Back in 2015, I did a poll asking how much physics background you guys had. Now four years and many new readers later, I’d like to revisit the question. I’ll explain the categories below the poll:
Amplitudeologist: You have published a paper about scattering amplitudes in quantum field theories, or expect to publish one within the next year or so.
Physics (or related field) PhD: You have a PhD in physics, or in a field with related background such as astronomy or some parts of mathematics.
Physics (or related field) Grad Student: You are a graduate student in physics or a related field. Specifically, you are either a PhD student, or a Master’s student in a research-focused program.
Undergrad or Lower: You are currently an undergraduate student (studying for a Bachelor’s degree) or are in an earlier stage of education (for example a high school student).
Physics Autodidact: Included by popular demand from the last poll: while you don’t have a physics PhD, you have taught yourself about the subject extensively beyond your formal schooling.
Other Academic: You work in Academia, but not in physics or a closely related field.
Other Technical Profession: You work in a technical profession, such as engineering, medicine, or STEM teaching.
None of the Above: Something else.
If you fit more than one category, pick the first that matches you: for example, if you are an undergrad with a published paper in Amplitudes, list yourself as an Amplitudeologist (also, well done!)
The title is a bit of a mouthful, but I’ll walk you through it:
The Cosmic Galois Group and Extended Steinmann Relations for Planar N = 4 SYM Amplitudes
I calculate scattering amplitudes (roughly, probabilities that elementary particles bounce off each other) in a (not realistic, and not meant to be) theory called planar N=4 super-Yang-Mills (SYM for short). I can’t summarize everything we’ve been doing here, but if you read the blog posts I linked above and some of the Handy Handbooks linked at the top of the page you’ll hopefully get a clearer picture.
We started using the Steinmann Relationsa few years ago. Discovered in the 60’s, the Steinmann relations restrict the kind of equations we can use to describe particle physics. Essentially, they mean that particles can’t travel two ways at once. In this paper, we extend the Steinmann relations beyond Steinmann’s original idea. We don’t yet know if we can prove this extension works, but it seems to be true for the amplitudes we’re calculating. While we’ve presented this in talks before, this is the first time we’ve published it, and it’s one of the big results of this paper.
The other, more exotic-sounding result, has to do with something called the Cosmic Galois Group.
Évariste Galois, the famously duel-prone mathematician, figured out relations between algebraic numbers (that is, numbers you can get out of algebraic equations) in terms of a mathematical structure called a group. Today, mathematicians are interested not just in algebraic numbers, but in relations between transcendental numbers as well, specifically a kind of transcendental number called a period. These numbers show up a lot in physics, so mathematicians have been thinking about a Galois group for transcendental numbers that show up in physics, a so-called Cosmic Galois Group.
(Cosmic here doesn’t mean it has to do with cosmology. As far as I can tell, mathematicians just thought it sounded cool and physics-y. They also started out with rather ambitious ideas about it, if you want a laugh check out the last few paragraphs of this talk by Cartier.)
For us, Cosmic Galois Theory lets us study the unusual numbers that show up in our calculations. Doing this, we’ve noticed that certain numbers simply don’t show up. For example, the Riemann zeta function shows up often in our results, evaluated at many different numbers…but never evaluated at the number three. Nor does any number related to that one through the Cosmic Galois Group show up. It’s as if the theory only likes some numbers, and not others.
For us, this has been enormously useful. We calculate our amplitudes by guesswork, starting with the right “alphabet” and then filling in different combinations, as if we’re trying all possible answers to a word jumble. Cosmic Galois Theory and Extended Steinmann have enabled us to narrow down our guess dramatically, making it much easier and faster to get to the right answer.
More generally though, we hope to contribute to mathematicians’ investigations of Cosmic Galois Theory. Our examples are more complicated than the simple theories where they currently prove things, and contain more data than the more limited results from electrons. Hopefully together we can figure out why certain numbers show up and others don’t, and find interesting mathematical principles behind the theories that govern fundamental physics.
For now, I’ll leave you with a preview of a talk I’m giving in a couple weeks’ time:
There’s a cynical truism we use to reassure grad students. A thesis is a big, daunting project, but it shouldn’t be too stressful: in the end, nobody else is going to read it.
Like every good truism, though, there is an exception. Some rare times, you will actually want to read someone else’s thesis. This isn’t usually because the material is new: rather it’s because it’s well explained.
When we academics publish, we’re often in a hurry, and there isn’t time to write well. When we publish more slowly, often we have more collaborators, so the paper is a set of compromises written by committee. Either way, we rarely make a concept totally crystal-clear.
A thesis isn’t always crystal-clear either, but it can be. It’s written by just one person, and that person is learning. A grad student who just learned a topic can be in the best position to teach it: they know exactly what confused them when they start out. Thesis-writing is also a slower process, one that gives more time to hammer at a text until it’s right. Finally, a thesis is written for a committee, and that committee usually contains people from different fields. A thesis needs to be an accessible introduction, in a way that a published paper doesn’t.
There are topics that I never really understood until I looked up the thesis of the grad student who helped discover it. There are tricks that never made it to published papers, that I’ve learned because they were tucked in to the thesis of someone who went on to do great things.
So if you’re finding a subject confusing, if you’ve read all the papers and none of them make any sense, look for the grad students. Sometimes the best explanation of a tricky topic isn’t in the published literature, it’s hidden away in someone’s thesis.
Growing up in the US there are a lot of age-based milestones. You can drive at 16, vote at 18, and drink at 21. Once you’re in academia though, your actual age becomes much less relevant. Instead, academics are judged based on academic age, the time since you got your PhD.
More generally, when academics apply for jobs they are often weighed in terms of academic age. Compared to others, how long have you spent as a postdoc since your PhD? How many papers have you published since then, and how well cited were they? The longer you spend without finding a permanent position, the more likely employers are to wonder why, and the reasons they assume are rarely positive.
This creates some weird incentives. If you have a choice, it’s often better to graduate late than to graduate early. Employers don’t check how long you took to get your PhD, but they do pay attention to how many papers you published. If it’s an option, staying in school to finish one more project can actually be good for your career.
Biological age matters, but mostly for biological reasons: for example, if you plan to have children. Raising a family is harder if you have to move every few years, so those who find permanent positions by then have an easier time of it. That said, as academics have to take more temporary positions before settling down fewer people have this advantage.
Beyond that, biological age only matters again at the end of your career, especially if you work somewhere with a mandatory retirement age. Even then, retirement for academics doesn’t mean the same thing as for normal people: retired professors often have emeritus status, meaning that while technically retired they keep a role at the university, maintaining an office and often still doing some teaching or research.
4 gravitons 