Honors Theses and Capstones

Date of Award

Spring 2022

Project Type

Senior Honors Thesis

College or School

CEPS

Department

Physics and Astronomy

Program or Major

Physics

Degree Name

Bachelor of Science

First Advisor

David Mattingly

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.

Comments

Future work on the subject includes quantization of what is currently a classical field theory as well as understanding how the quasiparticles may be produced in the laboratory or by natural processes.

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