Generation of Pauli Spin Matrices from Jones Vectors

Generación de las matrices de espín de Paulí a partir de los vectores de Jones;
Geração das matrizes de spin de Pauli a partir dos vetores de Jones

dc.creatorHurtado Murcia, Brahan Armando
dc.creatorGonzález Sierra, Hernando
dc.creatorMendoza Suárez, Jairo Alonso
dc.date2021-08-27
dc.date.accessioned2022-12-15T18:17:37Z
dc.date.available2022-12-15T18:17:37Z
dc.identifierhttps://revistas.unimilitar.edu.co/index.php/rfcb/article/view/5441
dc.identifier10.18359/rfcb.5441
dc.identifier.urihttps://repositorioslatinoamericanos.uchile.cl/handle/2250/5356277
dc.descriptionUsing the states of polarization of light represented by Jones vectors that belong to a complex linear vector space of one-dimension, algebraic structures are elaborated that are known as dyads or second-order tensors that in this case make up a complex vector space of two dimensions. With these second-order tensors, which can be expressed in a matrix form, sequences of switching relations are constructed with alternating states of light polarization. The sequences of commutation relations, with the property of alternation given by the permutation of the polarization states of light, are presented as linear combinations that generate Pauli spin matrices in a simple way. The polarization states of the Jones vectors used to construct the sequences of the commutation relations of the dyadic forms belong to forms of the circular, left and right, or linear type. The transition from a complex vector space, in which the Jones vectors act, to a complex linear vector space of two dimensions, in which the base of this last space is made up of the unit matrix and the Pauli spin matrices, is feasible through commutation relations using Jones vectors in states of linear and circular polarization.en-US
dc.descriptionUsando los estados de polarización de la luz representados por vectores de Jones que pertenecen a un espacio vectorial lineal complejo de una dimensión, se elaboran estructuras algebraicas que son conocidas como diadas o tensores de segundo orden que en este caso conforman un espacio vectorial complejo de dos dimensiones. Con estos tensores de segundo orden, que se pueden expresar de forma matricial, se construyen secuencias de relaciones de conmutación con alternancia de los estados de polarización de la luz. Las secuencias de relaciones de conmutación, con la propiedad de alternancia dada por la permutación de los estados de polarización de la luz, se presentan como combinaciones lineales que generan de forma simple las matrices de espín de Pauli. Los estados de polarización de los vectores de Jones utilizados para construir las secuencias de las relaciones de conmutación de las formas diádicas pertenecen a formas de tipo circular, a la izquierda y a la derecha, o lineal. La transición de un espacio vectorial complejo, en la que actúan los vectores de Jones, a un espacio vectorial lineal complejo de dos dimensiones, en el que la base de este último espacio lo conforman la matriz unidad y las matrices de espín de Pauli, es factible a través de relaciones de conmutación empleando vectores de Jones en estados de polarización lineal y circular.es-ES
dc.descriptionA partir do uso dos estados de polarização da luz representados por vetores de Jones que pertencem a um espaço vetorial linear complexo de uma dimensão, são elaboradas estruturas algébricas que são conhecidas como “díades” ou “tensores de segunda ordem” que, nesse caso, conformam um espaço vetorial complexo de duas dimensões. Com esses tensores de segunda ordem, que podem ser expressos de forma matricial, são construídas sequências de relações de comutação com alternância dos estados de polarização da luz. As sequências de relações de comutação, com a propriedade de alternância dada pela permutação dos estados de polarização da luz, são apresentadas como combinações lineares que geram de forma simples as matrizes de spin de Pauli. Os estados de polarização dos vetores de Jones utilizados para construir as sequências das relações de comutação das formas díades pertencem a formas de tipo circular, à esquerda e à direita ou linear. A transição de um espaço vetorial complexo, no qual os vetores de Jone agem, a um espaço vetorial linear complexo de duas dimensões, no qual a base deste último espaço é conformada pela matriz unidade e as matrizes de spin de Pauli, é factível por meio de relações de comutação e da utilização de vetores de Jones em estados de polarização linear e circular.pt-BR
dc.formatapplication/pdf
dc.formattext/xml
dc.languagespa
dc.publisherUniversidad Militar Nueva Granadaes-ES
dc.relationhttps://revistas.unimilitar.edu.co/index.php/rfcb/article/view/5441/4801
dc.relationhttps://revistas.unimilitar.edu.co/index.php/rfcb/article/view/5441/4849
dc.relation/*ref*/L. J. Vandergriff, "Nature and Properties of Light", en Fundamentals of Photonics, Chandrasekhar Roychoudhuri. University of Connecticut, Photonics Lab, 1999, pp. 1-38.
dc.relation/*ref*/V. V. Kotlyar, A. G. Nalimov y S. S. Stafeev, "Exploiting the circular polarization of light to obtain a spiral energy flow at the subwavelength focus", J. Opt. Soc. Am. B, vol. 36, n.° 10, pp. 2850-2855, 2019. https://doi.org/10.1364/JOSAB.36.002850
dc.relation/*ref*/F. L. Pedrotti y L. S. Pedrotti, Introduction to Optics, 2a ed. Englewood Cliffs: Prentice-Hall, 1993.
dc.relation/*ref*/C. Schrijver y C. Zwaan Solar and Stellar magnetic activity (Cambridge University Press, New York, 2000).
dc.relation/*ref*/E. Bowel y B. Zellner in Proceedings of the International Astronomical Union edited by T. Gehrels (University of Arizona Press Tucson, 1974).
dc.relation/*ref*/J.H. Oort y T Walraven Bulletin of the Astronomical Institutes of the Netherlands 12, 285 (1956).
dc.relation/*ref*/R. Kulsrud y E. Zweibel, Reports on progress in physics 71, 046901 (2008).
dc.relation/*ref*/A. Raftopoulos, N. Kalyfommatou y C. P. Constantinou, "The properties and the nature of light: The study of newton's work and the teaching of optics", Science and Education, vol. 14, n.° 7, pp. 649-673, 2005. [En línea]. https://doi.org/10.1007/s11191-004-5609-6
dc.relation/*ref*/H. G. Jerrard, "Modern description of polarized ligth: matrix methods", Optics & Laser Technology, vol. 14, n.° 6, pp. 309-319, 1982. https//doi.org/10.1016/0030-3992(82)90034-2
dc.relation/*ref*/J. Peatross y M. Ware, Physics of Light and Optics. Utah: Brigham Young University, 2008.
dc.relation/*ref*/N. C. Pistoni, "Simplified approach to the Jones calculus in retracing optical circuits", Applied Optics, vol. 34, n.° 34, pp. 7870-7876, 1995. https://doi.org/10.1364/AO.34.007870
dc.relation/*ref*/D. A. Steck, Classical and modern optics. University of Oregon: Oregon Center for Optics and Departament of Physics, 2006.
dc.relation/*ref*/L. L. Frenzel, Sistemas Electrónicos de comunicaciones, 3ª ed. México, D. F: Alfaomega, 2003.
dc.relation/*ref*/P. Gorroochurn, "The end of statistical independence: the story of Bose-Einstein Statistics", The Mathematical Intelligencer, vol. 40, n.° 3, pp. 12-17, 2018. https://doi.org/10.1007/s00283-017-9772-4
dc.relation/*ref*/J. Arnaud, J. M. Boé, L. y F. Philippe, "Illustration of the fermidirac statistics", American Journal of Physics, vol. 67, n.° 3, pp. 215-221, 1999. https://doi.org/10.1119/1.19228
dc.relation/*ref*/G. A. D. Briggs, J. N. Butterfield y A. Zeilinger, "The Oxford questions on the foundations of quantum physics", Proc R Soc A 469:20130299, 2013. https//doi.org/10.1098/rspa.2013.0299
dc.relation/*ref*/R. Muller y H. Wiesner, "Teaching quantum mechanics on an introductory level", American Journal of Physics, vol. 70, n.° 3, pp. 200-209, 2002. https://doi.org/10.1119/1.1435346
dc.relation/*ref*/A. I. Borisenko y I. E. Tarapov, Vector and tensor analysis with applications. Worth Publishers, 1979.
dc.relation/*ref*/G. R. Hext, "The estimation of second-order tensors, with related tests and designs", Biometrika, vol. 50, n.° 3-4, pp. 353-373, 1963. https://doi.org/10.1093/biomet/50.3-4.353
dc.relation/*ref*/J. O. Rodríguez, J. C. Rodríguez y A. C. Sevilla, "Un proceso de formalización matemática: Desde las rotaciones hasta las matrices de spin de Pauli", Lat. Am. J. Phys. Educ, vol. 2, n.° 3, pp. 323-330, 2008. [En línea]. Disponible en: http://www.lajpe.org/sep08/30_Orlando_Organista.pdf
dc.relation/*ref*/E. Witten, "Quantum field theory and the Jones polynomial", en Braid Group, Knot Theory And Statistical Mechanics II, pp. 361-451, 1994. https://doi.org/10.1142/9789812798275_0013
dc.relation/*ref*/S. M. Reyes, D. A. Nolan, L. Shi y R. R. Alfano, "Special classes of optical vector vortex beams are Majorana-like photons", Optics Communications, vol. 464, n.° 1, pp. 1-5(125425), 2020. https//doi.org/10.1016/j.optcom.2020.125425
dc.relation/*ref*/F. R. G. Díaz y R. G. Salcedo, "El fenómeno del espín semientero, cuaternios, y matrices de Pauli", Rev. Matem.: Teor. y Ap., vol. 24, n.° 1, pp. 45-60, 2017. https://doi.org/10.15517/rmta.v24i1.27749
dc.relation/*ref*/P. M. Morse y H. Feshbach, "§1.6: Diadas y otros operadores vector" Métodos de la Física Teórica, vol. 1, Nueva York: McGraw-Hill, 1953.
dc.relation/*ref*/P. Mitiguy, "Vectors and dyadics", en Introductory matrix algebra, 2009, pp. 19-28.
dc.relation/*ref*/G. F. Torres del Castillo, "Rotaciones y espinores", Rev. Mex. Fís., vol. 40, n.° 1, pp. 119-131. 1994. [En línea]. Disponible en: https://rmf.smf.mx/pdf/rmf/40/1/40_1_119.pdf
dc.relation/*ref*/D. S. Durfee y J. L. Archibald, "Applying classical geometry intuition to quantum spin", Eur. J. Phys, vol. 37, pp. 1-9, 2016. https://doi.org/10.1088/0143-0807/37/5/055409
dc.relation/*ref*/L. Desmarais, Applied electro-optics, New Jersey: Prentice Hall, 1998.
dc.relation/*ref*/J. M. Marcela, "Polarización de la luz: conceptos básicos y aplicaciones en astrofísica", Rev. Bras. Ensino Fís., vol. 40, n.° 4, pp. e4310, 2018, doi: 10.1590/1806-9126-rbef-2018-0024
dc.relation/*ref*/D. S. Kliger, J. W. Lewis y C. E. Randall, "Introduction to the Jones calculus, Mueller calculus, and Pincaré sphere", en Polarized Light in Optics and Spectroscopy, California: Academic Press, 1990.
dc.relation/*ref*/G. F. Torres del Castillo e I. R. García, "The Jones vector as a spinor and its representation on the Poincare sphere", Rev. Mex. Fís., vol. 57, n.° 5, pp. 406-413, 2011. [En línea]. Disponible en: http://www.scielo.org.mx/pdf/rmf/v57n5/v57n5a4.pdf
dc.relation/*ref*/E. V. Masalov, N. N. Krivin y S. Y. Eshchenko, "Analysis of the influence of a uniform hydrometeorological formation on the polarización characteristics of an electromagnetic wave", Russian Physics Journal, vol. 60, n.° 9, pp. 1469-1475, 2018.
dc.relation/*ref*/T. Nishiyama, "General plane or spherical electromagnetic waves with electric and magnetic fields parallel to each other", Wave Motion, vol. 54, pp. 58-65, 2015. https://doi.org/10.1016/j.wavemoti.2014.11.011
dc.relation/*ref*/R. Hubrich y M. Eckhardt, "Motion vector estimation employing line and column vectors", U. S. Patent 7,852,937 B2, dic. 14, 2010. [En línea]. Disponible en: https://patentimages.storage.googleapis.com/5f/c2/24/f4203476b78bf1/US7852937.pdf
dc.relation/*ref*/R. C. Jones, "A new calculus for the treatment of optical systems. I. Description and Discussion of the Calculus", Journal of the Optical Society of America, vol. 31, n.° 7, pp. 488-493, 1941. https://doi.org/10.1364/JOSA.31.000488
dc.relation/*ref*/R. C. Jones, "A New calculus for the treatment of optical systems. III. The Sohncke theory of optical activity", Journal of the Optical Society of America, vol. 31, n.° 7, pp. 500-503, 1941. https://doi.org/10.1364/JOSA.31.000500
dc.relation/*ref*/E. Bretislav y D. Herschbach, "Stern and Gerlach: how a bad cigar heped reorient atomic physics", Phy. Tod., vol. 56, n.° 12, pp. 53-59, 2003. https://doi.org/10.1063/1.1650229
dc.relation/*ref*/M. Danos, "Fully consistent phase conventions in angular momentum theory", Nucl., Part. Many Body Phy., pp. 319-334, 1972.
dc.relation/*ref*/Y. Mohammed y A. Emadaldeen, "Separation of angular momentum", Am. J. App. Mat.s, vol. 4, n.° 1, pp. 47-52, 2016. https://doi.org/10.11648/j.ajam.20160401.14
dc.relation/*ref*/A. Bertapelle y A. Candilera, "Eigenvectors and eigenvalues: a new formula?", Boll Un. Mat. Ital vol. 13, pp. 329-333, 2020. https://doi.org/10.1007/s40574-020-00222-z
dc.relation/*ref*/D. J. Griffiths, Intr. Quantum Mechs. Nueva Jersey: Prentice-Hall, 1995.
dc.relation/*ref*/I. M. Greca y O. Freire, "Teaching introductory quantum physics and chemistry: caveats from the history of science and science teaching to the training of modern chemists", Chem. Educ. Res. Pract, vol. 15, pp. 286-296, 2014. https://doi.org/10.1039/C4RP00006D
dc.relation/*ref*/J. Kronsbein, "Kinematics-Quaternions-Spinors-and Pauli's Spin Matrices", Am. J. Ph., vol. 35, pp. 335-342, 1967. https://doi.org/10.1119/1.1974074
dc.relation/*ref*/D. A. Konkowski, T. M. Helliwell y C. Wieland, "Quantum singularity of Levi-Civita spacetimes", Class. Quantum Grav., vol. 21, n.° 1, pp. 265-272, 2004. https://doi.org/10.1088/0264-9381/21/1/018
dc.relation/*ref*/G. B. Arfken y H. J. Weber, Física Matemática: Métodos Matemáticos para Engenharia e Física, 6a ed. Río de Janeiro: El Sevier, 2007.
dc.relation/*ref*/H. U. Haq, "Geometry of spin: clifford algebraic approach", Resonance., vol. 21, pp. 1105-1117, 2016. https://doi.org/10.1007/s12045-016-0422-5
dc.relation/*ref*/L. Boi, "Clifford geometric algebras, spin manifolds, and group actions in mathematics and physics", Adv. Appl. Clifford alg., vol. 19, pp. 611-656, 2009. https://doi.org/10.1007/s00006-009-0199-7
dc.relation/*ref*/H. Goldstein, C. P. Poole y J. L. Safko, Classical mechanics, 6a ed. Addison-Wesley, 2001.
dc.relation/*ref*/D. L. Schwartz, "The emergence of abstract representations in dyad problem solving", J. the Lear. Sc., vol.4, n.° 3, pp. 321-354, 1995. https://doi.org/10.1207/s15327809jls0403_3
dc.relation/*ref*/R. C. Jones, "A new calculus for the treatment of optical systems v. a more general formulation, and description of another calculus", J. Op. Soc. Am., vol.. 37, n.° 2, pp. 107-110, 1947. https://doi.org/10.1364/JOSA.37.000107
dc.relation/*ref*/P. Yeh, "Extended Jones matrix method", J. Soc. Am., vol.. 72, n.° 4, pp. 507-513, 1982. https//doi.org/10.1364/JOSA.72.000507
dc.relation/*ref*/A. V. Volyar, T. A. Fadeeva y V. G Shvedov, "Optical vortex generation and jones vector formalims", Op. Spec.,vol. 93, n.° 2, pp. 267-272, 2002. https://doi.org/10.1134/1.1503758
dc.relation/*ref*/A. Lien, "A detailed derivation of extended Jones matrix representation for twisted nematic liquid crystal displays", Liq. Crys., vol. 22, n.° 2, pp. 171-175, 1997. https://doi.org/10.1080/026782997209531
dc.relation/*ref*/S. R. Cloude, "Group theory and polarisation algebra", Optik, vol. 75, n.° 1, pp. 26-36, 1986. [En línea]. Disponible en: http://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=8138457
dc.rightsDerechos de autor 2021 Revista Facultad de Ciencias Básicases-ES
dc.rightshttp://creativecommons.org/licenses/by-nc-nd/4.0es-ES
dc.sourceRevista Facultad de Ciencias Básicas; Vol. 16 No. 2 (2020); 77-85en-US
dc.sourceRevista Facultad de Ciencias Básicas; Vol. 16 Núm. 2 (2020); 77-85es-ES
dc.source2500-5316
dc.source1900-4699
dc.subjectpolarizationen-US
dc.subjectdyadsen-US
dc.subjectspinen-US
dc.subjecttensionersen-US
dc.subjectswitchesen-US
dc.subjectpolarizaciónes-ES
dc.subjectdiadases-ES
dc.subjectespínes-ES
dc.subjecttensoreses-ES
dc.subjectconmutadoreses-ES
dc.subjectpolarizaçãopt-BR
dc.subjectdíadept-BR
dc.subjectspinpt-BR
dc.subjecttensorespt-BR
dc.subjectcomutadorespt-BR
dc.titleGeneration of Pauli Spin Matrices from Jones Vectorsen-US
dc.titleGeneración de las matrices de espín de Paulí a partir de los vectores de Joneses-ES
dc.titleGeração das matrizes de spin de Pauli a partir dos vetores de Jonespt-BR
dc.typeinfo:eu-repo/semantics/article
dc.typeinfo:eu-repo/semantics/publishedVersion


Este ítem pertenece a la siguiente institución