Honors Theses and Capstones

Date Completed

Spring 2022

Abstract

This report represents the creation of a field theory which is capable of describing quasiparticle excitations that preserve 2^k -pole moments. These quasiparticles exhibit certain ’semidynamic’ properties such as individual particle immobility but free movement of bound 2^L-tuples. We provide a review of work done on dipole conserving fractons and their dynamics [1] and expand upon it to describe higher moment conserving systems with global quadratic (and higher) phase symmetry. This requires the selection of the temporal and spatial directions. The selection of a temporal direction is done with a foliation defined by an anisotropic scaling of space and time, defining a hypersurface of constant time, the vector tangent to this hypersurface, u^µ, is our temporal direction. The selection of a spatial direction is done by introducing a ghost field, S, characterized by a wrong sign kinematic term. The gradient of this ghost field, s^µ, is our spatial direction. Dynamically selecting these directions and defining a Lagrangian which conserves a particular multipole moment creates a generally covariant theory of multipole conserving quasiparticles.

First Advisor

David Mattingly

College or School

CEPS

Department or Program

Physics

Degree Name

Bachelor of Science

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