theoretical physicist

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Research Interests

Here you can find a bit more about my research interests. This includes both themes I’ve actually worked on or have been working on and some themes that draw my attention.

Quantum Field Theory in Curved Spacetime

One of the biggest open problems in physics is the quest to obtain a quantum theory of gravity. Since the 1930’s it was known that general relativity—our best description of spacetime—and quantum mechanics—our best description of what the Universe’s fundamental laws should look like—seem to have weird behaviors when considered together. Since then, physicists have been working to figure out how to fit gravity and quantum phenomena together in the same picture and at all energies.

In the late 1960s and early 1970s, a particularly interesting line of research was born: the idea of considering a classical gravitational field alongside quantum mechanical fields. In this approach, known as quantum field theory in curved spacetime (QFTCS), one might still not be able to unravel all of the secrets behind full quantum gravity, but it is possible to obtain a better understanding of how gravity and quantum phenomena interact. For example, this approach has taught us that black holes can evaporate, particles can be created by strong fields, and much more.

Much of my interest in QFTCS lies mainly in foundational aspects. I believe an important task to be pursued is to understand what a quantum field theory is, especially on a nonperturbative level. I believe investigating our current understanding of the world on a deeper mathematical level might help us understand what lies beneath it.

Algebraic Quantum Field Theory

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.

My main interest in this quite mathematical approach consists in trying to understand what a quantum field theory is, especially in nonperturbative settings. Furthermore, I consider it a powerful set of techniques to understand QFTCS.

Entropy Bounds and Holography in General Spacetimes

The techniques of QFTCS 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 being due to 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.

The entropy of a black hole is proportional to its area. Thus, when an object is dropped into a black hole, its area must increase by an amount equal to or larger than the total entropy of the object. These sorts of considerations lead to the so-called entropy bounds, which bind the amount of entropy a given object can contain. Hence, they bound the amount of information that can be stored in a region of spacetime, typically by the area surrounding it. This leads to the notion that information must be somehow stored in spacetime surfaces and to the clue that this principle should be trivially implemented in a full quantum gravity theory.

My main interest in these topics is to peek at full quantum gravity from low energy considerations and further understand the structure of matter itself by using ideas from gravitational physics. I am also interested in the infrared physics that can be studied at the boundaries of spacetime.

Infrared Structure of Field Theories

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. The three paradigmatic examples of interesting infrared phenomena are the following.

Firstly one has the so-called Bondi—Van der Burg—Metzner—Sachs (BMS) group, which is the symmetry group at null infinity of asymptotically flat spacetimes. In principle, one would expect this group to be simply the Poincaré group (and hence the symmetries at infinity are just the symmetries of Minkowski spacetime), but actually one gets an infinite-dimensional lie group comprised of the Poincaré transformations and of the so-called supertranslations, which are direction-dependent translations. This means general relativity does not reduce to special relativity at very large distances, but rather to something much more complicated.

Secondly one has Weinberg’s soft graviton theorem. A soft particle is a particle with very small energy, small enough to not be measured by the detectors under consideration. Weinberg’s soft graviton theorem relates a scattering amplitude to the amplitude for the same scattering with the addition of a number of soft gravitons. This turns out to be a consequence of the BMS symmetries at null infinity.

Thirdly, one has the memory effect. This is the prediction that two nearby inertial detectors will be permanently displaced by the passage of a gravitational wave. The computations involved in the prediction of this effect can be matched to the soft graviton theorem, and the effect can be understood as a physical realization of a BMS translation.

My interest in these topics focuses on them per se, since I consider them to be interesting physics in their own, but also in their role understanding holographic structures in asymptotically flat spacetimes.

Energy Conditions

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 typically imposes some conditions on the energetic behavior of matter to force it to be physical.

Unfortunately, quantum effects violate all of the classical energy conditions imposed on classical matter. However, some ideas reminisce. Recently, particular attention has been devoted to the so-called averaged null energy condition (ANEC) and quantum null energy condition (QNEC), which are quantized versions of one particular energy condition. These conditions are believed to hold in quantum field theory and, hence, they specify what sorts of matter are physical within the realm of quantum mechanics.

My interest in these topics is mainly concerned with using these conditions to generalize results from classical general relativity and further understand the interplay between matter and gravitational physics.

Functional Renormalization Group

“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” 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.

My main interest in the FRG is concerned with its applications to QFTCS problems, although I am also curious about its applications to quantum gravity through the asymptotic safety program.