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Two questions on the geometry of gauge fields (1994)

Costa, N. C. A. ; Doria, F. A. ; Furtado-do-Amaral, A. F. ; [et al.]

Springer

Foundations of physics 24 (1994), S. 783-800

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ISSN: 1572-9516

Source: Springer Online Journal Archives 1860-2000

Topics: Physics

Notes: Abstract We first show that a theorem by Cartan that generalizes the Frobenius integrability theorem allows us (given certain conditions) to obtain noncurvature solutions for the differential Bianchi conditions and for higher-degree similar relations. We then prove that there is no algorithmic procedure to determine, for a reasonable restricted algebra of functions on spacetime, whether a given connection form satisfies the preceding conditions. A parallel result gives a version of Gödel's first incompleteness theorem within an (axiomatized) theory of gauge fields.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF02054673

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