Abstract
In the absence of electric charges and currents the Maxwell equations are clearly symmetric in the electric and magnetic fields. This symmetry would be conserved in the presence of field sources if, in addition to the electric charges and currents, magnetic charges (monopoles) and currents would exist.
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Notes
- 1.
Gaussian units are used in this chapter.
- 2.
This equation determines the sign of \(\mathbf {j}_m\) in Eq. (12.3).
- 3.
This relation, as for the Lorentz force, can be derived directly from the relativistic transformation of the electric and magnetic fields from a frame where the magnetic charge is at rest to a frame where it moves with velocity \(\mathbf {v}\).
- 4.
P.A.M. Dirac, Quantised singularities in the electromagnetic field, Proc. Roy. Soc., A 133, 60 (1931). The introduction is particularly interesting because Dirac presents some considerations on the evolution of the mathematics applied to theoretical physics and then he shortly reviews the studies on the negative energy states, inspired to his previous paper Electrons and protons, Proc. Roy. Soc., A 126, 360 (1930). Following the suggestion by J.R. Oppenheimer, one year before the discovery of the positive electron by C.D. Anderson (Science, 76, 238 (1932)), he introduces the idea of anti-electrons, of production and annihilation of electron-antielectron pair, and he also proposes the existence of the antiproton as the antiparticle of the proton. For a comment on the Dirac’s paper see the article by E. Amaldi and N. Cabibbo cited in a following note.
- 5.
After the first paper, in 1948 Dirac published a detailed analysis of the theory of the magnetic monopole (Physical Review, 74, 817 (1948)). An extensive review article on the theory and the searches of the magnetic monopole was done by E. Amaldi, On the Dirac Magnetic Poles, published in the volume Old and new problems in Elementary Particles, in honour of G. Bernardini, edited by G. Puppi, Academic Press, New York, (1968). This review was updated in 1972 by E. Amaldi and N. Cabibbo, On the Dirac Magnetic Poles, in Aspects of Quantum Theory, a volume in honour of P.M. Dirac, edited by Abdus Salam and E.P. Wigner, Cambridge, University Press, 1972. An introduction to the argument can be found in J.D. Jackson, Classical Electrodynamics, cited, Chap. 6.
- 6.
See for instance E. Amaldi, cited, p. 45.
- 7.
The potential of a magnetic dipole \(\mathbf {m}\) located in the origin is:
.
- 8.
Here the sign is positive because associated to the direction of the circular path of the integral that, at \(\theta =\pi \), is opposite to the direction of the outgoing flux.
- 9.
The quantization proof reported here, was given by E. Fermi (Acc. Naz. Lincei, Fondazione Donegani Conferenze, 1950, p. 117) and is reported in the paper by E. Amaldi, cited, p. 47.
- 10.
This argument was proposed by A.S. Goldhaber, Physical Review, 140 B, 1407 (1965). For the calculation of \(\varDelta L_{e}\) see also J.D. Jackson, Classical Electrodynamics, cited, Section 6.13.
- 11.
The result was first given by J.J. Thompson, Elements of the Mathematical Theory of Electricity and Magnetism, Cambridge, University Press, 1900–1904, and can be found in E. Amaldi, cited, p. 16, and in J.D. Jackson, Classical Electrodynamics, cited, Section 6.13.
- 12.
Terms for the density effect and the shell correction have to be added to this simple formula. See the Section Passage of Particles Through Matter in K.A. Olive et al. (Particle Data Group), Chin. Phys. C, 38, 090001 (2014).
- 13.
For this subject and its application to the present experiments, see: C. Bauer et al., Nucl. Instr. and Methods in Physics Research A 545 (2005) 503–515. For more details see: L. Patrizii and M. Spurio, Status of searches for magnetic monopoles, Annual Review of Nuclear Physics, 2015, 65:279–302.
- 14.
L. Patrizii and M. Spurio, cited; see also G. Giacomelli and L. Patrizii, Magnetic Monopoles Searches, arXiv:hep-ex/0506014v1, 7 June 2005. For the first searches see E. Amaldi, cited, 1965, updated by E. Amaldi and N. Cabibbo, cited, 1972.
- 15.
K.A. Olive et al. (Particle Data Group), cited, updated in url: http://pdg.lbl.gov.
- 16.
Aad et al., Physical Review Letters, 109, 261803 (2012).
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Lacava, F. (2016). Magnetic Monopoles. In: Classical Electrodynamics. Undergraduate Lecture Notes in Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-39474-9_12
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