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Long Range Forces and Broken Symmetries

P. A. M. Dirac
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences
Vol. 333, No. 1595 (Jun. 26, 1973), pp. 403-418
Published by: Royal Society
Stable URL: http://www.jstor.org/stable/78370
Page Count: 16
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Long Range Forces and Broken Symmetries
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Abstract

There are reasons for believing that the gravitational constant varies with time. Such a variation would force one to modify Einstein's theory of gravitation. It is proposed that the modification should consist in the revival of Weyl's geometry, in which lengths are non-integrable when carried around closed loops, the lack of integrability being connected with the electromagnetic field. A new action principle is set up, much simpler than Weyl's, but requiring a scalar field function to describe the gravitational field, in addition to the gμ ν. The vacuum field equations are worked out and also the equations of motion for a particle. An important feature of Weyl's geometry is that it leads to a breaking of the C and T symmetries, with no breaking of P or of CT. The breaking does not show itself up with the simpler kinds of charged particles, but requires a more complicated kind of term in the action integral for the particle.

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