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4 results

  • 27 - The Dirac Monopole and Dirac Quantization

  • from Part II - Solitons and Topology; Non-Abelian Theory
  • Horaƫiu Năstase, Universidade Estadual Paulista, São Paulo
  • Book:
    Classical Field Theory
    Published online:
    04 March 2019
    Print publication:
    14 March 2019, pp 244-255

  • Summary

    We define the Dirac monopole as a simple consequence of extending Maxwell duality to the Maxwell equations with sources, and we show that the resulting gauge fields are only defined on patches. We write formulas in terms of p-form language, and define the magnetic charge in terms of the gauge fields on patches. Then, from the quantization of the first Chern number, a topological number, we obtain Dirac quantization for the product of electric and magnetic charges. One obtains an unphysical Dirac string singularity, and its unphysical nature leads again to Dirac quantization. Finally, semiclassical nonrelativistic considerations also lead to the same Dirac quantization.

  • A Comparison of Methods for Constructing Probability Measures on Infinite Product Spaces

  • Charles W. Lamb
  • Journal:
    Canadian Mathematical Bulletin / Volume 30 / Issue 3 / 01 September 1987
    Published online by Cambridge University Press:
    20 November 2018, pp. 282-285
    Print publication:
    01 September 1987
    • Article
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  • The construction, from a consistent family of finite dimensional probability measures, of a probability measure on a product space when the marginal measures are perfect is shown to follow from a classical theorem due to Ionescu Tulcea and known results on the existence of regular conditional probability functions.