Scattering Amplitudes
Scattering amplitudes are the fundamental ingredients of quantum field theory. They constitute what is called the on-shell data at asymptotic past and future. In elementary classical physics, we deal with particle collisions all the time. The outcome of say a two particle collision is fixed and is dependent whether the collision is elastic or inelastic. In other words, we can have deterministic outcomes for the process of n-particle scattering in classical physics. In quantum physics and in quantum field theory more precisely, the outcomes of collisions of a bunch of particles is probabilistic in nature. Let us consider the process of electron-positron scattering. These particles can come from past infinity, scatter off each other and can either produce other particles in the process (like photons) or retain their identity and fly off to future infinity. Quantum field theory provides us the rule to determine the probability amplitude for any such outcome. This is what we call as the scattering amplitude.
To compute this object in the conventional way, one considers the set of all possible Feynman diagrams with external propagators amputated, external legs put on-shell and finally these legs are projected to polarization states. In recent years, and in particular over the last two decades, there has been tremendous development in the field of scattering amplitudes. On one hand, new techniques such as recursion relations and on-shell methods are implemented to simplify computations in Yang-Mills and gravity. While on the other, conceptual developments are made in both these theories and their supersymmetric counterparts have outlined the detailed computations of multi-photon/gluon/graviton scattering amplitudes. A corollary of these developments indicate that the UV behaviour of gravity is in some sense, better than Yang-Mills.
My prime interest in this field is related to computing amplitudes of interest in various non-supersymmetric theories using the BCJ double copy and understand the colour-kinematics duality in Yang-Mills theory.
Perturbative Quantum Gravity
Consider the gravitational scattering of two electrons. Since gravity is classical, we can in principle able to determine the position and the momentum of the outgoing electrons simultaneously. However, the electron is a quantum particle. According to the uncertainty principle, we cannot measure the momentum and the position at the same instant of time, to an arbitrary precision! This contradiction leads us to the program of quantum gravity. Quantum gravity is an attempt to unify the principles of quantum mechanics with that of general relativity, so that when the length scales are very small and gravity is very strong, one can consistently describe the situation with it. However, the first of these attempts, namely the quantum field theory of gravity (perturbative quantum gravity) failed. It suffered from the famous problem of "non-renormalizability". In layman terms, this means that when we add quantum corrections to a gravitational phenomena, it leads to infinities which cannot be absorbed into un-physical quantities. Anything infinite is not a sensible result in physics because it leads to other issues like loss of unitarity and predictability.
Several approaches emerged since then, in the likes of string theory, loop quantum gravity, causal sets, etc. However, each of these attempts are not complete and they lack several ingredients to consistently quantize gravity. In the recent decade, there has been a resurgence of ideas in scattering amplitudes and its connection to perturbative quantum gravity. The seminal works of Bern and company shed some light on the path of understanding the nature of these ill-tamed infinities.
My main interest is to deepen the understanding of the puzzle of perturbative quantum gravity using the tools of scattering amplitudes. I am pursuing this exercise voraciously with my PhD advisor and collaborator Prof. Kirill Krasnov.