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Supermanifolds, supersymmetry and berezin integration

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Complex Differential Geometry and Supermanifolds in Strings and Fields

Part of the book series: Lecture Notes in Physics ((LNP,volume 311))

Lecture for the 7th Scheveningen conference on “The mathematical structure of field theories” : August 24th, 1987.

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References

  1. V.Aldaya & J. de Azcarraga A note on the meaning of covariant derivatives in supersymmetry [JMP 26 p1818–21 1985]

    Google Scholar 

  2. — Quantisation as a consequence of the symmetry group: an approach to geometric quantisation [JMP 23(7) p1297–1305 1982]

    Google Scholar 

  3. L.Alvarez-Gaunre & D.Freedman Geometrical structure and Ultraviolet finiteness in the SUSY σ-model [CMP 80 p443–51 1981]

    Google Scholar 

  4. M.Batchelor Two approaches to supermanifolds [Trans A.M.S. 258 p257–70 1979]

    Google Scholar 

  5. — The structure of supermanifolds [Trans A.M.S. 253 p329–38 1979]

    Google Scholar 

  6. —“Graded manifolds and supermanifolds”, p91–134 of ref [S] (an extended version of these lectures is to appear shortly in book form)

    Google Scholar 

  7. M.Batchelor & P.Bryant Graded Riemann Surfaces (to appear in CMP)

    Google Scholar 

  8. U.Bruzzo & R.CianciStructure of supermanifolds and supersymmetry transformations [CMP 95 p393–400 1984]

    Google Scholar 

  9. — On the structure of superfields in a field theory on a supermanifold [Lett.Math.Phys 11 p21–6 1986]

    Google Scholar 

  10. [BC3]— Variational calculus on supermanifolds and invariance properties of superspace field theories [JMP 28(4) p786–91 April 1987]

    Google Scholar 

  11. C.Boyer & S.Gitler Theory of G∞-supermanifolds [Trans A.M.S. 285 p241–67 1984]

    Google Scholar 

  12. P.Bryant Sheaf representations and graded manifolds (to appear in J.Pure & Appl. Alg. 1987)

    Google Scholar 

  13. — de Witt supermanifolds and infinite-dimensional ground rings (submitted to Bull.L.M.S.)

    Google Scholar 

  14. — “GH ∞-supermanifolds, DPMMS preprint 1987

    Google Scholar 

  15. — “The structure of de Witt supermanifolds”, DPMMS preprint, 1987

    Google Scholar 

  16. K.Bugajska Nature of superspace [JMP 21(8) p2091–6 1980]

    Google Scholar 

  17. L.Crane & J.Rabin“Super Riemann surfaces: uniformisation and Teichmuller theory”, EFI preprint 86-25

    Google Scholar 

  18. R.Catenacci,C.Reina & P.Teofilatto On bodies of supermanifolds [JMP 26 p671–4 1985]

    Google Scholar 

  19. R.Cianci Supermanifolds and superLie groups [JMP 25(3) p451–5 1984]

    Google Scholar 

  20. J.Dell & L.SmolinGraded manifold theory as the geometry of supersymmetry [CMP 66 p197–221 1979]

    Google Scholar 

  21. B. de Witt “Supermanifolds”, CUP 1984

    Google Scholar 

  22. P.Freund“Introduction to supersymmetry”, CUP 1986

    Google Scholar 

  23. S.Gates,M.Grisaru,M.Rocek & W.Siegel “Superspace or 1001 lessons in SUSY” (Frontiers of physics 1983)

    Google Scholar 

  24. S. Gates, K. Stelle & P.West Algebraic origins of superspace constraints in Supergravity [Nucl.Phys. B169 p347 1980]

    Google Scholar 

  25. M.Green,A.Schwarz & E. Witten “Superstring theory I,II” CUP 1987

    Google Scholar 

  26. J. Hoyos, M. Quiros, F. de Urries & J.Mittelbrunn Generalised supermanifolds I, II & III [JMP 25 p833–54 1984]

    Google Scholar 

  27. A.Jadczyk & K.PilchSuperspaces and supermanifolds [CMP 78 p373–90 1981]

    Google Scholar 

  28. B.Kostant Graded manifolds, graded Lie theory and prequantisation in “Differential geometric methods in mathematical physics” (Proc. Bonn 1975) S-V lect. notes 570 p177–306 1977.

    Google Scholar 

  29. D.LeitesIntroduction to supermanifolds [Russ.Math. Surv. 35 p1–64 1980]

    Google Scholar 

  30. [L2]— Clifford algebras as superalgebras and quantisation [(transl. from Russ.) Theor.& Math. Phys. 58(2) p150–2 1984]

    Google Scholar 

  31. J.Lott Supersymmetric path integrals [CMP 108 p605–29 1987]

    Google Scholar 

  32. S.Matsumoto & K.Kakazu A note on topology of supermanifolds [JMP 27(11) p2690–2 1986]

    Google Scholar 

  33. H. Nakajina Characterisation of canonical Bose-Fermi systems by “anti-Hermitian” symplectic forms [JMP 24 p1731–512 1983]

    Google Scholar 

  34. R.Picken & K.Sundermeyer Integration on supermanifolds and a geeralised Cartan calculus [CMP 102 p585–604 1986]

    Google Scholar 

  35. J.Rabin Berezin integration on general fermionic supermanifolds [CAT 103 p431–9 1986]

    Google Scholar 

  36. — Supermanifold cohomology and the Wess-Zumino terms of the covariant superstring action [CMP 108 p375–89 1987]

    Google Scholar 

  37. J.Rawnsley “Graded harmonic maps”, Lecture at Trieste meeting on graded differential geometry 1985

    Google Scholar 

  38. J.Rabin & L.CraneHow different are the supermanifolds of de Witt and Rogers? [CMP 102 p123–37 1985]

    Google Scholar 

  39. A.Rogers A global theory of supermanifolds [JMP 21(6) p1352–65 1979]

    Google Scholar 

  40. — SuperLie groups: global topology and local structure [JMP 22 939–45 1981]

    Google Scholar 

  41. — On the existence of global integral forms on supermanifolds[JMP 26(11) p2749–53 1985]

    Google Scholar 

  42. — Consistent superspace integration [JMP 26 p385 1985]

    Google Scholar 

  43. — Graded manifolds,supermanifolds and infinite dimensional Grassmann algebras [CMP 105 p375–84 1986]

    Google Scholar 

  44. — “Fermionic path integration and Grassmann Brownian motion”, preprint, King's College,London 1986 and lectures here.

    Google Scholar 

  45. M.Rothstein“Integration on non-compact supermanifolds”, Washington preprint 1985

    Google Scholar 

  46. H.Ruiperez& J.Munoz MasqueGraded variational calculus [J.de Math. Pures et Appl. 63 and 64 p87–194 1984]

    Google Scholar 

  47. — An intrinsic construction of the Berezinian sheaf on a graded manifold [CR Acd Sci Paris ?]

    Google Scholar 

  48. H-J.Seifert,C.J.S.Clarke & A.Rosenblum (eds) “Mathematical aspects of superspace”, (NATO workshop, Hamburg 1983), Reidel Pub. Co., Dordrecht 1984

    Google Scholar 

  49. A.S.SchwarzSupergravity,complex structure and G-structures [CMP 87 p37–63 1982]

    Google Scholar 

  50. A.S.Schwarz (also A.Voronov) On the definition of superspace [(trans. from Russ.) Theor.& Math.Phys. 60(1) p657–63 1984]

    Google Scholar 

  51. M.Sohnius Supersymmetry in superspace [Phys.Reports 128 p39–204 1985]

    Google Scholar 

  52. P.Srivasta “Supersymmetry,superfields and supergravity”, (Grad. student series in Phys), Adam Hilger 1986

    Google Scholar 

  53. A.Salam & J.Strathdee Superfields and Fermi-Bose symmetry [Phys.Rev.DlI p1521–33 1975]

    Google Scholar 

  54. V.Vladimirov & I.Volovich Superanalysis [(trans. from Russ.) Theor. & Math.Phys. 59(1) p317–34 1984]

    Google Scholar 

  55. J.Wess & J.Bagger“Supersymmetry and Supergravity”, (Princeton series in physics) PUP 1983

    Google Scholar 

  56. R.Yates Fibre bundles and supersymmetry [CMP 76 255–68 1980]

    Google Scholar 

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Authors and Affiliations

  1. Department of Pure Mathematics and Mathematical Statistics, Cambridge University, 16 Mill Lane, CBI 1SB, Cambridge, United Kingdom

    Peter Bryant

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  1. Peter Bryant
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P. J. M. Bongaarts R. Martini

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© 1988 Springer-Verlag

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Bryant, P. (1988). Supermanifolds, supersymmetry and berezin integration. In: Bongaarts, P.J.M., Martini, R. (eds) Complex Differential Geometry and Supermanifolds in Strings and Fields. Lecture Notes in Physics, vol 311. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0038541

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  • DOI: https://doi.org/10.1007/BFb0038541

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  • Print ISBN: 978-3-540-50324-8

  • Online ISBN: 978-3-540-45969-9

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