David Tong: Research
Quantum Field Theory
Quantum field theory is the language in which all of modern physics is formulated. It represents the marriage of quantum mechanics with special relativity and provides the mathematical framework in which to describe the creation and destruction of hoards of particles as they pop in and out of their ethereal existence and interact. Whether you want to understand the collisions of protons in the next high-energy collider, how teams of electrons co-operate inside solids, or how black holes evaporate, you need to work with quantum field theory. Moreover, it has also proven to be a remarkably subtle and rich subject for mathematicians, providing insights into many new areas of mathematics.
String theory is an ambitious project. It purports to be an all-encompassing
theory of the universe, unifying the forces of nature, including
gravity, in a single quantum mechanical framework. The theory
involves many elegant mathematical ideas, woven together to
form a rich and beautiful tapestry of unprecedented sophistication.
It is also quite hard.
While string theory is often paraded as the ultimate theory of everything, a less trumpeted facet is the way in which the theory reveals insights and connections between other, seemingly unrelated, aspects of physics. Much of the today's research in string theory is aimed at understanding more down-to-earth physical systems and is often concerned with unraveling the surviving mysteries of quantum field theory.
Mathematically, solitons are solutions to tricky non-linear equations. Physically, solitons are new objects that appear in a system due to the cooperative behaviour of the underlying constituents. A familiar example is the vortex that forms everytime you flush the toilet or pull the plug in the sink. The vortex appears as an empty region around which the water molecules swirl. In a zen-like manouevre, physicists consider the absence of water in the vortex as a new object in its own right and study its properties. More exotic examples of solitons which are conjectured to exist somewhere in the universe include cosmic strings stretched across the sky, and magnetic monopoles.
Cosmology is the study of the universe as a whole and attempts to answer the very biggest questions: How old is the universe? What happened when the universe was a baby? Where did the structure of galaxies evolve from? Why is the universe expanding? How is it expanding? And why the hell is the expansion speeding up? In recent years, new experiments have turned cosmology into a precise science and left us with many important open questions which starkly reveal our ignorance about the universe.