John Joseph M. Carrasco

Current Research:

Experimentalists have the best way to shape and test the consistency and usefulness of their ideas: controlled observation. For theorists, calculation is key to building accurate intuition. Experimentally we can probe the smaller scales of our universe by smashing particles together with greater gusto. With a theory, we describe (and predict) the outcome of such experiments by calculating scattering amplitudes. Some scales are very difficult to reach experimentally, e.g. the scales at which high-energy gravitational waves would scatter in a particle-like manner. Having theoretical descriptions, which admit calculation, of gauge and gravity bosonic scattering, is one of the few ways we can probe the consistency of some of our most fundamental ideas.

In quantum field theory, we describe classical scattering amplitudes using tree graphs: graphs without loops (cycles). We associate increasingly quantum effects (scaling as increasing powers of Plank's constant) with graphs containing larger numbers of loops. Physicists find multi-loop calculations in gauge and gravity theories notoriously difficult when applying traditional methods. This is not, however, because the integrals associated with the graphs are tricky to evaluate (which they are). Rather the difficulty arises because of an inherent combinatorial explosion in distinct graph topologies crossed with the sheer size of the analytic expressions associated with each graph. The fact that many of these graphs fail to contribute, and that many of these expressions can be simplified to compact forms, suggests deep structure. Due to technical difficulties, until very recently, multi-loop calculations of gauge and gravity quantum field theories have proven very elusive.

Along with fantastic collaborators (Zvi Bern, Lance Dixon, Darren Forde, Harold Ita, Henrik Johansson, David Kosower, and Radu Roiban), I have developed efficient and powerful techniques for writing down higher-loop amplitudes in (relatively) compact representations, based upon the modern generalized unitarity method. I should note that while I have mostly focused on higher-loop four-particle interactions, these techniques apply to lower-loop n-particle interactions, such as those needed to reduce the theoretical uncertainty obscuring upcoming LHC analysis. By applying and generalizing these techniques to gauge and gravity theories we find deep and, at times, unexpected structures, most easily seen in the most symmetric generalizations of these theories.

One of the most surprising and important results we found stood in stark contrast to popular wisdom at the time; quantum field theory may admit perturbatively consistent and probability-conserving quantum descriptions of gravity in four dimensions. Previously physicists believed in the irreconcilability of (point-like) quantum field theory and Einstein's general theory of relativity, even under the protection of maximal supersymmetry. Calculating amplitudes where consensus predicted divergence, and discovering, instead, surprisingly good behavior in the ultraviolet, suggests that these assertions of incompatibility may be overly pessimistic. Rather, we find evidence of cancellations that propagate to all loop orders as can be seen using the unitarity method. We still have no proof of perturbative finiteness, and it is quite possible that an all-order proof will require very different (perhaps even non-perturbative) methods. Even so, through explicit calculation we have exposed a mystery that almost nobody suspected, suggesting that point-like quantum field theory may present a more powerful theoretical framework than has been fashionable to suspect(*) for quite some time.

(*) Despite the fact that quantum field theory has undoubtedly been the most experimentally successful framework found so far.

Open data:

Old TA lecture notes, handouts, and solutions:

Physics 108 (Optics), Spring 07

Physics 114 (Fluids), Winter 07

Physics 110b, Spring 06

Physics 110a, Winter 06