Oxford University Press, 1990.
[17] , Conceptual Foundations of Quantum Mechanics, second edition, Westview Press, 1999.
[18] , Principles of Quantum Mechanics, fourth edition, Oxford University Press, 1958 (reprinted 1981).
[19] et al., The Principle of Relativity, Dover, 1952.
[20] Lawrence Evans, Partial Differential Equations, Graduate Studies in Mathematics, Volume 19, American Mathematical Society, 1998.
[21] , and , The Feynman Lectures on Physics Volume 1, Addison-Wesley, 1963.
[22] , Introduction to Partial Differential Equations, Mathematical Notes, Vol. 17, Princeton University Press, 1976.
[23] , Quantum Field Theory: A Tourist Guide for Mathematicians, Mathematical Surveys and Monographs, Volume 149, American Mathematical Society, 2008.
[24] , Real Analysis: Modern Techniques and Their Applications, Wiley, 1999.
[25] , Special Relativity, Chapman & Hall, 1989.
[26] , All the Mathematics You Missed but Need to Know for Graduate School, Cambridge, 2002.
[27] , Henri Poincaré: A Scientific Biography, Princeton University Press, 2012.
[28] , The Elegant Universe, Vintage Books, 2000.
[29] and , Electromagnetic Theory and Computation: A Topological Approach, Mathematical Science Research Institute Publication, 48, Cambridge Unversity Press, 2004.
[30] and , Differential Topology, American Mathematical Society, reprint edition, 2010.
[31] , Functional Analysis. Volume I: A Gentle Introduction, Matrix Editions, 2006.
[32] and , Physics, third edition, John Wiley and Sons, 1977.
[33] and , Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach, Prentice Hall, 1999.
[34] , Lebesgue Integration on Euclidean Space, Jones and Bartlett Learning; revised edition, 2000.
[35] , The Noether Theorems: Invariance and Conservation Laws in the Twentieth Century, Springer-Verlag, 2011.
[36] Jr., The Theory of Gauge Fields in Four Dimensions, American Mathematical Society, 1985.
[37] and , Electromagnetic Fields and Waves, second edition, W. H. Freeman and Company, 1970.
[38] , Mathematical Foundations of Quantum Mechanics, Dover, 2004.
[39] , Seiberg-Witten Gauge Theory, Hindustan Book Agency, 1999.
[40] , “A topologist's account of Yang-Mills theory,” Expositiones Mathematicae, Volume 10 (1992), pp. 311–352.
[41] , The Quantum Vacuum: An Introduction to Quantum Electrodynamics, Academic Press, 1994.
[42] , Lectures on Seiberg-Witten Invariants, Lecture Notes in Mathematics, Volume 1629, Springer-Verlag, 2001.
[43] , A Traveler's Guide to Spacetime: An Introduction to the Special Theory of Relativity, McGraw-Hill, 1995.
[44] , Real Analysis and Applications: Including Fourier Series and the Calculus of Variations, American Mathematical Society, 2005.
[45] , The Seiberg-Witten Equations and Applications to the Topology of Smooth Four-Manifolds, Princeton University Press, 1995
[46] , Joseph Henry: The Rise of an American Scientist, Smithsonian Institution Press, 1997.
[47] , Emmy Noether's Wonderful Theorem, Johns Hopkins University Press, 2011.
[48] , Notes on Seiberg-Witten Theory, Graduate Studies in Mathematics, Vol. 28, American Mathematical Society, 2000.
[49] , Applications of Lie Groups to Differential Equations, second edition, Graduate Text in Mathematics, Vol. 107, Springer-Verlag, 2000.
[50] (editor), The Dawning of Gauge Theory, Princeton University Press, 1997.
[51] , Subtle Is the Lord: The Science and the Life of Albert Einstein, Oxford University Press, 1982.
[52] , Niels Bohr's Times: In Physics, Philosophy, and Polity, Oxford University Press, 1991.
[53] , Inward Bound, Oxford University Press, 1988.
[54] , “The Present and the Future of Mathematical Physics,” Bulletin of the American Mathematical Society, 2000, Volume 37, Number 1, pp. 25–38.Google Scholar
[55] and , Quantum Mechanics, Addison-Wesley, 1961.
[56] , Real Analysis, Prentice Hall, 1988.
[57] , Real and Complex Analysis, McGraw-Hill Science/Engineering/Math, third edition, 1986.
[58] , Functional Analysis, McGraw-Hill Science/Engineering/Math, second edition, 1991.
[59] , Differential Equations with Applications and Historical Notes, McGraw-Hill, 1972.
[60] and , “Monopole Condensation and Confinement in N = 2 Supersymmetric Yang-Mills Theory,” Nuclear Physics, B426, (1994).Google Scholar
[61] , Calculus on Manifolds: A Modern Approach to Classical Theorems of Advanced Calculus, Westview Press, 1971.
[62] , Electromagnetism and Field Theory, Chapter 18 in The Oxford Handbook of The History of Physics (edited by and ), Oxford University Press, 2013.
[63] , Group Theory and Physics, Cambridge University Press, 1994.
[64] and , Seiberg-Witten and Gromov Invariants for Symplectic 4-Manifolds, International Press of Boston, 2010.
[65] , Relativity, Thermodynamics and Cosmology, Oxford University Press, 1934.
[66] , The Contributions of Faraday and Maxwell to Electrical Science, Pergamon Press, 1966.
[67] , Henri Poincaré: Impatient Genius, Springer-Verlag, 2012.
[68] R. Jr., Differential Analysis on Complex Manifolds, third edition, Springer Verlag, 2010.
[69] and , “Concept of nonintegrable phase factors and gobal formulation of gauge fields,” Physical Review D, Volume 12, Number 12 (1975), pp. 3845–3857.Google Scholar
[70] , Quantum Field Theory. I: Basics in Mathematics and Physics, Springer-Verlag, 2006.
[71] , Quantum Field Theory. II: Quantum Electrodynamics, Springer-Verlag, 2009.
[72] , Quantum Field Theory. III: Gauge Theory, Springer-Verlag, 2009.