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Relativistic generation of vortex and magnetic field a)
a)Paper XI3 5, Bull. Am. Phys. Soc. 55, 374 (2010).
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10.1063/1.3566081
/content/aip/journal/pop/18/5/10.1063/1.3566081
http://aip.metastore.ingenta.com/content/aip/journal/pop/18/5/10.1063/1.3566081
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Image of FIG. 1.
FIG. 1.

Transport of a loop and circulation. Given a loop in space, the circulation of a vector field is the integral . Two loops and , connected by the “flow” (the parameter may be regarded as time), are shown in the figure. A circulation theorem pertains to a “movement” of loops; the rate of change of circulation is calculated as . To generalize the argument to the relativistic regime, we have to immerse the loop in the four-dimensional space-time and transport it by the four-velocity ( is the proper time) (Ref. 1). The space-time circulation obeys ; compare the right-hand side with (10).

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2011-04-08
2014-04-20
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Relativistic generation of vortex and magnetic field a)
http://aip.metastore.ingenta.com/content/aip/journal/pop/18/5/10.1063/1.3566081
10.1063/1.3566081
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