Ultraviolet Scalar Unification and Gravitational Radiation Reaction from Quantum Field Theory

Citation

Moss, Alexander Lorenzo (2023) Ultraviolet Scalar Unification and Gravitational Radiation Reaction from Quantum Field Theory. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/f997-ts08. https://resolver.caltech.edu/CaltechTHESIS:06032023-002035574

Abstract

Since its inception, the development of quantum field theory has been driven by a desire to describe nature at the highest energy scales, where both relativistic and quantum mechanical aspects of matter and radiation are manifest. The theory has been wildly successful in this respect, giving rise to the standard model of particle physics, as well as quantum cosmologies of the early universe. The applications of quantum field theory are not, however, restricted to high-energy physics. The theory is just as spectacular in the infrared as it is in the ultraviolet, and it serves as a mathematical nexus for physical processes spanning the energy spectrum.

We will investigate two such connections in this work. In the first part, we will relate the analytic structure of the scattering amplitudes of scalar quantum field theories in the far infrared to unifying symmetries of their actions in the ultraviolet. In the sequel, we will study a system of two massive scalar fields coupled to the spacetime metric. Identifying the classical limit with the gravitational infrared, we will sift the classical dynamics of binary gravitational inspiral from the scattering amplitudes of canonical quantum gravity.

In Chapter 1, we argue that symmetry and unification can emerge as byproducts of certain physical constraints on dynamical scattering. To accomplish this we parameterize a general Lorentz invariant, four-dimensional theory of massless and massive scalar fields coupled via arbitrary local interactions. Assuming perturbative unitarity and an Adler zero condition, we prove that any finite spectrum of massless and massive modes will necessarily unify at high energies into multiplets of a linearized symmetry. Certain generators of the symmetry algebra can be derived explicitly in terms of the spectrum and three-particle interactions. Furthermore, our assumptions imply that the coset space is symmetric.

In Chapter 2, we introduce the gravitational inspiral problem.In Chapter 3, we review the Hamiltonian formulation of binary dynamics and outline the extraction of the effective Hamiltonian from scattering amplitudes. We then augment the equations of motion with a gravitational radiation reaction force, thus incorporating dissipation. In Chapter 4, we extend the setup of Kosower, Maybee, and O'Connell (KMOC), which expresses classical observables in terms of scattering amplitudes, to study the evolution of angular momentum during two-body scattering in gravity and electromagnetism. From the associated scattering amplitudes, we explicitly compute the total radiated angular momentum through the third Post-Minkowskian order (3PM) in general relativity and the third Post-Coulombic order (3PC) in electromagnetism.

In Chapter 5, starting with the classical expressions for radiated energy and angular momentum, we compute the corresponding instantaneous radiative fluxes in isotropic gauge. We then use these fluxes to derive the relative radiation reaction force associated to a gravitational binary system at third post-Minkowskian order by imposing flux balance. Together with the conservative Hamiltonian, this force provides a complete equation of motion for the relative degree of freedom of a (bound or unbound) gravitational binary at 3PM. Finally, in Chapter 6 we compare our results with the post-Newtonian literature, finding agreement to G³, 3PN (relative) order.

Thesis Files