Topics in quantum field theory: on-shell methods and vacuum polarization near a boundary

Abstract

In this dissertation, we discuss current topics related to the quantum description of fields, a fundamental tool in the description of elementary particles and fundamental interactions. We will discuss the traditional methods for calculation of matrix elements and scattering amplitudes, and the newer on-shell paradigm, specifically, the Britto-Cachazo- Feng-Witten (BCFW) recursion and the discontinuity cuts featured in the generalized unitarity method. We will then, apply these tools in the calculation of QED processes, and in the context of the Einstein-Hilbert theory, showing how on-shell methods can be economic and efficient. We also discuss nontrivial phenomena which can occur when the presence of nontrivial boundary conditions induces classes of boundary dependent vacuum fluctuations.