Publications, Casually

I wrote a very linear narrative sort of course notes for an introductory course on Einstein's gravity, General Relativity. It assumes you know some classical mechanics, linear algebra, calculus, and a touch of special relativity, then takes you in a logically continuous path to the construction of General Relativity, through to its big-pillar applications (gravitational waves, black holes, and cosmology).

In deriving the mathematical solution for the simplest black holes, every calculation uses one or another approximation that makes interpreting the "mass" of the black hole somewhat dubious. I found a way to do it that's a little more logically consistent, tucking the approximation away into a more systematic parameterization of ignorance (for the technical folks: regularizing the geometry near the singularity) which leaves the interpretation of the mass much more clear. Unfortunately, gravity journals are very purely mathematical and don't like my physicist way of doing things, so I have to re-phrase some things and find a more physics-y journal to submit to. Which I won't get around to for a long time.

All of the galaxies and galaxy clusters out there in the universe came together over time because gravity little random dimples in an otherwise smooth universe attracted the material nearby and over time they just grew and grew. One way those dimples might have arisen is if there had been some light primordial quantum field that in a sense got synced up with the expanding universe (parametrically resonated) then solidified that pattern with a pinch of gravity before it decayed away, leaving a kind of gravitational imprint on the universe. This paper is about simulating that process start to finish whereas the "syncing" and "solidifying" stages are usually thought about quite separately.

The legacy of my work as an undergraduate research assistant continues as analysis code I wrote about a decade prior still makes an impact. I explain more in the first paper from this below, look for the paper with "GEM" in the title.

The long version: this is a behemoth paper mostly by my esteemed colleague Dr. Zalavári about incorporating the effects of a quantumly-spinning nucleus in our framework for parameterizing the ways nuclear properties enter into interactions with electrons (see the first Point-Particle Effective Field Theory paper below). I cannot stress enough how unreasonably hard it was to incorporate that quantum spin into the works, Nature was not kind about this.

The short version: this is a short summary of the next paper because no one in the community was going to sit through those 143 pages.

Using our framework for parameterizing nuclear effects on their lighter companions, I applied it situations where the interaction might catalyze a change to the nucleus itself (maybe excite it, or cause some kind of decay). Nifty little paper and was fun accidentally re-deriving a result by Bethe from 1935 (https://dx.doi.org/10.1103/PhysRev.47.747).

Applying our nuclear parameterization framework to the spinless Helium atom (applying it to a spinning atom like hydrogen is a preposterous task—see above).

Deriving our nuclear parameterization framework for effects felt by spinning things. Bit of a pain (though not nearly as much as for effects caused by spinning things) but turns out to be kind of neat. For theoretical physicist nerds anyway.

Deriving our nuclear parameterization framework for effects felt by spinless but fast/energetic things. No real surprises with this one, but a necessary step to bigger things.

A legacy of my time as an undergraduate research associate. This paper used software I wrote as an undergraduate student at Carleton. I helped develop software to analyze the output of a type of particle detector called a Time Projection Chamber. This kind of detector is a big tube of gas that is easily excited. The idea is that energetic (electrically charged) particles like electrons fly through the chamber and leave a trail of electrons as they knock them out of the gas molecules. Then strong electric fields carefully drag that trail to the end of the tube where we have little readout pads waiting to take a metaphorical picture. Our project was about developing better readout pads, and my software's job was to reconstruct the path of the passing particle from the readout data.

Sometimes in life a fun happy-go-lucky character is weighed down by a great lummox, and though their stories beg to be told in very different ways, one or the other must come out on top. I speak of course of atoms (though analogous systems are more prevalent than you think, as for example in solar systems and galaxies). In the case of atomic systems, a really accurate description of the electrons requires a more complex and sophisticated "quantum field theory" approach, while in principle the nucleus shouldn't need such theoretical baggage until you start doing unorthodox things with it. Nevertheless, since they're together the traditional approach to treating the electrons properly was to overdo the math on the nucleus, so here we worked up a scheme where we could still treat the nucleus in a simple ("first-quantized") way while systematically incorporating its effects on the complicated treatment of the electrons. For most cases this amounts to just re-packaging what's already known about atoms, but the generality of the framework meant it could also make it cleaner to talk about things like electrons falling onto a conducting wire, particles falling into a black hole, and even particles inducing others to decay.

In the very very early universe, there is thought to have been a period of exponential expansion called Inflation, driven by some quantum field. In order to have this expansion last long enough to make a mark, the quantum field driving it has to "move slowly" in a kind of abstract mathematical sense. Well normally anyway—in this paper we found a sneaky way to construct a model where it's actually a set of two or more quantum fields inflating the universe, and they can actually move quite quickly but in a way that sort of "cancels" each other out so the universe doesn't notice.

In the very very early universe, there is thought to have been a period of exponential expansion called Inflation, driven by some quantum field. Now imagine that the universe actually has two extra dimensions to space (so a total of 6 dimensions including time). The question is: is it possible that all the dimensions could have started off expanding during Inflation, but the extra dimensions settled down early so they aren't noticeable today? The answer is "kinda!" Theoretically, you can tune things just so so it happens naturally, but it's rather contrived.