{"@context":"http://iiif.io/api/presentation/2/context.json","@type":"sc:Manifest","@id":"https://iiif.quartexcollections.com/berry/iiif/b033c56c-3d75-4a5f-8cd4-6f9dc1a9f313/manifest","label":"ScarborKeith_2026_Honors","metadata":[{"label":"Identifier","value":"ScarborKeith_2026_Honors"},{"label":"Title","value":"Symmetry Arguments in Electrodynamics"},{"label":"Creator","value":["Keith Scarbor"]},{"label":"Date (Filter)","value":"D:31 M:03 Y:2026"},{"label":"Date","value":"March 31 2026"},{"label":"Description","value":"Symmetry principles can be applied in the study of electrodynamics to streamline\nthe development of proofs and provide efficient problem-solving methods. It is often\npossible, for example, to gain information about electric/magnetic fields from the symmetries\nof their corresponding charge/current densities. The goal of our research is\nto place such principles of symmetry on a mathematically rigorous foundation. To do\nthis, we need certain results about the relationships between divergence/curl operations\nand vector field transformations. In particular, it should not matter whether one\ntransforms a vector field then calculates divergence/curl, or calculates divergence/curl\nthen transforms the result. Though physically intuitive, proving this is rather involved,\nand there are some transformations for which these relationships do not hold at all. So\nfar we have been investigating the transformations for which these relationships can\nbe proven. Key results include successfully proving these relationships for a particular\ngroup of transformations, proving several symmetry theorems relying on them, developing\na precise and consistent definition of vector field transformations, and exploring\nhow group theory can be applied in this project to further mathematical rigor and\nelegance."},{"label":"Format","value":["application/pdf"]},{"label":"Language","value":["English"]},{"label":"Language (DLG)","value":["eng"]},{"label":"Publisher","value":["Berry College"]},{"label":"Medium","value":["theses"]},{"label":"Extent","value":"32 pages"},{"label":"Holding Institution","value":["Berry College"]},{"label":"Type","value":["Text"]},{"label":"Decade","value":["2020s"]},{"label":"Rights","value":["In Copyright"]},{"label":"Rights Link","value":"<a href=\"https://rightsstatements.org/page/InC/1.0/?language=en\" target=\"_blank\"> In Copyright</a>"},{"label":"Rightsholder","value":["Keith Scarbor"]},{"label":"Access Restrictions","value":["immediate unrestricted access"]},{"label":"Subject","value":["Mathematical Physics"]},{"label":"School","value":["School of Mathematical and Natural Sciences"]},{"label":"Department","value":["Physics and Technology"]},{"label":"Author","value":["Keith Scarbor"]},{"label":"Author Supplied Keywords","value":"Mathematical Physics; Electromagnetism; Symmetry Principles"},{"label":"Research Funding","value":["Student Presentation Travel Fund","Summer Undergraduate Research Fellowship"]},{"label":"Research Funding Link","value":"Learn more about <a href=\"https://berry.edu/academics/faculty-resources/undergraduate-research/student-grants\" target=\"_blank\">student grants</a> and <a href=\"https://berry.edu/academics/faculty-resources/undergraduate-research/summer-research\" target=\"_blank\"> summer research. </a>"},{"label":"Project Type","value":["Thesis"]},{"label":"Degree","value":["Bachelor of Science"]},{"label":"Committee Chair","value":["Charles D. Lane"]},{"label":"Faculty Advisor","value":["Kenneth L. Martin"]},{"label":"Major","value":["Physics"]}],"description":"Symmetry Arguments in 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