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Electromagnetic fields on manifolds: Betti numbers, monopoles and strings, minimal coupling

Chapter I. Gauge Theories

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Part of the Lecture Notes in Mathematics book series (LNM,volume 676)

Abstract

The differential geometric study of electromagnetic fields on manifolds is extended to nonexact and even to nonclosed forms. Duality and variational principles are discussed and minimal coupling is derived.

Keywords

  • Electromagnetic Field
  • Variational Principle
  • Fundamental Period
  • Harmonic Form
  • Minimal Coupling

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References

  1. A. O. Barut, in Quantum Theory and Structure of Time and Space (edited by L. Castell et al.), C. Hanser Verlag, Vol. I (1975), Vol. II (1977).

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  2. A. O. Barut, De Rham currents, extended singularities of fields and magnetic monopoles, Reports Math. Phys. 11, 415–422 (1977).

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  3. A. O. Barut, Charge quantization condition with N strings. A new quantum number of charge-monopole systems, Lett. Math. Phys. 1, 367–370 (1977).

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  4. P. Bidal and G. de Rham, Les formes différentielles harmoniques, Comm. math. Helvetici, 19, 1–49 (1946).

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  5. W. V. D. Hodge, The Theory and Applications of Harmonic Integrals (Cambridge Univ. Press, 1946).

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© 1978 Springer-Verlag

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Barut, A.O. (1978). Electromagnetic fields on manifolds: Betti numbers, monopoles and strings, minimal coupling. In: Bleuler, K., Reetz, A., Petry, H.R. (eds) Differential Geometrical Methods in Mathematical Physics II. Lecture Notes in Mathematics, vol 676. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0063671

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  • DOI: https://doi.org/10.1007/BFb0063671

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-08935-3

  • Online ISBN: 978-3-540-35721-6

  • eBook Packages: Springer Book Archive