Modern physics is based upon two great pillars: one of them is quantum mechanics, which describes the essential rules all physical entities should obey, while the other one is general relativity, which describes the stage in which everything takes place. Ironically, classical general relativity does not abide by the rules of quantum mechanics, which means our best understanding of reality is inconsistent. Some of these descriptions must be modified. The most popular bet is that general relativity must be modified to respect the rules of quantum mechanics (i.e., it needs to be quantized). The issue is that while it is possible to quantize gravity, the result is a theory that becomes problematic at high energies (precisely those at which the theory would be the most interesting). Most of my work revolves around these basic ideas, intending to understand better the interface between gravity and quantum mechanics.
Below you'll be able to find more details about the main topics I like to think about. Some of those have already been the subject of my work, some may be in the back of my head awaiting future projects. Click on the headings to keep reading each description.
General relativity is our best description of how gravity works on a fundamental level: spacetime is intrinsically curved, and “gravity” is how we perceive matter evolving on this curved spacetime. The curvature, on the other hand, is determined precisely by the matter present in spacetime. As summarized by John A. Wheeler, spacetime tells matter how to move, while matter tells spacetime how to curve. Not only is general relativity an experimental success, but it is also an extremely rich mathematical theory.
Understanding quantum gravity is difficult. However, a much easier problem is understanding how quantum fields behave in the presence of strong gravity. This led in the 1960s and 1970s to a framework known as quantum field theory in curved spacetime. In this framework, we make the simplifying assumption that gravity is approximately classical. This allows us to obtain a classical spacetime (often described by general relativity) upon which we can describe the behavior of quantum fields. While this is not a take on what gravity is fundamentally like, this framework has proven to be fruitful in understanding better the interplay between quantum mechanical systems and gravity, hence giving us hints about what full quantum gravity should look like.
Many of the traditional techniques used in quantum field theory in flat spacetime become problematic when working in curved spacetime. The absence of a general notion of time implies it is impossible to find a preferred vacuum state in spacetimes without a time translation symmetry, which makes both the canonical and the path integral approach troublesome to deal with. Instead, a sophisticated approach that can be used to formulate QFTCS is the algebraic approach, which deals directly with the algebraic structure of the theory’s observables.
In general relativity, any spacetime geometry is possible, as long as one has the necessary type and distribution of matter. However, this means that some geometries require exotic kinds of matter that do not exist in reality. To avoid this, one can impose some conditions on the energetic behavior of matter to force it to be physical. For example, one can require that energy is always positive and that all energy fluxes are causal. But which conditions do real matter, and in particular quantum matter, actually satisfy?
Quantum field theory in curved spacetime gave birth to an area nowadays known as black hole thermodynamics (BHT). Within BHT, black holes are understood as thermodynamical objects, with non-vanishing temperature and entropy, which are originated by quantum effects. In particular, the second law of thermodynamics must be patched to also consider the entropy contained in black holes, hence leading to the generalized second law: the sum of the entropies of black holes and of matter outside black holes can never decrease. When considering these ideas, we can learn that nature seems to bind the maximum amount of entropy that can fit in a certain spacetime region.
“Renormalization group” is a fancy name we give to understanding how theories change with scale. Theories in larger scales don’t need to be treated with all of the details found in smaller scales. For example, when describing the motion of the ocean, it is usually unnecessary to consider the molecular structure of water. The renormalization group helps us to do this “zoom-out” procedure within the framework of quantum field theories. “Functional renormalization group,” in turn, is the name given to some nonperturbative incarnations of the renormalization group. It then consists of a technique to obtain information about a theory that goes beyond the typical approximations done in physics.
While the ultraviolet behavior of quantum field theories was tamed by the renormalization program, the infrared structure was for a long time considered to be trivial and uninteresting. Nevertheless, it turns out this is not the case. One has very interesting behavior at the infrared limit.