In a hypothetical Grand Unified Theory, magnetic monopoles are a particle which would act as a charge carrier for the magnetic force. Evidence of magnetic monopoles has yet to be found and based off of their relatively high mass (4-10 TeV) will be difficult to find with current technology. The goal of my thesis is to mathematically model the magnetic monopole by finding numerical solutions to the equations of motion. In my analysis, I consider four cases: kinks, cosmic strings, global monopoles, and magnetic monopoles. I will also study electromagnetic gauge fields to prepare to include gauge fields in the magnetic monopole case. Numerical solutions are found for the cosmic string and global monopole cases. As expected, the energy is high at small distance r and drops off as r goes to infinity. Currently numerical solutions are being worked towards for electromagnetic gauge fields and the magnetic monopole case.
in particle physics, where it explains the origin of pion and hadron mass hierarchy
among other things.
Despite its microscopic origin chirality may also lead to observable effects
in macroscopic physical systems -- relativistic plasmas made of chiral
(spin-$\frac{1}{2}$) particles.
Such plasmas are called \textit{chiral}.
The effects include non-dissipative currents in external fields that could be present
even in quasi-equilibrium, such as the chiral magnetic (CME) and separation (CSE)
effects, as well as a number of inherently chiral collective modes
called the chiral magnetic (CMW) and vortical (CVW) waves.
Applications of chiral plasmas are truly interdisciplinary, ranging from
hot plasma filling the early Universe, to dense matter in neutron stars,
to electronic band structures in Dirac and Weyl semimetals, to quark-gluon plasma
produced in heavy-ion collisions.
The main focus of this dissertation is a search for traces of chiral physics
in the spectrum of collective modes in chiral plasmas.
I start from relativistic chiral kinetic theory and derive
first- and second-order chiral hydrodynamics.
Then I establish key features of an equilibrium state that describes many
physical chiral systems and use it to find the full spectrum of collective modes
in high-temperature and high-density cases.
Finally, I consider in detail the fate of the two inherently chiral waves, namely
the CMW and the CVW, and determine their detection prospects.
The main results of this dissertation are the formulation of a fully covariant
dissipative chiral hydrodynamics and the calculation of the spectrum of collective
modes in chiral plasmas.
It is found that the dissipative effects and dynamical electromagnetism play
an important role in most cases.
In particular, it is found that both the CMW and the CVW are heavily damped by the usual
Ohmic dissipation in charged plasmas and the diffusion effects in neutral plasmas.
These findings prompt a search for new physical observables in heavy-ion collisions,
as well as a revision of potential applications of chiral theories in
cosmology and solid-state physics.