SIMPLIFYING QUANTUM GRAVITY CALCULATIONS With examples of scalar-graviton and graviton-graviton scattering

The Einstein-Hilbert Lagrangian for gravity is non-renormalizable at loop level. However, it can be treated in the effective field theory framework which means that gravity as an effective theory can be renormalized when a proper expansion of the effective Lagrangian is made. At the same time, the Feynman rules for gravity are very complicated, although the resulting amplitudes do not have the same complications. Therefore, in this thesis we want to simplify the Feynman rules as much as possible by using the most general parameterized gauge condition, adding all possible parameterized total derivative terms and redefining the gravitational, ghosts and scalar fields in a general parameterization way. By choosing the parameters in a specific way, we obtain simplified Feynman rules, especially the triple and quadruple graviton vertices are simplified. In addition, we verify our simplified rules by calculating the amplitudes of scalar-graviton and graviton-graviton scattering at tree level using the simplified and standard Feynman rules. Finally, we show the utility of these simplified rules by calculating some one-loop diagrams for scalar-graviton scattering and comparing to the standard Feynman rules. Popular Science Description In physics, the story of gravity is still incomplete. It began under an apple tree when Newton started his journey to discover his laws about the gravitational force, but these laws were not enough to describe all the gravitational phenomena. To describe gravity in a more accurate way, Einstein came with the theory of general relativity. This theory treats the gravitational force as a consequence of the curvature of spacetime. This should be compared with the other forces in nature (the electromagnetic, weak and strong force) which are described by the standard model of particle physics. This model treats the forces as a consequence of exchanging particles which are called quanta. There have been many attempts in the last century to study gravity as a quantized theory, quantum gravity, where the exchanged particles are called gravitons. Quantum gravity is still not fully understood because of many obstacles, one of them being its complicated calculations. The purpose of this thesis is to address this latter problem of complicated calculations, following the belief that nature should be described in a beautiful and simple mathematical way. Moreover, a simplified form with fewer terms that contribute to gravitational effects can lead to a deeper understanding of gravity. To treat this problem, we want to find mathematical tools that can simplify the math of the theory without changing the information that it contains. Fortunately, in quantum physics such tools exist as field redefinition which means that we can redefine the gravitons in order to find a simpler expression that can describe exchanging these particles. As a result of applying these mathematical tools, we successfully simplify the math that describes the gravitational interaction between particles. In particular, we show that the interaction between three gravitons can be reduced from 40 to just 4 terms, and the interaction between four gravitons can be reduced from 113 to 12 terms. Finally, we verify our simplification by comparing the results for physical processes using the standard approach and using our simplified approach.