Delving into the Phenomenology of Very Special Relativity: From Subatomic Particles to Binary Stars

TL;DR

This thesis explores the phenomenology of Very Special Relativity (VSR), examining its theoretical foundations, modifications to fundamental equations, and experimental bounds, including implications for neutrino masses, particle spectra, and gravitational phenomena.

Contribution

It develops a Hamiltonian formalism for VSR, extends it to non-relativistic limits, and constructs a gauge-invariant graviton mass model within VSR, connecting theory with experimental constraints.

Findings

Set upper bounds on VSR parameters from various physical systems.

Developed a Hamiltonian formalism addressing VSR non-localities.

Constructed a VSR field theory for spin-2 fields with a gauge-invariant graviton mass.

Abstract

In this thesis, we investigate the implications of Lorentz-violating (LV) theories, focusing on Very Special Relativity (VSR) and its phenomenological consequences. Initially presented as an alternative mechanism for neutrino masses, VSR has since become a significant part of the general LV framework, distinguished by its unique group structure and non-local operators. After a comprehensive introduction to the principles of LV and VSR, we present the corresponding modifications to the Dirac equation. A significant part of the thesis is dedicated to the development of a Hamiltonian formalism within the VSR context, addressing its inherent non-localities. This approach is further extended to the non-relativistic limit, connecting it to the conventional Schr\"odinger picture. We then set upper bounds on the VSR parameters by examining its corrections to a wide range of physical systems and scenarios, such as Landau levels of charged particles, the $\mathsf g-$factor of electrons, the energy spectrum of ultracold neutrons in Earth's gravitational field, and the gravitational emission from binary stars. The latter analysis led us to the construction of a VSR field theory for spin-2 fields in flat space, which was surprisingly found to accommodate a gauge-invariant graviton mass. Through this comprehensive study, we bridged theoretical predictions with experimental data, paving the way for future explorations in Lorentz-violating theories and highlighting their potential to address unresolved questions in modern physics.