{"id":{"repo_id":"umn","oai_identifier":"oai:conservancy.umn.edu:11299/140030"},"canonical_url":"https://search.dev.ndltd.org/etd/umn/oai:conservancy.umn.edu:11299/140030","repository":{"repo_id":"umn","name":"University of Minnesota","base_url":"https://conservancy.umn.edu/server/oai/request"},"display":{"title":"Application of wavelets in few-body problems.","abstract":"This study is an application of wavelet numerical techniques in solving a non-perturbative Yukawa Hamiltonian in light-front quantum field theory. Once the problem is stated in the form of an integral equation, a wavelet basis of a particular scale is used to discretize the problem into a dense matrix. Wavelets are a class of functions with special properties. Daubachies wavelets are a subset of wavelets defined to have vanishing lower order moments, enabling Daubachies 2 and 3 wavelet bases to exactly represent polynomials of degree up to two. These properties make them useful as a basis set for various numerical methods. It was observed that a kernel containing structure in fine scales requires a fine scaling function basis to converge closer to analytical results. Once the kernel matrix is obtained, the wavelet transform followed by an absolute thresholding filters the dense kernel matrix to a sparse matrix. The sparse matrix eigenvalue problem was then solved and compared with the original eigenvalue problem. It was observed that as long as the problem is discretized with a scale fine enough to resolve the features of the kernel, higher levels of filtering would still reproduce eigenvalues that agree with the unfiltered problem.","abstract_html":"This study is an application of wavelet numerical techniques in solving a non-perturbative Yukawa Hamiltonian in light-front quantum field theory. Once the problem is stated in the form of an integral equation, a wavelet basis of a particular scale is used to discretize the problem into a dense matrix. Wavelets are a class of functions with special properties. Daubachies wavelets are a subset of wavelets defined to have vanishing lower order moments, enabling Daubachies 2 and 3 wavelet bases to exactly represent polynomials of degree up to two. These properties make them useful as a basis set for various numerical methods. It was observed that a kernel containing structure in fine scales requires a fine scaling function basis to converge closer to analytical results. Once the kernel matrix is obtained, the wavelet transform followed by an absolute thresholding filters the dense kernel matrix to a sparse matrix. The sparse matrix eigenvalue problem was then solved and compared with the original eigenvalue problem. It was observed that as long as the problem is discretized with a scale fine enough to resolve the features of the kernel, higher levels of filtering would still reproduce eigenvalues that agree with the unfiltered problem.","abstract_has_math":false,"creators":["Hewawasam, Kuravi"],"institution":null,"degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2012,"date_issued":"2012-08","date_published":"2012-08","updated_at":"2026-07-24T05:19:56Z","subjects":["Few-body problems","Numerical methods","Quantum field theory","Wavelets","Yukawa hamiltonian"],"languages":["en_US"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://purl.umn.edu/140030","outbound_label":"Repository record","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Hewawasam, Kuravi"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2012-12-04T14:57:33Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2012-12-04T14:57:33Z"]},{"key":"dc:date.issued","label":"Date","values":["2012-08"]},{"key":"dc:type","label":"Dc Type","values":["Thesis or Dissertation"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Few-body problems","Numerical methods","Quantum field theory","Wavelets","Yukawa hamiltonian"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en_US"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://purl.umn.edu/140030"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["University of Minnesota M.S. thesis. August 2012. Major: Physics. Advisor: John R Hiller. 1 computer file (PDF); viii, 82 pages, appendices A-B."]},{"key":"dc:description.abstract","label":"Abstract","values":["This study is an application of wavelet numerical techniques in solving a non-perturbative Yukawa Hamiltonian in light-front quantum field theory. Once the problem is stated in the form of an integral equation, a wavelet basis of a particular scale is used to discretize the problem into a dense matrix. Wavelets are a class of functions with special properties. Daubachies wavelets are a subset of wavelets defined to have vanishing lower order moments, enabling Daubachies 2 and 3 wavelet bases to exactly represent polynomials of degree up to two. These properties make them useful as a basis set for various numerical methods. It was observed that a kernel containing structure in fine scales requires a fine scaling function basis to converge closer to analytical results. Once the kernel matrix is obtained, the wavelet transform followed by an absolute thresholding filters the dense kernel matrix to a sparse matrix. The sparse matrix eigenvalue problem was then solved and compared with the original eigenvalue problem. It was observed that as long as the problem is discretized with a scale fine enough to resolve the features of the kernel, higher levels of filtering would still reproduce eigenvalues that agree with the unfiltered problem."]},{"key":"dc:title","label":"Title","values":["Application of wavelets in few-body problems."]}]}],"canonical_facts":{"dc:creator":["Hewawasam, Kuravi"],"dc:date.accessioned":["2012-12-04T14:57:33Z"],"dc:date.available":["2012-12-04T14:57:33Z"],"dc:date.issued":["2012-08"],"dc:description":["University of Minnesota M.S. thesis. August 2012. Major: Physics. Advisor: John R Hiller. 1 computer file (PDF); viii, 82 pages, appendices A-B."],"dc:description.abstract":["This study is an application of wavelet numerical techniques in solving a non-perturbative Yukawa Hamiltonian in light-front quantum field theory. Once the problem is stated in the form of an integral equation, a wavelet basis of a particular scale is used to discretize the problem into a dense matrix. Wavelets are a class of functions with special properties. Daubachies wavelets are a subset of wavelets defined to have vanishing lower order moments, enabling Daubachies 2 and 3 wavelet bases to exactly represent polynomials of degree up to two. These properties make them useful as a basis set for various numerical methods. It was observed that a kernel containing structure in fine scales requires a fine scaling function basis to converge closer to analytical results. Once the kernel matrix is obtained, the wavelet transform followed by an absolute thresholding filters the dense kernel matrix to a sparse matrix. The sparse matrix eigenvalue problem was then solved and compared with the original eigenvalue problem. It was observed that as long as the problem is discretized with a scale fine enough to resolve the features of the kernel, higher levels of filtering would still reproduce eigenvalues that agree with the unfiltered problem."],"dc:identifier.uri":["http://purl.umn.edu/140030"],"dc:language.iso":["en_US"],"dc:subject":["Few-body problems","Numerical methods","Quantum field theory","Wavelets","Yukawa hamiltonian"],"dc:title":["Application of wavelets in few-body problems."],"dc:type":["Thesis or Dissertation"]},"updated_at":"2026-07-24T05:19:56Z"}