Date of Award:


Document Type:


Degree Name:

Master of Science (MS)



Committee Chair(s)

James T. Wheeler


James T. Wheeler


T. -C. Shen


Maria J. Rodriguez


There is a robust and unifying approach to unraveling the roiling mysteries of the universe. Our most compelling accounts of physical reality at present rest on symmetry arguments that are conspicuously geometrical!

105 years ago, Albert Einstein derived gravity from Riemannian geometry. In the general theory of relativity, the world of our experience is a pseudo-Riemannian manifold whose curvature represents the gravitational field. Encoded in the Einstein field equation is how matter sources (energy-momentum tensor) couple to gravity (spacetime curvature). Schematically, the Einstein equation exhibits a more general structure:

Curvature of Spacetime = Material Sources

On one side of the equation are mathematical expressions that characterize in detail the curved shape of space and time. On the source side we write an expression collecting the energy and momentum densities of the different matter fields that move about in the world. Due to a profound theorem by Emmy Noether, these sources are built of conserved "currents" corresponding to matter sources that are described by certain symmetries.

In this thesis, we confront and resolve the question of how Yang-Mills matter fields couple to a scale-invariant model of gravity, called biconformal gravity. Biconformal gravity arises from a construction that imposes, in addition to local Lorentz symmetry, local dilatational symmetry. The need of the latter symmetry in a physical theory is nothing more inscrutable than the realization that the laws of physics should not change when we change units (i.e. meters, miles, kilograms) of our experimental measurements.

Assuming vanishing torsion, biconformal gravity not only reduces to scale invariant general relativity, but time emerges as part of the physical theory. Somewhat remarkably, we have shown that biconformal gravity also requires the sources to take the expected form.



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