{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/132469"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/132469","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"On the exact renormalization of states in quantum field theories","abstract":"The study of renormalization is a cornerstone of our modern understanding of quantum field theory and many body physics. As quantum information becomes an increasingly important tool in our understanding of continuum theories, new techniques are needed to understand how renormalization interacts with the strictly quantum features of field theories. By using path integral methods, we can port our understanding of the renormalization of Euclidean field theories to states of the QFT Hilbert space. Such constructions require the use of manifolds with boundary in the path integral, presenting technical and conceptual problems in the usual implementation of the renormalization group (RG). The solution to these problems are not necessarily unique, and in this work we explore two distinct approaches with largely different qualitative behavior. First, we consider half space path integrals with specially modified regulating schemes. The resulting renormalization group flows result in a class of unitary flows which are designed to capture the behavior of a class of continuous entanglement renormalization schemes known as the continuous multiscale renormalization ansatz (cMERA). Then, we consider a renormalization scheme which is in some sense “minimally” modified from a standard renormalization approach of Polchinski, and demonstrate that the resulting ERG flows are described by a non-unitary quantum channels generated by a Lindbladian which we derive. We solve the resulting Lindblad equation for Gaussian density matrices and compute the flow equation to second order in perturbation theory for a φ4 self interaction. We also calculate channel monotones such as the relative entropy and fidelity of ground states flowing under the RG.","abstract_html":"The study of renormalization is a cornerstone of our modern understanding of quantum field theory and many body physics. As quantum information becomes an increasingly important tool in our understanding of continuum theories, new techniques are needed to understand how renormalization interacts with the strictly quantum features of field theories. By using path integral methods, we can port our understanding of the renormalization of Euclidean field theories to states of the QFT Hilbert space. Such constructions require the use of manifolds with boundary in the path integral, presenting technical and conceptual problems in the usual implementation of the renormalization group (RG). The solution to these problems are not necessarily unique, and in this work we explore two distinct approaches with largely different qualitative behavior. First, we consider half space path integrals with specially modified regulating schemes. The resulting renormalization group flows result in a class of unitary flows which are designed to capture the behavior of a class of continuous entanglement renormalization schemes known as the continuous multiscale renormalization ansatz (cMERA). Then, we consider a renormalization scheme which is in some sense “minimally” modified from a standard renormalization approach of Polchinski, and demonstrate that the resulting ERG flows are described by a non-unitary quantum channels generated by a Lindbladian which we derive. We solve the resulting Lindblad equation for Gaussian density matrices and compute the flow equation to second order in perturbation theory for a φ4 self interaction. We also calculate channel monotones such as the relative entropy and fidelity of ground states flowing under the RG.","abstract_has_math":false,"creators":["Goldman, Samuel"],"institution":"University of Illinois Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Physics","degree_department":null,"school":null,"contributors":["Leigh, Robert","Faulkner, Thomas","Hughes, Taylor","Kahn, Yonatan"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2025,"date_issued":"2025-12","date_published":"2025-12","updated_at":"2026-07-22T22:25:07Z","subjects":["Renormalization","Open quantum systems"],"languages":["en"],"rights":["Copyright 2025 Samuel Goldman"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/2142/132469","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Leigh, Robert","Faulkner, Thomas","Hughes, Taylor","Kahn, Yonatan"]},{"key":"dc:creator","label":"Author","values":["Goldman, Samuel"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2025-12","2025-11-30"]},{"key":"dc:type","label":"Dc Type","values":["text","Thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Physics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Renormalization","Open quantum systems"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2025 Samuel Goldman"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://hdl.handle.net/2142/132469"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["The study of renormalization is a cornerstone of our modern understanding of quantum field theory and many body physics. As quantum information becomes an increasingly important tool in our understanding of continuum theories, new techniques are needed to understand how renormalization interacts with the strictly quantum features of field theories. By using path integral methods, we can port our understanding of the renormalization of Euclidean field theories to states of the QFT Hilbert space. Such constructions require the use of manifolds with boundary in the path integral, presenting technical and conceptual problems in the usual implementation of the renormalization group (RG). The solution to these problems are not necessarily unique, and in this work we explore two distinct approaches with largely different qualitative behavior. First, we consider half space path integrals with specially modified regulating schemes. The resulting renormalization group flows result in a class of unitary flows which are designed to capture the behavior of a class of continuous entanglement renormalization schemes known as the continuous multiscale renormalization ansatz (cMERA). Then, we consider a renormalization scheme which is in some sense “minimally” modified from a standard renormalization approach of Polchinski, and demonstrate that the resulting ERG flows are described by a non-unitary quantum channels generated by a Lindbladian which we derive. We solve the resulting Lindblad equation for Gaussian density matrices and compute the flow equation to second order in perturbation theory for a φ4 self interaction. We also calculate channel monotones such as the relative entropy and fidelity of ground states flowing under the RG.","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2026-02-19 without embargo terms","The student, Samuel Goldman, accepted the attached license on 2025-10-23 at 22:50.","The student, Samuel Goldman, submitted this Dissertation for approval on 2025-10-23 at 22:50.","This Dissertation was approved for publication on 2025-11-30 at 11:44.","DSpace SAF Submission Ingestion Package generated from Vireo submission #22815 on 2026-02-19 at 18:24:19"]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["On the exact renormalization of states in quantum field theories"]}]}],"canonical_facts":{"dc:contributor":["Leigh, Robert","Faulkner, Thomas","Hughes, Taylor","Kahn, Yonatan"],"dc:creator":["Goldman, Samuel"],"dc:date":["2025-12","2025-11-30"],"dc:description":["The study of renormalization is a cornerstone of our modern understanding of quantum field theory and many body physics. As quantum information becomes an increasingly important tool in our understanding of continuum theories, new techniques are needed to understand how renormalization interacts with the strictly quantum features of field theories. By using path integral methods, we can port our understanding of the renormalization of Euclidean field theories to states of the QFT Hilbert space. Such constructions require the use of manifolds with boundary in the path integral, presenting technical and conceptual problems in the usual implementation of the renormalization group (RG). The solution to these problems are not necessarily unique, and in this work we explore two distinct approaches with largely different qualitative behavior. First, we consider half space path integrals with specially modified regulating schemes. The resulting renormalization group flows result in a class of unitary flows which are designed to capture the behavior of a class of continuous entanglement renormalization schemes known as the continuous multiscale renormalization ansatz (cMERA). Then, we consider a renormalization scheme which is in some sense “minimally” modified from a standard renormalization approach of Polchinski, and demonstrate that the resulting ERG flows are described by a non-unitary quantum channels generated by a Lindbladian which we derive. We solve the resulting Lindblad equation for Gaussian density matrices and compute the flow equation to second order in perturbation theory for a φ4 self interaction. We also calculate channel monotones such as the relative entropy and fidelity of ground states flowing under the RG.","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2026-02-19 without embargo terms","The student, Samuel Goldman, accepted the attached license on 2025-10-23 at 22:50.","The student, Samuel Goldman, submitted this Dissertation for approval on 2025-10-23 at 22:50.","This Dissertation was approved for publication on 2025-11-30 at 11:44.","DSpace SAF Submission Ingestion Package generated from Vireo submission #22815 on 2026-02-19 at 18:24:19"],"dc:format":["application/pdf"],"dc:identifier":["https://hdl.handle.net/2142/132469"],"dc:language":["en"],"dc:rights":["Copyright 2025 Samuel Goldman"],"dc:subject":["Renormalization","Open quantum systems"],"dc:title":["On the exact renormalization of states in quantum field theories"],"dc:type":["text","Thesis"],"thesis:degree_discipline":["Physics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois Urbana-Champaign"]},"updated_at":"2026-07-22T22:25:07Z"}