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Topic: Dirac monopole

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Magnetic monopole

Dirac equation

Vector potential

Gauge transformation

Clifford algebra

Cosmic string

Solenoid

	Dirac biography
		Dirac had been hoping to have his research supervised by Ebenezer Cunningham, for by this time Dirac had become fascinated in the general theory of relativity and wanted to undertake research on this topic.
		Dirac was appointed Lucasian professor of mathematics at the University of Cambridge in 1932, a post he held for 37 years.
		Dirac unified the theories of quantum mechanics and relativity theory, but he also is remembered for his outstanding work on the magnetic monopole, fundamental length, antimatter, the d-function, bra-kets, etc.
	www-groups.dcs.st-and.ac.uk /~history/Biographies/Dirac.html (2515 words)

	Monopoles
		First, the Dirac string of the classical Dirac monopole is connected to topological properties of fermions (spin 1/2 particles).
		Due to their topological nature, monopoles are naturally produced in great numbers at the beginning of the Universe via the Kibble mechanism. Because of their unique properties, as will be seen later, monopole** production rate must be constrained significantly by other factors, such as inflation of the Universe.
		The ability of monopoles to catalyze energy release sets limits upon the primordial monopole flux, F. For example, only 10E28 monopoles in the center of the sun are required to produce the entire solar luminosity of 4E33 ergs/second.
	www.orionsarm.com /tech/monopoles.html (1577 words)

	Dirac string - Wikipedia, the free encyclopedia
		In physics, a Dirac string is a fictitious one-dimensional curve in space, stretched from a magnetic monopole - also called the Dirac monopole - to infinity.
		The Dirac string acts as the solenoid in the Aharonov-Bohm effect, and the requirement that the position of the Dirac string should not be observable implies the Dirac quantization rule: the product of a magnetic charge and an electric charge must always be an integer multiple of 2π.
		The quantization forced by the Dirac string can be understood in terms of the cohomology of the fibre bundle representing the gauge fields over the base manifold of space-time.
	en.wikipedia.org /wiki/Dirac_string (291 words)

	Paul Adrien Maurice Dirac - Cambridge University Press (Site not responding. Last check: 2007-10-08)
		Paul Dirac, who died in 1984, was without question one of the greatest physicists of the twentieth century.
		Dirac at the University of Miami H. Stanford; 9.
		Dirac's magnetic monopole and the fine structure constant W. Marciano and M. Goldhaber; 14.
	www.cambridge.org /asia/catalogue/catalogue.asp?isbn=0521340136 (385 words)

	TIME.com: Detecting a Twist of Space -- May 10, 1982 -- Page 1
		Dirac, one of the fathers of quantum theory, said that magnetic particles might exist that are exclusively "north" or "south." Recent developments in quantum theory suggest that these single-poled units, or "monopoles," would have immense mass, about 10 million billion times that of a proton at rest.
		Monopoles might also account for the mass in the universe that cosmologists say is "missing" and would confirm current ideas about the basic building blocks of matter.
		To detect a fugitive monopole, Cabrera used a kind of magnetic mousetrap, which was connected to a SQUID (superconducting quantum interference device).
	www.time.com /time/magazine/article/0,9171,925385,00.html (663 words)

	Paul Adrien Maurice Dirac - Cambridge University Press (Site not responding. Last check: 2007-10-08)
		Dirac, who died in 1984, was unquestionably one of the greatest physicists of the twentieth century.
		Dirac was awarded the Nobel Prize for Physics in 1933 at the age of thiry-one.
		His formulations of the quantum field theory, statistics of particles and fields, his work on gravitational waves, and his prediction of magnetic monopoles stand as monuments to his originality and deep understanding of natural phenomena.
	www.cambridge.org /us/catalogue/catalogue.asp?isbn=0521386888 (442 words)

	Magnetic monopole - Wikipedia, the free encyclopedia
		This is known as the Dirac quantization condition.
		The quantization condition comes from the requirement that the phases around the Dirac string are trivial, which means that the Dirac string must be unphysical.
		In this model the dyons arise due to the vacuum configuration in a particular area of the universe, according to the original Dirac theory.
	en.wikipedia.org /wiki/Dirac_monopole (2470 words)

	E-Space: Monopoles (Site not responding. Last check: 2007-10-08)
		Properties: Monopoles are easily accelerated by strong magnetic fields.
		Massless monopoles are first used in giga-scale powerplants to generate energy via monopole-catalyzed fusion.
		Finally, a massive monopole can be efficiently used to produce more monopoles, without the expense and trouble of a high-energy particle accelerator.
	www.phoenyx.net /macrospace/2005/01/msg00192.html (1255 words)

	[No title] (Site not responding. Last check: 2007-10-08)
		] The theory that the continuum of negative energy states that are solutions to the Dirac equation are filled with electrons, and the vacancies in this continuum (holes) are manifested as positrons with energy and momentum that are the negative of those of the state.
		is the Kronecker delta function, which matrices operate on the four-component wave function in the Dirac equation.
		] A particle behaving according to the Dirac theory, which describes the behavior of electrons and muons except for radiative corrections, and is envisaged as describing a central core of a hadron of spin
	www.accessscience.com /Dictionary/D/D21/DictD21.html (1562 words)

	Teaching activities (Site not responding. Last check: 2007-10-08)
		In the Fall and Winter terms 1995-6, I gave a series of ten lectures on electromagnetic duality to members of the QMW String Theory group.
		The lectures started from very basic material and ended with Sen's test of the predicted dyonic spectrum at monopole number 2 for the gauge group SU(2).
		Details of the calculation of the number of collective coordinates: an example of an index theorem calculation for operators on open spaces.
	www.maths.ed.ac.uk /~jmf/Teaching/EDC.html (218 words)

	Double-Gauge Invariant Local Quantum Field Theory of Charges and Dirac Magnetic Monopoles
		Exploiting the recently found extra monopole gauge symmetry which ensures the physical irrelevance of the Dirac strings in electromagnetism with Dirac magnetic monopoles, we formulate a local quantum field theory of charges and monopoles.
		Fortunately, however, due to the monopole gauge invariance of the action (3) under (9), most configurations of the surfaces S are physically irrelevant.
		Here the monopole gauge transformations (9) reduce the dimensionality of the fluctuations from surfaces S to lines L.
	www.physik.fu-berlin.de /~kleinert/kleiner_re205/monopqf2.html (1087 words)

	Dual map of a 3D superconductor
		Equation (54) confirms Dirac's statement that the magnetic flux emanating from a monopole must be supplied by an infinitesimally thin string of magnetic dipoles and that in order to obtain the true local field of a genuine point monopole, this string has to be subtracted.
		While this string is indeed completely unphysical in the normal phase, it acquires a physical relevance in the superconducting phase [22] where it serves as the core of the Abrikosov flux tube.
		For a monopole-antimonopole pair, (60) amounts to a confining linear potential between the monopole and antimonopole in the superconducting phase.
	www.physik.fu-berlin.de /~kleinert/232/node5.html (2182 words)

	Dirac (MW) (Site not responding. Last check: 2007-10-08)
		Therein are two 1/2 spin particles, the large fl object in the diagram represents a positive highly charged dipole particle.
		Similar to a Dirac monopole, an electron bound to this highly charged particle is confined to one pole, and its orbit is outlined.
		Thus we see that subsequent to utilizing Dalton's method of stoichiometric analysis to establish the New Quark Theory, the concept of Dirac that there are highly charged particles wherein an electron (or positron) is confined to a pole has proved exceptionally fruitful.
	www.wbabin.net /saba/saba15.htm (445 words)

	700-718 (Site not responding. Last check: 2007-10-08)
		Dirac monopoles in the cosmic space are expected to be accelerated by cosmic magnetic fields and decelerated mainly by Hubble's recession of galaxies.
		The estimated average energy of cosmic monopoles, carrying the Dirac's elementary magnetic charge, is 10
		Preliminary discussions about the structure of monopole initiated EAS's and about more extensive monopole experiments are also given.
	ptp.ipap.jp /link?PTP/30/700 (187 words)

	Amazon.com: "monopole field": Key Phrase page (Site not responding. Last check: 2007-10-08)
		This concept, in its global ramifications, is studied through an examination of Dirac's magnetic monopole field.
		Generalizations to non-Abelian groups are carried out, and result in identification with the mathematical concept of connections on principal fiber...
		The spherically symmetrical field is often called a monopole field by analogy with the electrostatic field from a point charge.
	www.amazon.com /phrase/monopole-field (551 words)

	TGD diary: Some problems of TGD as almost-topological QFT and their resolution
		The central extension parameter k determines the over-all scaling of the eigenvalues of the modified Dirac operator.
		The Maxwell field in question is not covariantly constant and does not define a generalization of the CP Kähler form.
		A charged Dirac monopole would be in question.
	matpitka.blogspot.com /2006/08/some-problems-of-tgd-as-almost.html (1267 words)

	High Energy Magnetic Monopole Sequestered by U.S. Government
		The materials of which I am referring, were (high energy magnetic monopole materials) with resistive forces of at least 10 to 20 tons per square meter x 1/4" thickness.
		I have since attempted to find information about these materials on the Internet but as is to be expected, the closest thing resembling such materials to what I have described are what are referred to as high energy Dirac Monopoles.
		Google search on "Dirac Monopoles" - the science behind the high energy magnetic monopole.
	pesn.com /2004/06/05/HighEnergyMagneticMonopole/index.html (3716 words)

	The Dirac monopole and induced representations., R. Langlands
		The Dirac monopole and induced representations., R. Langlands
		[2] P. Dirac, Quantised singularities in the electromagneticfield, Roy.
		[6] Y. Kazama, C. Yang, and A. Goldhaber, Scattering of a Dirac particle with charge ze by afixed magnetic monopole, Phys.
	projecteuclid.org /Dienst/UI/1.0/Summarize/euclid.pjm/1102699904 (123 words)

	Bohm Compton Radius Vortex Sidharth Sarfatti
		A self consistent solution to Dirac equation in a Kerr Newman space-time with M^2 > a^2 + Q^2 is presented for the case when the Dirac particle is the source of the curvature and the electromagnetic field.
		The ordinary free particle solutions of the Dirac equation are completely delocalised; the curvature however, now causes the Dirac wave functions to be localised over a region comparable in dimension to the Compton wavelength of the particle.
		In Unruh's case of a wedge region or in the analogous case of conformal matter enclosed in a double cone, the hidden quantum symmetry passes to the one described by a Killing vector associated with the Lorentz or conformal- group.
	www.valdostamuseum.org /hamsmith/Sidharth.html (5379 words)

	THEORY AND DETECTION OF MAGNETIC MONOPOLES IN GAUGE THEORIES (Site not responding. Last check: 2007-10-08)
		These lecture notes discusses the developments both in the theoretical understanding of the physics and mathematics of magnetic monopoles as well as the ways in which they can be detected experimentally.
		The subject has now become highly interdisciplinary and recent monopole meetings have attracted participants from low temperature physics at one extreme to cosmology at the other.
		Monopoles and Astrophysics: Galactic Magnetic Fields and the Parker Bound
	www.worldscibooks.com /books/physics/0129.html (182 words)

	General Information (Site not responding. Last check: 2007-10-08)
		It is known that one cannot construct a consistent quantum theory describing the interaction of massive photons interacting with electric charges and magnetic monopoles.
		The conclusion is that Proca’s theory of massive photons and Dirac’s theory of magnetic monopoles cannot coexist within the very same classical theoretical framework: there are no spherically symmetric solutions for the magnetic field of a point monopole.
		However, spherically symmetric solutions are the only one compatible with the basic commutation rules of the classical Poisson bracket structure describing the short-range electromagnetic interaction of a point electric charge in the field of a fixed Dirac monopole.
	www.albany.edu /physics/html/pascal05/cafaro.html (305 words)

	Physics does not explain why astro bodies spin or rotate whi
		Please note that Dirac failed in his monopole quest.
		So the monopoles in the Universe would be two monopoles.
		monopole equation to be a positive q/e instead of a zero.
	www.groupsrv.com /science/about181856-30.html (5092 words)

	Magnetic Monopole Text - Physics Forums Library
		The fact is that no magnetic monopoles have been ever found (like a point particle being the source of a magnetic field).
		On this point the gauge fields have a singularity and their form (i mean their equation) looks just like the tensor-form of a Dirac string.
		This thing is an anti-symmetrival tensorfield that represents a magnetic monopole of certain magnetic charge.
	www.physicsforums.com /archive/index.php/t-38096.html (700 words)

	Basis for magnetic monopoles
		Dirac's monopole was topological in origin, arising from the closed
		magnetic monopoles are found have been known for a long time.
		Dirac realized that these strings were phony, but
	www.groupsrv.com /science/about40873-0-asc-45.html (5516 words)

	Science News Online (7/4/98): References for "Monopole search comes up empty-handed"
		Fermilab physicists report no evidence of magnetic monopoles in high-energy collisions between protons and antiprotons.
		He, Y.D. Search for a Dirac magnetic monopole in high energy nucleus-nucleus collisions.
		Additional information about the Fermilab search for heavy magnetic monopoles is available at http://www-D0.fnal.gov/public/pubs/monopole_prl/monopole_prl.html.
	www.sciencenews.org /pages/sn_arc98/7_4_98/fob2ref.htm (61 words)

	Amazon.com: "Dirac Monopole Without Strings": Key Phrase page (Site not responding. Last check: 2007-10-08)
		See all pages with references to Dirac Monopole Without Strings.
		Q76cl Dirac Monopole Without Strings: Monopole Harmonics Article Nuclear Physics B107, 365 (1976) begins Tai Tsun Wu and Chen Ning Yang page 493 Commentary After...
		Wu, T. and Yang, C. Dirac monopole without strings: monopole Harmonics, Nucl.
	www.amazon.com /phrase/Dirac-Monopole-Without-Strings (484 words)

	Table of contents for Library of Congress control number 86033409 (Site not responding. Last check: 2007-10-08)
		Table of contents for Reminiscences about a great physicist : Paul Adrien Maurice Dirac / editors, Behram N. Kursunoglu, Eugene P. Wigner.
		Bibliographic record and links to related information available from the Library of Congress catalog
		Library of Congress subject headings for this publication: Dirac, P, A, M, (Paul Adrien Maurice), 1902-Physics History
	www.loc.gov /catdir/toc/cam028/86033409.html (267 words)

	Math arXiv: Search results (Site not responding. Last check: 2007-10-08)
		hep-th/0503040 Infinite-dimensional representations of the rotation group and Dirac's monopole problem.
		hep-th/0403146 On infinite-dimensional representations of the rotation group and Dirac monopole.
		hep-th/0402226 On representations of the rotation group and magnetic monopoles.
	front.math.ucdavis.edu /author/Cruz-F* (131 words)

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