Abstract
The global symmetry implied by the fact that one can multiply all masses with a common constant is made into a local, gauge symmetry. The matter action then becomes Conformally invariant and it seems natural to choose for the corresponding scalar gauge field the action for a conformally invariant (massless) scalar field. The resulting conformally invariant theory turns out to be equivalent to general relativity. Since this means that the usual Einstein-Hilbert action is not, in fact, a true gauge action for the space-time geometry, the full theory ought to be supplied with such a term. Gauge-theoretic arguments and conformal invariance requirements dictate its form.
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Essén, H. General relativity as a conformally invariant scalar gauge field theory. Int J Theor Phys 29, 183–187 (1990). https://doi.org/10.1007/BF00671328
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DOI: https://doi.org/10.1007/BF00671328