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Eikonal analysis of linearized quantum gravity : a functional approach DeLisle, Colby L.


The low energy effective theory of quantized gravity is currently our most successful attempt at unifying general relativity and quantum mechanics. It is expected to serve as the universal low energy limit of any future microscopic theory of quantum gravitation, so it is crucial to properly understand its low frequency, long wavelength, "infrared" limit. However, this effective theory suffers from the same kind of infrared divergences as theories like quantum electrodynamics. It is the aim of this work to characterize these divergences and isolate the infrared behavior of quantum gravity using functional methods. We begin with a review of infrared divergences, and how they are treated in QED. This includes a brief overview of the known applications of functional methods to the problem. We then discuss the construction of the effective field theory of quantum gravity in the linearized limit, coupled to scalar matter. Proceeding to the main body of the work, we employ functional techniques to derive the form of the scalar propagator after soft graviton radiation is integrated out. An eikonal form for the generating functional of the theory is then presented. In the final chapter, we use this generating functional to derive the soft graviton theorem and the eikonal form of the two-body scalar scattering amplitude. The result is a concise derivation of multiple known results, as well as a demonstration of the factorization of soft graviton radiation against the eikonal amplitude. We conclude with some comments on how these results can be extended, and we argue that the functional framework is the best candidate for a unified understanding of all relevant infrared features of quantum gravity.

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