Academic literature on the topic 'Supergeometry'
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Journal articles on the topic "Supergeometry"
Goertsches, O. "Riemannian supergeometry." Mathematische Zeitschrift 260, no. 3 (December 9, 2007): 557–93. http://dx.doi.org/10.1007/s00209-007-0288-z.
Full textTsimpis, Dimitrios. "Curved 11D Supergeometry." Journal of High Energy Physics 2004, no. 11 (December 2, 2004): 087. http://dx.doi.org/10.1088/1126-6708/2004/11/087.
Full textFioresi, R., and F. Zanchetta. "Representability in supergeometry." Expositiones Mathematicae 35, no. 3 (September 2017): 315–25. http://dx.doi.org/10.1016/j.exmath.2016.10.001.
Full textCATTANEO, ALBERTO S., and FLORIAN SCHÄTZ. "INTRODUCTION TO SUPERGEOMETRY." Reviews in Mathematical Physics 23, no. 06 (July 2011): 669–90. http://dx.doi.org/10.1142/s0129055x11004400.
Full textVoronov, A. A., Yu I. Manin, and I. B. Penkov. "Elements of supergeometry." Journal of Soviet Mathematics 51, no. 1 (August 1990): 2069–83. http://dx.doi.org/10.1007/bf01098184.
Full textSchwarz, A., and I. Shapiro. "Supergeometry and arithmetic geometry." Nuclear Physics B 756, no. 3 (November 2006): 207–18. http://dx.doi.org/10.1016/j.nuclphysb.2006.08.024.
Full textHoker, E. D., and D. H. Phong. "Complex geometry and supergeometry." Current Developments in Mathematics 2005, no. 1 (2005): 1–40. http://dx.doi.org/10.4310/cdm.2005.v2005.n1.a1.
Full textLott, John. "Torsion constraints in supergeometry." Communications in Mathematical Physics 133, no. 3 (November 1990): 563–615. http://dx.doi.org/10.1007/bf02097010.
Full textSchmitt, Thomas. "Supergeometry and hermitian conjugation." Journal of Geometry and Physics 7, no. 2 (January 1990): 141–69. http://dx.doi.org/10.1016/0393-0440(90)90009-r.
Full textSchwarz, Albert. "Noncommutative supergeometry, duality and deformations." Nuclear Physics B 650, no. 3 (February 2003): 475–96. http://dx.doi.org/10.1016/s0550-3213(02)01088-x.
Full textDissertations / Theses on the topic "Supergeometry"
Kleppe, Anne Friederike. "Supersymmetry, spinors and supergeometry." Thesis, University of Cambridge, 2006. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.613938.
Full textPilato, Alejandro Miguel. "Elementary states, supergeometry and twistor theory." Thesis, University of Oxford, 1986. http://ora.ox.ac.uk/objects/uuid:d86c78d7-2e6e-4a5c-a37a-81d8dbf3ccd8.
Full textZanchetta, Ferdinando. "Supergeometry: a categorical point of view." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2015. http://amslaurea.unibo.it/9027/.
Full textCovolo, Tiffany. "(Z2)n-Superalgebra and (Z2)n-Supergeometry." Thesis, Lyon 1, 2014. http://www.theses.fr/2014LYO10203.
Full textThe present thesis deals with a development of linear algebra, geometry and analysis based on (Z2)n-superalgebras ; associative unital algebras which are (Z2)n-graded and graded-commutative, i.e. statisfying ab=(-1)ba, for all homogeneous elements a, b of respective degrees deg(a), deg(b) in (Z2)n (<.,.> denoting the usual scalar product). This generalization widens the range of applications of supergeometry to many mathematical structures (quaternions and more generally Clifford algebras, Deligne algebra of superdifferential forms, higher vector bundles) and appears also in physics (for describing paraparticles) proving its worth and relevance. In this dissertation, we first focus on (Z2)n-superalgebra theory ; we define and characterize the notions of trace and (super)determinant of matrices over graded-commutative algebras. Special attention is given to the case of Clifford algebras, where our study gives a new approach to treat the classical problem of finding a “good” determinant for matrices with noncommuting (quaternionic) entries. Further, we undertake the study of (Z2)n-graded differential geometry. Privileging the ringed space approach, we define (smooth) (Z2)n-supermanifolds modeling their algebras of functions on the (Z2)n-commutative algebra of formal power series in graded variables, and develop the theory along the lines of supergeometry. Notable results are : the graded Berezinian and its cohomological interpretation (essential to establish integration theory) ; the theorem of morphism, which states that a morphism of (Z2)n-supermanifolds can be recovered from its coordinate expression ; Batchelor-Gawedzki theorem for (Z2)n-supermanifolds
NOJA, SIMONE. "TOPICS IN ALGEBRAIC SUPERGEOMETRY OVER PROJECTIVE SPACES." Doctoral thesis, Università degli Studi di Milano, 2018. http://hdl.handle.net/2434/554352.
Full textThe aim of this thesis is to study some topics in algebraic supergeometry, in particular in the case the supermanifolds have their reduced manifolds given by complex projective spaces $\mathbb{P}^n$. After the main definitions and notions in supergeometry are introduced, the geometry of complex projective superspaces $\mathbb{P}^{n|m}$ is studied in detail. Invertible sheaves and their cohomology, infinitesimal automorphisms and deformations are studied for $\mathbb{P}^{n|m}$. Special attention is paid to the case of the Calabi-Yau supercurve $\mathbb{P}^{1|2}$. The focus is then moved to non-projected supermanifolds over $\mathbb{P}^n$. A complete classification is given in the case the odd dimension is $2$, showing that there exist non-projected supermanifolds only over the projective line $\mathbb{P}^1$ and projective plane $\mathbb{P}^2$. In particular, it is shown that all of the non-projected supermanifolds over $\mathbb{P}^2$ are Calabi-Yau's, i.e.\ they have trivial Berezinian sheaf, and they are all non-projective, i.e.\ they cannot be embedded into any ordinary projective superspace $\mathbb{P}^{n|m}$. Instead, it is shown that there always exist an embedding of these supermanifolds in super Grassmannians, and some meaningful examples are realised explicitly. Finally, a new construction of $\Pi$-projective spaces as non-projected supermanifolds related to the cotangent sheaf over $\mathbb{P}^n $ is given.
Cuzzola, Angelo. "Aspects of supergeometry in locally covariant quantum field theory." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2016. http://amslaurea.unibo.it/10391/.
Full textGreitz, Jesper. "Supergravity in superspace : supergeometry, differential forms and algebraic structure." Thesis, King's College London (University of London), 2012. https://kclpure.kcl.ac.uk/portal/en/theses/supergravity-in-superspace(4ef77d1c-bdc8-4d1c-aa99-254929a3c14b).html.
Full textHanisch, Florian. "Variational problems on supermanifolds." Phd thesis, Universität Potsdam, 2011. http://opus.kobv.de/ubp/volltexte/2012/5975/.
Full textIn dieser Dissertation wird die Formulierung von Variationsproblemen auf Supermannigfaltigkeiten diskutiert. Supermannigfaltigkeiten enthalten sowohl bosonische als auch fermionische Freiheitsgrade. Fermionische Felder nehmen Werte im ungeraden Teil einer Grassmannalgebra an, sie antikommutieren deshalb untereinander. Eine systematische Behandlung dieser Grassmann-Parameter erfordert jedoch die Beschreibung von Räumen durch Funktoren, z.B. von der Kategorie der Grassmannalgebren in diejenige der Mengen (der topologischen Räume, Mannigfaltigkeiten, ...). Nach einer Einführung in das allgemeine Konzept dieses Zugangs verwenden wir es um eine Beschreibung der resultierenden Supermannigfaltigkeit der Felder bzw. Abbildungen anzugeben. Wir zeigen, dass jede Abbildung eindeutig durch eine Familie von Differentialoperatoren geeigneter Ordnung charakterisiert wird. Darüber hinaus beweisen wir, dass jede solche Abbildung eineindeutig durch ihre Komponentenfelder, d.h. durch die Koeffizienten einer Taylorentwickelung bzgl. von ungeraden Koordinaten bestimmt ist. Im Allgemeinen sind Komponentenfelder nur lokal definiert. Wir stellen einen Weg vor, der diese Einschränkung umgeht: Durch das Vergrößern der betreffenden Supermannigfaltigkeit ist es immer möglich, mit globalen Koordinaten zu arbeiten. Schließlich wenden wir diesen Formalismus an, um Variationsprobleme zu untersuchen, genauer betrachten wir eine super-Version der Geodäte und eine Verallgemeinerung von harmonischen Abbildungen auf Supermannigfaltigkeiten. Bewegungsgleichungen werden von Energiefunktionalen abgeleitet und wir zeigen, wie sie sich in Komponenten zerlegen lassen. Schließlich kann in Spezialfällen die Existenz von kritischen Punkten gezeigt werden, indem das Problem auf Gleichungen der gewöhnlichen geometrischen Analysis reduziert wird. Es kann dann gezeigt werden, dass die Lösungen dieser Gleichungen sich zu kritischen Punkten im betreffenden Funktor-Raum der Felder zusammensetzt.
Papantonis, Theocharis [Verfasser]. "Z-graded supergeometry: Differential graded modules, higher algebroid representations, and linear structures / Theocharis Papantonis." Göttingen : Niedersächsische Staats- und Universitätsbibliothek Göttingen, 2021. http://d-nb.info/1236401727/34.
Full textOstermayr, Dominik [Verfasser], Alexander [Gutachter] Alldridge, George [Gutachter] Marinescu, and Tilmann [Gutachter] Wurzbacher. "Some results in supergeometry: Harmonic maps from super Riemann surfaces and Automorphism supergroups of supermanifolds / Dominik Ostermayr ; Gutachter: Alexander Alldridge, George Marinescu, Tilmann Wurzbacher." Köln : Universitäts- und Stadtbibliothek Köln, 2017. http://d-nb.info/1129872475/34.
Full textBooks on the topic "Supergeometry"
Keßler, Enno. Supergeometry, Super Riemann Surfaces and the Superconformal Action Functional. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-13758-8.
Full textKeßler, Enno. Supergeometry, Super Riemann Surfaces and the Superconformal Action Functional. Springer, 2019.
Find full textBook chapters on the topic "Supergeometry"
Manin, Yuri Ivanovich. "Introduction to Supergeometry." In Grundlehren der mathematischen Wissenschaften, 181–232. Berlin, Heidelberg: Springer Berlin Heidelberg, 1997. http://dx.doi.org/10.1007/978-3-662-07386-5_5.
Full textJulia, B. "Supergeometry and Kac-Moody Algebras." In Mathematical Sciences Research Institute Publications, 393–409. New York, NY: Springer US, 1985. http://dx.doi.org/10.1007/978-1-4613-9550-8_19.
Full textGrosse, H., and G. Reiter. "Noncommutative Supergeometry of Graded Matrix Algebras." In Geometry and Quantum Physics, 386. Berlin, Heidelberg: Springer Berlin Heidelberg, 2000. http://dx.doi.org/10.1007/3-540-46552-9_11.
Full textKeßler, Enno. "Introduction." In Supergeometry, Super Riemann Surfaces and the Superconformal Action Functional, 1–9. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-13758-8_1.
Full textKeßler, Enno. "Connections on Super Riemann Surfaces." In Supergeometry, Super Riemann Surfaces and the Superconformal Action Functional, 169–83. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-13758-8_10.
Full textKeßler, Enno. "Metrics and Gravitinos." In Supergeometry, Super Riemann Surfaces and the Superconformal Action Functional, 185–213. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-13758-8_11.
Full textKeßler, Enno. "The Superconformal Action Functional." In Supergeometry, Super Riemann Surfaces and the Superconformal Action Functional, 215–34. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-13758-8_12.
Full textKeßler, Enno. "Computations in Wess–Zumino Gauge." In Supergeometry, Super Riemann Surfaces and the Superconformal Action Functional, 235–78. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-13758-8_13.
Full textKeßler, Enno. "Linear Superalgebra." In Supergeometry, Super Riemann Surfaces and the Superconformal Action Functional, 13–40. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-13758-8_2.
Full textKeßler, Enno. "Supermanifolds." In Supergeometry, Super Riemann Surfaces and the Superconformal Action Functional, 41–66. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-13758-8_3.
Full textConference papers on the topic "Supergeometry"
Heller, Marc Andre, Noriaki Ikeda, and Satoshi Watamura. "Courant algebroids from double field theory in supergeometry." In Workshop on Strings, Membranes and Topological Field Theory. WORLD SCIENTIFIC, 2017. http://dx.doi.org/10.1142/9789813144613_0008.
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