The classical Derrick relation only sees the global picture — it can't distinguish a monopole's dense core from its diffuse magnetic tail. By introducing a tunable parameter \(\alpha\), we can "focus" on different layers: the topological core where field gradients are steepest, or the asymptotic region where the configuration melts into the vacuum.

This reveals how different stabilization mechanisms dominate at different scales. In Skyrmions, the Skyrme term fights collapse in the core while the sigma-model term shapes the outer profile. In the electroweak sphaleron, the Higgs mass sets a length scale that breaks the conformal symmetry of pure Yang-Mills.

I worked with Prof. Manuel Torres Labansat studying the properties of topological solitons in potentials that have many local minima trapped between two global minima.

I simulated the collision between multikinks of a modulated double sine-Gordon potential we proposed. The generalization to higher-dimensional topological solitons arising in gauge theories is a potential research topic. Presented at the AMC National Physics Congress.

Due to the particle-like properties of solitons, it's natural to ask whether they have a corresponding one-particle state in the quantum theory.

Given the non-analytic behavior of the potential, solving for the normal modes was highly non-trivial. With a suitable transformation the eigenvalue equation can be cast as a Pöschl–Teller Schrödinger equation. The force between interacting kinks was calculated using asymptotic analysis.

Published in J. Phys. Commun. (2021).

We examine in detail three effects which can provide alternative explanations:

(1) A "top heavy" initial mass function (IMF) — high mass stars produce far more light than low mass stars

(2) A variety of star formation histories — constant, exponentially decreasing, and peaked star formation rates

(3) A variety of initial metallicities

Modeled spectral energy distributions using the Pégase population synthesis code.

The technique involves measuring the azimuthal angle difference between a high-\(p_T\) trigger particle and a lower-\(p_T\) associate particle.

If the trigger momentum is high enough, it serves as a proxy for the jet axis. The angle difference \(\Delta\phi\) provides information about the production region: small \(\Delta\phi\) corresponds to production in the jet, while \(\Delta\phi \approx \pi\) corresponds to the recoil jet where production could be modified by medium-jet interactions.

Analysis uses the ALICE \(O^2\) framework.

In field theory, it's impossible for a system at a false vacuum to decay to a true vacuum by standard means — an infinite amount of energy would be necessary. However, Coleman theorized that tunneling occurs through nucleation of bubbles that expand at near-\(c\) speed.

Coleman's formalism involves finding solutions to the non-linear field equations in Euclidean space — special non-topological solitons called bounces.

While working on a generalized \(\phi^4\) model, we found a general set of virial relations that reproduce well-known results and lead to new relations still being studied.

This was my first research project. Motivated by foundational questions about photon position operators and wave functions.

Constructed the photon wave function, found its wave equation, constructed Hamiltonian and spin operators. Used representation group theory to examine transformation properties of the wave function and verified expected symmetries.