{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/80693"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/80693","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Improvement of Stress -Energy Tensor Using Space -Time Symmetries","abstract":"In 1970 Callan, Coleman, and Jackiw found that it is always possible to improve the symmetric stress-energy tensor of a renormalizable relativistic field theory over (3+1)-dimensional flat space-time manifold. The improved stress-energy tensor defines the same field energy-momentum and angular momentum as the conventional tensor, and it is traceless for a non-interacting field theory when all coupling constants are physically dimensionless. The question for existence of an improved stress-energy tensor for a scale invariant relativistic field theory on a (1+1)-dimensional flat space-time manifold has been a long standing open problem for almost 30 years. In this thesis, I develop the weakest set of necessary and sufficient conditions for existence of a conserved symmetric traceless stress-energy tensor for a scale invariant relativistic field theory over a d-dimensional flat space-time manifold. This improved tensor, which defines the same conserved charges as the canonical tensor, has been explicitly constructed for arbitrary space-time dimensions including d = 2 intrinsically from the flat space-time field theory without coupling it with gravity. As an example, I derive the improved tensor of (1+1)-dimensional Liouville field theory. We discuss two remarkable results: (1) full conformal symmetry over the flat space-time is sufficient but not necessary for the existence of the improved tensor; (2) quite surprisingly, the improved stress-energy tensor exists in all space-time dimensions for a free massless Abelian U(1) gauge theory provided the gauge symmetry has been broken in favor of Lorentz gauge for d ≠ 2, 4.","abstract_html":"In 1970 Callan, Coleman, and Jackiw found that it is always possible to improve the symmetric stress-energy tensor of a renormalizable relativistic field theory over (3+1)-dimensional flat space-time manifold. The improved stress-energy tensor defines the same field energy-momentum and angular momentum as the conventional tensor, and it is traceless for a non-interacting field theory when all coupling constants are physically dimensionless. The question for existence of an improved stress-energy tensor for a scale invariant relativistic field theory on a (1+1)-dimensional flat space-time manifold has been a long standing open problem for almost 30 years. In this thesis, I develop the weakest set of necessary and sufficient conditions for existence of a conserved symmetric traceless stress-energy tensor for a scale invariant relativistic field theory over a d-dimensional flat space-time manifold. This improved tensor, which defines the same conserved charges as the canonical tensor, has been explicitly constructed for arbitrary space-time dimensions including d = 2 intrinsically from the flat space-time field theory without coupling it with gravity. As an example, I derive the improved tensor of (1+1)-dimensional Liouville field theory. We discuss two remarkable results: (1) full conformal symmetry over the flat space-time is sufficient but not necessary for the existence of the improved tensor; (2) quite surprisingly, the improved stress-energy tensor exists in all space-time dimensions for a free massless Abelian U(1) gauge theory provided the gauge symmetry has been broken in favor of Lorentz gauge for d ≠ 2, 4.","abstract_has_math":false,"creators":["Bandyopadhyay, Akash"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Physics","degree_department":null,"school":null,"contributors":["Oono, Yoshitsugu"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015-09-25T20:03:38Z","date_published":"2015-09-25T20:03:38Z","updated_at":"2026-07-22T22:26:14Z","subjects":["Mathematics"],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["(MiAaPQ)AAI9996612"],"render_values":[{"text":"(MiAaPQ)AAI9996612","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/80693","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Oono, Yoshitsugu"]},{"key":"dc:creator","label":"Author","values":["Bandyopadhyay, Akash"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2015-09-25T20:03:38Z","10000-01-01","2001"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"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 at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Mathematics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/80693","(MiAaPQ)AAI9996612"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["In 1970 Callan, Coleman, and Jackiw found that it is always possible to improve the symmetric stress-energy tensor of a renormalizable relativistic field theory over (3+1)-dimensional flat space-time manifold. The improved stress-energy tensor defines the same field energy-momentum and angular momentum as the conventional tensor, and it is traceless for a non-interacting field theory when all coupling constants are physically dimensionless. The question for existence of an improved stress-energy tensor for a scale invariant relativistic field theory on a (1+1)-dimensional flat space-time manifold has been a long standing open problem for almost 30 years. In this thesis, I develop the weakest set of necessary and sufficient conditions for existence of a conserved symmetric traceless stress-energy tensor for a scale invariant relativistic field theory over a d-dimensional flat space-time manifold. This improved tensor, which defines the same conserved charges as the canonical tensor, has been explicitly constructed for arbitrary space-time dimensions including d = 2 intrinsically from the flat space-time field theory without coupling it with gravity. As an example, I derive the improved tensor of (1+1)-dimensional Liouville field theory. We discuss two remarkable results: (1) full conformal symmetry over the flat space-time is sufficient but not necessary for the existence of the improved tensor; (2) quite surprisingly, the improved stress-energy tensor exists in all space-time dimensions for a free massless Abelian U(1) gauge theory provided the gauge symmetry has been broken in favor of Lorentz gauge for d ≠ 2, 4.","Made available in DSpace on 2015-09-25T20:03:38Z (GMT). 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The improved stress-energy tensor defines the same field energy-momentum and angular momentum as the conventional tensor, and it is traceless for a non-interacting field theory when all coupling constants are physically dimensionless. The question for existence of an improved stress-energy tensor for a scale invariant relativistic field theory on a (1+1)-dimensional flat space-time manifold has been a long standing open problem for almost 30 years. In this thesis, I develop the weakest set of necessary and sufficient conditions for existence of a conserved symmetric traceless stress-energy tensor for a scale invariant relativistic field theory over a d-dimensional flat space-time manifold. This improved tensor, which defines the same conserved charges as the canonical tensor, has been explicitly constructed for arbitrary space-time dimensions including d = 2 intrinsically from the flat space-time field theory without coupling it with gravity. As an example, I derive the improved tensor of (1+1)-dimensional Liouville field theory. We discuss two remarkable results: (1) full conformal symmetry over the flat space-time is sufficient but not necessary for the existence of the improved tensor; (2) quite surprisingly, the improved stress-energy tensor exists in all space-time dimensions for a free massless Abelian U(1) gauge theory provided the gauge symmetry has been broken in favor of Lorentz gauge for d ≠ 2, 4.","Made available in DSpace on 2015-09-25T20:03:38Z (GMT). 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