Academic literature on the topic 'Spacetime algebra'
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Journal articles on the topic "Spacetime algebra"
KAY, BERNARD S. "THE PRINCIPLE OF LOCALITY AND QUANTUM FIELD THEORY ON (NON GLOBALLY HYPERBOLIC) CURVED SPACETIMES." Reviews in Mathematical Physics 04, spec01 (December 1992): 167–95. http://dx.doi.org/10.1142/s0129055x92000194.
Full textDA ROCHA, R., and J. VAZ. "CONFORMAL STRUCTURES AND TWISTORS IN THE PARAVECTOR MODEL OF SPACETIME." International Journal of Geometric Methods in Modern Physics 04, no. 04 (June 2007): 547–76. http://dx.doi.org/10.1142/s0219887807002193.
Full textGRESNIGT, N. G., P. F. RENAUD, and P. H. BUTLER. "THE STABILIZED POINCARE–HEISENBERG ALGEBRA: A CLIFFORD ALGEBRA VIEWPOINT." International Journal of Modern Physics D 16, no. 09 (September 2007): 1519–29. http://dx.doi.org/10.1142/s0218271807010857.
Full textKOVAČEVIĆ, DOMAGOJ, and STJEPAN MELJANAC. "KAPPA-MINKOWSKI SPACETIME, KAPPA-POINCARÉ HOPF ALGEBRA AND REALIZATIONS." International Journal of Geometric Methods in Modern Physics 09, no. 06 (August 3, 2012): 1261009. http://dx.doi.org/10.1142/s0219887812610099.
Full textDASZKIEWICZ, MARCIN. "CANONICAL AND LIE-ALGEBRAIC TWIST DEFORMATIONS OF GALILEI ALGEBRA." Modern Physics Letters A 23, no. 07 (March 7, 2008): 505–17. http://dx.doi.org/10.1142/s0217732308026479.
Full textObaidullah, U., and Sameerah Jamal. "pp-wave potential functions: A complete study using Noether symmetries." International Journal of Geometric Methods in Modern Physics 18, no. 07 (March 18, 2021): 2150108. http://dx.doi.org/10.1142/s0219887821501085.
Full textMoia, Alessandro. "Noncommutative Spacetime Symmetries from Covariant Quantum Mechanics." Advances in High Energy Physics 2017 (2017): 1–8. http://dx.doi.org/10.1155/2017/4042314.
Full textMORETTI, VALTER. "ASPECTS OF NONCOMMUTATIVE LORENTZIAN GEOMETRY FOR GLOBALLY HYPERBOLIC SPACETIMES." Reviews in Mathematical Physics 15, no. 10 (December 2003): 1171–217. http://dx.doi.org/10.1142/s0129055x03001886.
Full textSCIPIONI, R. "G-ALGEBRA AND CURVED SPACETIME." Modern Physics Letters A 10, no. 23 (July 30, 1995): 1705–9. http://dx.doi.org/10.1142/s0217732395001824.
Full textRoque, Waldir L., and Renato P. Dos Santos. "Computer algebra in spacetime embedding." Journal of Symbolic Computation 12, no. 3 (September 1991): 381–89. http://dx.doi.org/10.1016/s0747-7171(08)80156-3.
Full textDissertations / Theses on the topic "Spacetime algebra"
Joly, Gordon Charles. "Applications of computer algebra systems to general relativity theory." Thesis, Queen Mary, University of London, 1986. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.284039.
Full textHicks, Jesse W. "Classification of Spacetimes with Symmetry." DigitalCommons@USU, 2016. https://digitalcommons.usu.edu/etd/5054.
Full textBär, Christian, and Nicolas Ginoux. "Classical and quantum fields on Lorentzian manifolds." Universität Potsdam, 2012. http://opus.kobv.de/ubp/volltexte/2012/5997/.
Full textPollney, Denis. "Algebraic and numerical techniques in general relativity : the classification of spacetimes via the Cartan-Karlhede method, and Cauchy-characteristic matching for numerically generated spacetimes." Thesis, University of Southampton, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.393927.
Full textEltzner, Benjamin. "Local Thermal Equilibrium on Curved Spacetimes and Linear Cosmological Perturbation Theory." Doctoral thesis, Universitätsbibliothek Leipzig, 2013. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-117472.
Full textIn dieser Arbeit wird die von Schlemmer eingeführte Erweiterung des Kriteriums für lokales thermisches Gleichgewicht in Quantenfeldtheorien von Buchholz, Ojima und Roos auf gekrümmte Raumzeiten untersucht. Dabei werden verschiedene Probleme identifiziert und insbesondere die bereits von Schlemmer gezeigte Instabilität unter Zeitentwicklung untersucht. Es wird eine alternative Herangehensweise an lokales thermisches Gleichgewicht in Quantenfeldtheorien auf gekrümmten Raumzeiten vorgestellt und deren Probleme diskutiert. Es wird dann eine Untersuchung des dynamischen Systems der linearen Feld- und Metrikstörungen im üblichen Inflationsmodell mit Blick auf Uneindeutigkeit der Quantisierung durchgeführt. Zuletzt werden die Temperaturfluktuationen der kosmischen Hintergrundstrahlung auf Kompatibilität mit lokalem thermalem Gleichgewicht überprüft
Ribeiro, Pedro Lauridsen. "Aspectos estruturais e dinâmicos da correspondência AdS/CFT: Uma abordagem rigorosa." Universidade de São Paulo, 2007. http://www.teses.usp.br/teses/disponiveis/43/43134/tde-14012008-131931/.
Full textWe elaborate a detailed study of certain aspects of (a version of) the AdS/CFT correspondence, conjectured by Maldacena and Witten, between quantum field theories in a gravitational background given by an asymptotically anti-de Sitter (AAdS) spacetime, and conformally covariant quantum field theories in the latter\'s conformal infinity (in the sense of Penrose), aspects such that: (a) are independent from (the pair of) specific models in Quantum Field Theory, and (b) susceptible to a recast in a mathematically rigorous mould. We adopt as a starting point the theorem demonstrated by Rehren in the context of Local Quantum Physics (also known as Algebraic Quantum Field Theory) in anti-de Sitter (AdS) spacetimes, called algebraic holography or Rehren duality. The main body of the present work consists in extending Rehren\'s result to a reasonably general class of d-dimensional AAdS spacetimes (d>3), scrutinizing how the properties of such an extension are weakened and/or modified as compared to AdS spacetime, and probing how non-trivial gravitational effects manifest themselves in the conformal infinity\'s quantum theory. Among the obtained results, we quote: not only does the imposition of reasonably general conditions on bulk null geodesics (whose plausibility we justify through geometrical rigidity techniques) guarantee that our generalization is geometrically consistent with causality, but it also allows a ``holographic\'\' reconstruction of the bulk topology in the absence of horizons and singularities; the implementation of conformal symmetries in the boundary, which we explicitly associate to an intrinsically constructed family of bulk asymptotic isometries, have a purely asymptotic character and is dynamically attained through a process of return to equilibrium, given suitable boundary conditions at infinity; gravitational effects may cause obstructions to the reconstruction of the bulk quantum theory, either by making the latter trivial in sufficiently small regions or due to the existence of multiple inequivalent vacua, which on their turn lead to the existence of solitonic excitations localized around domain walls, similar to D-branes. The proofs make extensive use of global Lorentzian geometry. The language employed for the quantum theories relevant for our generalization of Rehren duality follows the functorial formulation of Local Quantum Physics due to Brunetti, Fredenhagen and Verch, extended afterwards by Sommer in order to incorporate boundary conditions. (An English translation of the full text can be found at arXiv:0712.0401)
Švarc, Robert. "Studium přesných prostoročasů." Doctoral thesis, 2012. http://www.nusl.cz/ntk/nusl-306311.
Full textMühlhoff, Rainer. "Higher spin fields on curved spacetimes." 2007. https://ul.qucosa.de/id/qucosa%3A16477.
Full textEltzner, Benjamin. "Local Thermal Equilibrium on Curved Spacetimes and Linear Cosmological Perturbation Theory." Doctoral thesis, 2012. https://ul.qucosa.de/id/qucosa%3A12005.
Full textIn dieser Arbeit wird die von Schlemmer eingeführte Erweiterung des Kriteriums für lokales thermisches Gleichgewicht in Quantenfeldtheorien von Buchholz, Ojima und Roos auf gekrümmte Raumzeiten untersucht. Dabei werden verschiedene Probleme identifiziert und insbesondere die bereits von Schlemmer gezeigte Instabilität unter Zeitentwicklung untersucht. Es wird eine alternative Herangehensweise an lokales thermisches Gleichgewicht in Quantenfeldtheorien auf gekrümmten Raumzeiten vorgestellt und deren Probleme diskutiert. Es wird dann eine Untersuchung des dynamischen Systems der linearen Feld- und Metrikstörungen im üblichen Inflationsmodell mit Blick auf Uneindeutigkeit der Quantisierung durchgeführt. Zuletzt werden die Temperaturfluktuationen der kosmischen Hintergrundstrahlung auf Kompatibilität mit lokalem thermalem Gleichgewicht überprüft.:1. Introduction 5 2. Technical Background 10 2.1. The Free Scalar Field on a Globally Hyperbolic Spacetime . . . . . . 10 2.1.1. Construction of the Scalar Field . . . . . . . . . . . . . . . . . 10 2.1.2. Algebra of Wick Products . . . . . . . . . . . . . . . . . . . . 13 2.1.3. Local Covariance Principle . . . . . . . . . . . . . . . . . . . . 17 2.2. Local Thermal Equilibirum . . . . . . . . . . . . . . . . . . . . . . . 21 2.2.1. Global Thermodynamic Equilibrium - KMS States . . . . . . 21 2.2.2. Local Thermal Observables . . . . . . . . . . . . . . . . . . . 24 2.2.3. LTE on Flat Spacetime . . . . . . . . . . . . . . . . . . . . . . 29 2.2.4. LTE in Cosmological Spacetimes . . . . . . . . . . . . . . . . 32 2.3. Linear Scalar Cosmological Perturbations . . . . . . . . . . . . . . . . 34 2.3.1. Robertson-Walker Cosmology . . . . . . . . . . . . . . . . . . 35 2.3.2. Mathematical Background . . . . . . . . . . . . . . . . . . . . 38 2.3.3. Technical Framework and Formulae . . . . . . . . . . . . . . . 40 2.3.4. The Boltzmann Equation . . . . . . . . . . . . . . . . . . . . 46 2.3.5. The Sachs-Wolfe Effect for Adiabatic Perturbations . . . . . . 49 3. Towards a Refinement of the LTE Condition on Curved Spacetimes 54 3.1. Non-Minimal Coupling . . . . . . . . . . . . . . . . . . . . . . . . . . 54 3.1.1. Commutator Distribution . . . . . . . . . . . . . . . . . . . . 55 3.1.2. KMS Two-Point Function . . . . . . . . . . . . . . . . . . . . 57 3.1.3. Balanced Derivatives . . . . . . . . . . . . . . . . . . . . . . . 61 3.2. Conformally Static Spacetimes . . . . . . . . . . . . . . . . . . . . . . 65 3.2.1. Conformal KMS States . . . . . . . . . . . . . . . . . . . . . . 66 3.2.2. Extrinsic LTE in de Sitter Spacetime . . . . . . . . . . . . . . 71 3.3. Massive Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 3.3.1. Properties of the Model . . . . . . . . . . . . . . . . . . . . . 78 3.3.2. Bogoliubov Transformation . . . . . . . . . . . . . . . . . . . 80 3.3.3. Thermal Observables . . . . . . . . . . . . . . . . . . . . . . . 82 3.4. Towards an Alternative Concept . . . . . . . . . . . . . . . . . . . . . 91 3.4.1. Problems and Open Questions Concerning LTE . . . . . . . . 92 3.4.2. Dynamic Equations . . . . . . . . . . . . . . . . . . . . . . . . 94 3.4.3. Positivity Inequalities . . . . . . . . . . . . . . . . . . . . . . . 96 3.4.4. Macroobservable Interpretation . . . . . . . . . . . . . . . . . 100 3.5. An Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 4. Cosmological Perturbation Theory 105 4.1. Dynamics of Perturbations in Inflation . . . . . . . . . . . . . . . . . 106 4.1.1. CCR Quantisation is Ambiguous . . . . . . . . . . . . . . . . 106 4.1.2. Canonical Symplectic Form . . . . . . . . . . . . . . . . . . . 111 4.1.3. The Algebraic Point of View . . . . . . . . . . . . . . . . . . . 117 4.2. LTE States in Cosmology . . . . . . . . . . . . . . . . . . . . . . . . 120 4.2.1. The Link to Fluid Dynamics . . . . . . . . . . . . . . . . . . . 120 4.2.2. Incompatibility of LTE with Sachs-Wolfe Effect . . . . . . . . 125 5. Conclusion and Outlook 131 A. Technical proofs 136 A.1. Proof of Lemma 3.2.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . 136 A.2. Proof of Lemma 3.2.6 . . . . . . . . . . . . . . . . . . . . . . . . . . . 138 A.3. Proof of Lemma 3.4.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 A.4. Idea of Proof for Conjecture 3.4.3 . . . . . . . . . . . . . . . . . . . . 144 B. Introduction to Probability Theory 146 Bibliography 150 Correction of Lemma 3.1.2 155
Books on the topic "Spacetime algebra"
Dodson, C. T. J. Categories, Bundles and Spacetime Topology. Dordrecht: Springer Netherlands, 1988.
Find full textCallahan, James. The geometry of spacetime: An introduction to special and general relativity. New York: Springer, 2000.
Find full textNoncommutative spacetimes: Symmetries in noncommutative geometry and field theory. Berlin: Springer, 2009.
Find full textHack, Thomas-Paul. Cosmological Applications of Algebraic Quantum Field Theory in Curved Spacetimes. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-21894-6.
Full textConformal Algebra In Spacetime And Operator Product Expansion. Springer-Verlag Berlin and Heidelberg GmbH &, 2013.
Find full textSobczyk, Garret. Matrix Gateway to Geometric Algebra, Spacetime and Spinors. Independently Published, 2019.
Find full textAschieri, Paolo, Fedele Lizzi, Julius Wess, Marija Dimitrijevic, and Petr Kulish. Noncommutative Spacetimes: Symmetries in Noncommutative Geometry and Field Theory. Springer, 2011.
Find full textAschieri, Paolo, Fedele Lizzi, Julius Wess, Marija Dimitrijevic, and Petr Kulish. Noncommutative Spacetimes: Symmetries in Noncommutative Geometry and Field Theory. Springer London, Limited, 2009.
Find full textBaker, David John. The Philosophy of Quantum Field Theory. Oxford University Press, 2016. http://dx.doi.org/10.1093/oxfordhb/9780199935314.013.33.
Full textBook chapters on the topic "Spacetime algebra"
Arzano, Michele, and Jerzy Kowalski-Glikman. "Hopf Algebra Relativistic Symmetries: The $$\kappa $$-Poincaré Algebra." In Deformations of Spacetime Symmetries, 115–39. Berlin, Heidelberg: Springer Berlin Heidelberg, 2021. http://dx.doi.org/10.1007/978-3-662-63097-6_5.
Full textCosgrove, Joseph K. "The Historical Sense-Structure of Symbolic Algebra." In Relativity without Spacetime, 69–100. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-72631-1_4.
Full textBabin, Anatoli, and Alexander Figotin. "Basics of Spacetime Algebra (STA)." In Neoclassical Theory of Electromagnetic Interactions, 431–39. London: Springer London, 2016. http://dx.doi.org/10.1007/978-1-4471-7284-0_23.
Full textMaks, Johannes G. "Spacetime Algebra and Line Geometry." In Clifford (Geometric) Algebras, 449–57. Boston, MA: Birkhäuser Boston, 1996. http://dx.doi.org/10.1007/978-1-4612-4104-1_31.
Full textSomaroo, Shyamal. "Higher Spin and the Spacetime Algebra." In Clifford Algebras and Their Application in Mathematical Physics, 347–68. Dordrecht: Springer Netherlands, 1998. http://dx.doi.org/10.1007/978-94-011-5036-1_27.
Full textLewis, Antony, Anthony Lasenby, and Chris Doran. "Electron Scattering in the Spacetime Algebra." In Clifford Algebras and their Applications in Mathematical Physics, 49–71. Boston, MA: Birkhäuser Boston, 2000. http://dx.doi.org/10.1007/978-1-4612-1368-0_4.
Full textRodrigues, Waldyr A., and Edmundo Capelas de Oliveira. "A Clifford Algebra Lagrangian Formalism in Minkowski Spacetime." In The Many Faces of Maxwell, Dirac and Einstein Equations, 331–58. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-27637-3_8.
Full textHavel, Timothy F., and Chris J. L. Doran. "Interaction and Entanglement in the Multiparticle Spacetime Algebra." In Applications of Geometric Algebra in Computer Science and Engineering, 227–47. Boston, MA: Birkhäuser Boston, 2002. http://dx.doi.org/10.1007/978-1-4612-0089-5_21.
Full textSugon, Quirino M., and Daniel McNamara. "A Hestenes Spacetime Algebra Approach to Light Polarization." In Applications of Geometric Algebra in Computer Science and Engineering, 297–306. Boston, MA: Birkhäuser Boston, 2002. http://dx.doi.org/10.1007/978-1-4612-0089-5_26.
Full textDoran, Chris, Anthony Lasenby, and Stephen Gull. "Gravity as a Gauge Theory in the Spacetime Algebra." In Clifford Algebras and their Applications in Mathematical Physics, 375–85. Dordrecht: Springer Netherlands, 1993. http://dx.doi.org/10.1007/978-94-011-2006-7_42.
Full textConference papers on the topic "Spacetime algebra"
Morgan, Matthew A. "A Macroscopic Field Equation in Spacetime Algebra." In 2022 3rd URSI Atlantic and Asia Pacific Radio Science Meeting (AT-AP-RASC). IEEE, 2022. http://dx.doi.org/10.23919/at-ap-rasc54737.2022.9814283.
Full textArzano, Michele. "Quantum fields, Noether charges and Hopf algebra spacetime symmetries." In From Quantum to Emergent Gravity: Theory and Phenomenology. Trieste, Italy: Sissa Medialab, 2008. http://dx.doi.org/10.22323/1.043.0005.
Full textMatos, S. A., C. R. Paiva, and A. M. Barbosa. "A spacetime algebra approach to moving bi-isotropic media." In amp; USNC/URSI National Radio Science Meeting. IEEE, 2009. http://dx.doi.org/10.1109/aps.2009.5172315.
Full textLuo, Wen, Linwang Yuan, Minjie Wu, and Zhaoyuan Yu. "Spatial-temporal data analysis with spacetime algebra: A case study with satellite altimetry data." In 2010 18th International Conference on Geoinformatics. IEEE, 2010. http://dx.doi.org/10.1109/geoinformatics.2010.5567880.
Full textAGNEW, ALFONSO F. "SPACETIME ALGEBRAS AND TWISTOR THEORY." In Proceedings of the 3rd ISAAC Congress. World Scientific Publishing Company, 2003. http://dx.doi.org/10.1142/9789812794253_0046.
Full textRAPTIS, IOANNIS, PETROS WALLDEN, and ROMÀN R. ZAPATRIN. "ALGEBRAIC APPROACH TO 'QUANTUM SPACETIME GEOMETRY'." In Proceedings of the MG11 Meeting on General Relativity. World Scientific Publishing Company, 2008. http://dx.doi.org/10.1142/9789812834300_0522.
Full textAMELINO-CAMELIA, G., M. ARZANO, and L. DOPLICHER. "FIELD THEORIES ON CANONICAL AND LIE-ALGEBRA NONCOMMUTATIVE SPACETIMES." In Proceedings of the 25th Johns Hopkins Workshop on Current Problems in Particle Theory. WORLD SCIENTIFIC, 2003. http://dx.doi.org/10.1142/9789812791368_0027.
Full textMorita, Katsusada. "Algebraic Gauge Theory of Quarks and Leptons." In Proceedings of CST-MISC Joint Symposium on Particle Physics — from Spacetime Dynamics to Phenomenology —. Journal of the Physical Society of Japan, 2015. http://dx.doi.org/10.7566/jpscp.7.010010.
Full textDappiaggi, Claudio. "An overview on algebraic quantum field theory on curved spacetimes." In Proceedings of the Corfu Summer Institute 2015. Trieste, Italy: Sissa Medialab, 2016. http://dx.doi.org/10.22323/1.263.0098.
Full textšvarc, Robert, and Jiří Podolský. "Algebraic aspects of general non-twisting and shear-free spacetimes." In Proceedings of the MG14 Meeting on General Relativity. WORLD SCIENTIFIC, 2017. http://dx.doi.org/10.1142/9789813226609_0301.
Full textReports on the topic "Spacetime algebra"
Ashby, S. F., S. L. Lee, L. R. Petzold, P. E. Saylor, and E. Seidel. Computing spacetime curvature via differential-algebraic equations. Office of Scientific and Technical Information (OSTI), January 1996. http://dx.doi.org/10.2172/221033.
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