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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
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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.

Local Transition Functions of Quantum Turing Machines
Masanao Ozawa, Harumichi Nishimura
Journal:

RAIRO - Theoretical Informatics and Applications / Volume 34 / Issue 5 / September 2000

Published online by Cambridge University Press:

15 April 2002, pp. 379-402

Print publication:

September 2000
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Foundations of the notion of quantum Turing machines areinvestigated. According to Deutsch's formulation, the time evolution of a quantum Turing machine is to be determined by the localtransition function. In this paper, the local transition functions are characterized for fully general quantum Turing machines, including multi-tape quantum Turing machines, extending the results due to Bernstein and Vazirani.

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
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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.

The transition probabilities of the extended simple stochastic epidemic model and the Haskey model
Richard J. Kryscio
Journal:

Journal of Applied Probability / Volume 9 / Issue 3 / June 1972

Published online by Cambridge University Press:

14 July 2016, pp. 471-485

Print publication:

June 1972
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We present a solution to a special system of Kolmogorov forward equations. We use this result to present a useful expression for the transition probabilities of the extended simple stochastic epidemic model and an epidemic model involving cross-infection between two otherwise isolated groups.

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