My Research Interests

I am a mathematical physicist. I am interested in the theoretical aspects of virtually any branch of physics, but my publications so far broadly falls into high energy physics and cosmology. If you are a fellow researcher and would like to collaborate, please feel free to contact me directly: I am eager to start new projects and am willing to expand into other fields.

In comparison, I am a little bit more conservative about the topics of the project if I will be working with a student (be it a bachelor’s, a master’s, or a PhD); indeed, I would prefer to have a project with a student (as their mentor or thesis advisor or collaborator) only if we are going to study on a topic that I’m already sufficiently proficient at. In this page, I will be detailing these areas and will be providing various sources.

The common theme of my work thus far is the usage of quantum field theory in various areas, please check out my previous papers here. To understand them in a broader setting, you may want to check out this snowmass report: it is a long paper, so do not bother reading it. You may just check out the table of contents to get an idea of what kind of phenomenological, computational, or formal work there currently are in the literature. To investiate the literature further, you may find the websites mentioned here useful.

A project that I would conduct with a student will be an application of the field theory: it could be in holography, cosmology, condensed matter, or simply high energy physics; nevertheless, the student will need to learn field theory to a degree. Let me expand on this:

1.

I do not expect the student (even a PhD candidate) to know field theory. They will learn the necessary amount during the project.

2.

I expect the student (even an undergraduate one) to know special relativity and the relevant math (four vectors, Lorentz metric, tensor contractions, etc.).

3.

I expect the student (even an undergraduate one) to know basic particle physics (what a boson means, what the spin of an electron is, how many polarizations a gluon has, etc.).

4.

I expect the student (even an undergraduate one) to know basics of Mathematica. For instance, they should be able to compute the following convergent integral of the Bessel functions

$$\underset{0}{\overset{\infty }{\int \; <!--\; nolimits\; -->}}{z}^{9∕2}{K}_{\frac{3}{2}}(\mathit{az})K_{\frac{3}{2}}(\mathit{bz})K_{\frac{3}{2}}(\mathit{cz})\mathit{dz}$$

or the seemingly-divergent similar integral

$$\underset{0}{\overset{\infty }{\int \; <!--\; nolimits\; -->}}{z}^4{K}_{\frac{3}{2}}(\mathit{az})K_{\frac{3}{2}}(\mathit{bz})K_{\frac{3}{2}}(\mathit{cz})\mathit{dz}$$

using Mathematica. Note that computing the latter would require a regularization. Likewise, the student should be sufficiently proficient at Mathematica to understand what the following code achieves and how and why each component works towards that end:

Module[{differentialEquation, solution, formatNicer, nMax, style}, 
 
differentialEquation[n_] := Sum[a[i] D[f[x], {x, i}], {i, 0, n}] == g[x]; (*Most general order-n linear-ordinary-differential-equation with constant coefficients*) 
 
solution[n_] := Equal["f[x]", f[x]] /. DSolve[differentialEquation[n], f[x], x][[1]]; (*the solution, c will denote undetermined coefficients in the solution*) 
 
formatNicer = # /. {a[i_] :> Subscript[a, i], K[a_] :> Subscript[k, a], Root[_, i_] :> Subscript[r, i]} & ;(*Let r denote the roots of the characteristic polynomial*) 
 
nMax = 5; (*List the solutions up to order-5*) 
 
style = Style[#, Bold, Blue] &; (*For formatting the title*) 
 
RightComposition[formatNicer, Join[{{"Order" // style, "Differential Equation" // style, "Solution" // style}}, #] &, Grid[#, Frame -> All] &][Table[{n, differentialEquation[n], solution[n]}, {n, nMax}]] 
]

Remark: I am not getting paid by Wolfram for advocating their products. It is just that the fields I am specialized in make great use of computer aided computations and this is actually true for most of the formal physics. Indeed, if you would like to, say, expand in the eigenfunctions of a quadratic casimir and then do a harmonic analysis with that, you need to do symbolic computations involving highly specialized functions (Gegenbauer, Bessel, Hypergeometric ${}_2{F}_1$, etc.): Mathematica is the most convenient tool for this.

Is Mathematica the only tool for such computations? No; for instance, Maple is also capable of handling symbolic computations with specialized mathematical functions, and there may be other software that I am unbeknownst to! However, I will insist on Mathematica because (a) I am quite familiar with it, (b) it is the default software used in the field both in US and Europe (so your knowledge of it will be to your advantage in your future collaborations), (c) Wolfram engine is free to use for non-commercial purposes.