Show simple item record

dc.contributor.advisorCardona Guio, Alexander
dc.contributor.advisorReyes Lega, Andrés Fernando
dc.contributor.authorCalderón Gómez, Julián David
dc.date.accessioned2022-11-01T13:29:22Z
dc.date.available2022-11-01T13:29:22Z
dc.date.issued2022-06-02
dc.identifier.urihttp://hdl.handle.net/1992/62981
dc.description.abstractLa idea principal de este trabajo es entender las conexiones que existen entre teoría del índice y el problema de implementación de simetrías unitarias en estructuras algebraicas como las álgebras de Clifford y las álgebras de relaciones de anticonmutación canónicas -Álgebras CAR. Se logra entender, además, la conexión de este índice con otra estructura adicional asociada con las C* álgebras que surgen en este trabajo, como lo es la K-Teoría. Finalmente, se analizan algunos ejemplos motivados desde la física como el modelo Su-Schriefer-Heeger (SSH) y la cadena de Kitaev, los cuales ilustran los dos posibles invariantes que pueden surgir en lo que se conoce como la correspondencia Bulk - Edge (tipo Z y tipo Z_2).
dc.format.extent111 páginases_CO
dc.format.mimetypeapplication/pdfes_CO
dc.language.isoenges_CO
dc.publisherUniversidad de los Andeses_CO
dc.rights.urihttps://repositorio.uniandes.edu.co/static/pdf/aceptacion_uso_es.pdf
dc.titleIndex theory and implementability of unitary representations of CAR algebras
dc.title.alternativeTeoría del índice e implementabilidad de representaciones unitarias de álgebras CAR
dc.typeTrabajo de grado - Maestríaes_CO
dc.publisher.programMaestría en Matemáticases_CO
dc.subject.keywordÁlgebra CAR
dc.subject.keywordÁlgebras de Clifford
dc.subject.keywordTransformaciones de Bogoliubov
dc.subject.keywordCorrespondencia Bulk - Edge
dc.publisher.facultyFacultad de Cienciases_CO
dc.publisher.departmentDepartamento de Matemáticases_CO
dc.contributor.juryRecht, Lázaro
dc.contributor.juryWinklmeier, Monika Anna
dc.type.driverinfo:eu-repo/semantics/masterThesis
dc.type.versioninfo:eu-repo/semantics/acceptedVersion
dc.description.degreenameMagíster en Matemáticases_CO
dc.description.degreelevelMaestríaes_CO
dc.description.researchareaGeometría y física matemática.es_CO
dc.identifier.instnameinstname:Universidad de los Andeses_CO
dc.identifier.reponamereponame:Repositorio Institucional Sénecaes_CO
dc.identifier.repourlrepourl:https://repositorio.uniandes.edu.co/es_CO
dc.relation.referencesP. de la Harpe, Classical Banach-Lie Algebras and Banach-Lie Groups of Operators in Hilbert Space, 1st ed., ser. Lecture notes in mathematics, 285. Springer-Verlag, 1972.es_CO
dc.relation.referencesP. de la Harpe and V. Jones., An introduction to C*-algebras. Université de Genéve, Jul 1995.es_CO
dc.relation.referencesI. Gohberg and M. Krein, Introduction to the theory of linear nonselfadjoint operators, ser. Translations of Mathematical Monographs. AMS, 1969.es_CO
dc.relation.referencesD. Husemoller, Fibre Bundles, 3rd ed., ser. Graduate Texts in Mathematics 20. Springer New York, 1966.es_CO
dc.relation.referencesB. Lawson and M. Michelsohn, Spin Geometry, ser. Princeton mathematical series volume 38. Princeton University Press, 1990.es_CO
dc.relation.referencesJ. Lesmes and T. Abuabara, Elementos de análisis funcional. Catálogo Público Uniandes, 2010.es_CO
dc.relation.referencesJ. Milnor, Morse Theory, 1st ed., ser. Annals of Mathematic Studies AM-51. Princeton University Press, 1963.es_CO
dc.relation.referencesR. Plymen and P. Robinson, Spinors in Hilbert Space, ser. Cambridge Tracts in Mathematics 114. Cambridge University Press, 1994.es_CO
dc.relation.referencesE. Prodan and H. Schulz-Baldes, Bulk and Boundary Invariants for Complex Topological Insulators: From K-Theory to Physics, 1st ed., ser. Mathematical Physics Studies. Springer International Publishing, 2016.es_CO
dc.relation.referencesM. Reed and B. Simon, Functional Analysis, Volume 1, ser. Methods of Modern Mathematical Physics. Academic Press, 1981, vol. Volume 1.es_CO
dc.relation.referencesJ. Roe, Winding Around: The Winding Number in Topology, Geometry, and Analysis, ser. Student Mathematical Library. American Mathematical Society, 2015.es_CO
dc.relation.referencesM. Rordam, F. Larsen, and N. Laustsen, Introduction to K-theory for C* algebras, 1st ed., ser. London Mathematical Society Student Texts. Cambridge University Press, 2000.es_CO
dc.relation.referencesV. Sunder, Functional Analysis: Spectral Theory, ser. Birkhäuser Advanced Texts Basler Lehrbücher. Birkhäuser Basel, 1998.es_CO
dc.relation.referencesJ. Varilly, H. Figueroa, and J. Gracia-Bondia, Elements of Noncommutative Geometry (Birkhäuser Advanced Texts Basler Lehrbücher), 1st ed. Birkhäuser Boston, 2000.es_CO
dc.relation.referencesF. Arici and B. Mesland, Toeplitz extensions in noncommutative topology and mathematical physics, in Trends in Mathematics. Springer International Publishing, 2020, pp. 3-29.es_CO
dc.relation.referencesR. Bott, The stable homotopy of the classical groups, Annals of Mathematics, vol. 70, no. 2, pp. 313-337, 1959.es_CO
dc.relation.referencesJ. Calderon-Garcia and A. Reyes-Lega, Majorana fermions and orthogonal complex structures, Modern Physics Letters A, vol. 33, no. 14, p. 1840001, 2018.es_CO
dc.relation.referencesA. Carey, Some infinite dimensional groups and bundles, Publications of the Research Institute for Mathematical Sciences, vol. 20, no. 6, pp. 1103-1117, 1984.es_CO
dc.relation.referencesA. Carey and D. M. O¿Brien, Automorphisms of the infinite dimensional Clifford algebra and the Atiyah-Singer mod 2 index, Topology, vol. 22, 1983.es_CO
dc.relation.referencesA. Carey, D. M. O¿Brien, and C. Hurst, Automorphisms of the canonical anticommutation relations and index theory, Functional Analysis, vol. 48, 1982.es_CO
dc.relation.referencesA. Carey, J. Phillips, and H. Schulz-Baldes, Spectral flow for skew-adjoint fredholm operators, Journal of Spectral Theory, vol. 9, no. 1, pp. 137-170, 2019.es_CO
dc.relation.referencesA. Devinatz and M. Shinbrot, General Weiner - Hopf operators, Transactions of the American Mathematical Society, vol. 145, 1969.es_CO
dc.relation.referencesJ. Espinoza and B. Uribe, Topological properties of the unitary group, JP Journal of Geometry and Topology, vol. 16, pp. 45-55, 2014.es_CO
dc.relation.referencesA. Y. Kitaev, Unpaired majorana fermions in quantum wires, Physics-Uspekhi, vol. 44, no. 10S, pp. 131-136, 2001.es_CO
dc.relation.referencesN. Kuiper, The homotopy type of the unitary group of hilbert space, Topology, vol. 3, no. 1, pp. 19-30, 1965.es_CO
dc.relation.referencesG. Murphy, Continuity of the spectrum and spectral radius, Proceedings of the American Mathematical Society, vol. 82, no. 4, pp. 619-621, 1981.es_CO
dc.relation.referencesS. Pandey, Symmetrically-normed ideals and characterizations of absolutely norming operators, Ph.D. dissertation, University of Waterloo, 2018.es_CO
dc.relation.referencesA. Ramsay, The Mackey-Glimm dichotomy for foliations and other polish groupoids, Journal of Functional Analysis, vol. 94, no. 2, pp. 358-374, 1990.es_CO
dc.relation.referencesA. F. Reyes-Lega, Some Aspects of operator algebras in quantum physics, in Geometric, Algebraic and Topological Methods for Quantum Field Theory. World Scientific, sep 2016.es_CO
dc.rights.accessrightsinfo:eu-repo/semantics/openAccess
dc.type.coarhttp://purl.org/coar/resource_type/c_bdcc
dc.type.coarversionhttp://purl.org/coar/version/c_ab4af688f83e57aa
dc.type.contentTextes_CO
dc.type.redcolhttps://purl.org/redcol/resource_type/TM
dc.rights.coarhttp://purl.org/coar/access_right/c_abf2
dc.subject.themesMatemáticases_CO


Files in this item

Thumbnail

Name: Master_Thesis.pdf

This item appears in the following Collection(s)

Show simple item record