The thesis consists of nine chapters and two appendices. In chapter II I discuss the connection given by the transfer matrix formulation between a classical statistical mechanical system and an associated quantum Hamiltonian, using as an example the familiar two- 4 dimensional Ising model. Next, in chapter III, I show how this applies to Baxter's 8-vertex model and the XYZ Hamiltonian, and how an infinite set of conserved charges for the XYZ model arises from properties of the transfer matrix. In Chapter IV I discuss the meaning of self-duality as it applies to quantum Hamiltonians, and develop a general form for a self-dual Hamiltonian. In Chapter V I show how one can find the explicit form for conserved charges in the XY model by a heuristic technique which takes advantage of the models' self-duality. In chapter VI it is shown how the solution to the XYZ model by the quantum inverse scattering method leads to the infinite set of conserved charges associated with it. The thesis culminates in the statement and proof of the theorem mentioned above, which stipulates a condition under which self-dual theories possess an infinite set of conserved charges (Chapter VII), after which I briefly discuss applications of the theorem (VIII) and draw some conclusions (IX).
","abstract_html":"<p>The thesis consists of nine chapters and two appendices. In chapter II I discuss the connection given by the transfer matrix formulation between a classical statistical mechanical system and an associated quantum Hamiltonian, using as an example the familiar two- 4 dimensional Ising model. Next, in chapter III, I show how this applies to Baxter's 8-vertex model and the XYZ Hamiltonian, and how an infinite set of conserved charges for the XYZ model arises from properties of the transfer matrix. In Chapter IV I discuss the meaning of self-duality as it applies to quantum Hamiltonians, and develop a general form for a self-dual Hamiltonian. In Chapter V I show how one can find the explicit form for conserved charges in the XY model by a heuristic technique which takes advantage of the models' self-duality. In chapter VI it is shown how the solution to the XYZ model by the quantum inverse scattering method leads to the infinite set of conserved charges associated with it. The thesis culminates in the statement and proof of the theorem mentioned above, which stipulates a condition under which self-dual theories possess an infinite set of conserved charges (Chapter VII), after which I briefly discuss applications of the theorem (VIII) and draw some conclusions (IX).</p>","abstract_has_math":false,"creators":["Grady, Michael Patrick"],"institution":null,"degree_name":"Doctor of Philosophy (PhD)","degree_level":"Thesis","degree_discipline":null,"degree_department":null,"school":null,"contributors":["Louise Dolan"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":1982,"date_issued":"1982-01-01T08:00:00Z","date_published":"1982-01-01T08:00:00Z","updated_at":"2026-07-24T04:10:47Z","subjects":["transfer matrix","quantum Hamiltonian","self-duality","conserved charges","XYZ model","8-vertex model","Life Sciences"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://digitalcommons.rockefeller.edu/student_theses_and_dissertations/455","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Louise Dolan"]},{"key":"dc:creator","label":"Author","values":["Grady, Michael Patrick"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctor of Philosophy (PhD)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["transfer matrix","quantum Hamiltonian","self-duality","conserved charges","XYZ model","8-vertex model","Life Sciences"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://digitalcommons.rockefeller.edu/student_theses_and_dissertations/455"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["The thesis consists of nine chapters and two appendices. In chapter II I discuss the connection given by the transfer matrix formulation between a classical statistical mechanical system and an associated quantum Hamiltonian, using as an example the familiar two- 4 dimensional Ising model. Next, in chapter III, I show how this applies to Baxter's 8-vertex model and the XYZ Hamiltonian, and how an infinite set of conserved charges for the XYZ model arises from properties of the transfer matrix. In Chapter IV I discuss the meaning of self-duality as it applies to quantum Hamiltonians, and develop a general form for a self-dual Hamiltonian. In Chapter V I show how one can find the explicit form for conserved charges in the XY model by a heuristic technique which takes advantage of the models' self-duality. In chapter VI it is shown how the solution to the XYZ model by the quantum inverse scattering method leads to the infinite set of conserved charges associated with it. The thesis culminates in the statement and proof of the theorem mentioned above, which stipulates a condition under which self-dual theories possess an infinite set of conserved charges (Chapter VII), after which I briefly discuss applications of the theorem (VIII) and draw some conclusions (IX).
"]},{"key":"dc:title","label":"Title","values":["Infinite Sets of Conserved Charges and Duality in Quantum Field Theory"]}]}],"canonical_facts":{"dc:contributor":["Louise Dolan"],"dc:creator":["Grady, Michael Patrick"],"dc:description.abstract":["The thesis consists of nine chapters and two appendices. In chapter II I discuss the connection given by the transfer matrix formulation between a classical statistical mechanical system and an associated quantum Hamiltonian, using as an example the familiar two- 4 dimensional Ising model. Next, in chapter III, I show how this applies to Baxter's 8-vertex model and the XYZ Hamiltonian, and how an infinite set of conserved charges for the XYZ model arises from properties of the transfer matrix. In Chapter IV I discuss the meaning of self-duality as it applies to quantum Hamiltonians, and develop a general form for a self-dual Hamiltonian. In Chapter V I show how one can find the explicit form for conserved charges in the XY model by a heuristic technique which takes advantage of the models' self-duality. In chapter VI it is shown how the solution to the XYZ model by the quantum inverse scattering method leads to the infinite set of conserved charges associated with it. The thesis culminates in the statement and proof of the theorem mentioned above, which stipulates a condition under which self-dual theories possess an infinite set of conserved charges (Chapter VII), after which I briefly discuss applications of the theorem (VIII) and draw some conclusions (IX).
"],"dc:identifier":["https://digitalcommons.rockefeller.edu/student_theses_and_dissertations/455"],"dc:subject":["transfer matrix","quantum Hamiltonian","self-duality","conserved charges","XYZ model","8-vertex model","Life Sciences"],"dc:title":["Infinite Sets of Conserved Charges and Duality in Quantum Field Theory"],"thesis:degree_level":["Thesis"],"thesis:degree_name":["Doctor of Philosophy (PhD)"]},"updated_at":"2026-07-24T04:10:47Z"}