Skip to main content

Introduction

  • Chapter
  • First Online:
Supersymmetry in Mathematics and Physics

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 2027))

  • 2126 Accesses

Abstract

The purpose of this brief introduction is to give a bird’s eye view of supersymmetry for a general mathematical audience. In particular it will include a brief outline of some of the themes that have emerged in recent (and not so recent) work in supersymmetry.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. D. Gross, The coming revolutions in fundamental physics. Talk at UCLA, Feb 22, 2010: http://www.ipam.ucla.edu/videos.aspx

  2. I.Yu. Kobzarev, Yu.I. Manin, Elementary Particles (Kluwer, Dordrecht, 1989)

    MATH  Google Scholar 

  3. J. Wess, B. Zumino, Supergauge invariant extension of quantum electrodynamics. Nucl. Phys. B78, 1–13 (1974)

    Article  MathSciNet  Google Scholar 

  4. S. Ferrara, B. Zumino, Supergauge invariant Yang-Mills Theories. Nucl. Phys. B79, 413–421 (1974)

    Google Scholar 

  5. D.Z. Freedman, P. van Nieuwenhuizen, S. Ferrara, Progress toward a theory of supergravity. Phys. Rev. B113, 3214–3218 (1976)

    Google Scholar 

  6. S. Deser, B. Zumino, Consistent supergravity. Phys. Lett. 62B, 335–337 (1976)

    MathSciNet  Google Scholar 

  7. A. Salam, J. Strathdee, Supergauge tansformations. Nucl. Phys. B76, 477–482 (1974)

    Article  MathSciNet  Google Scholar 

  8. V.S. Varadarajan, Supersymmetry for Mathematicians: An Introduction. AMS-Courant Institute Lecture Notes (2004)

    Google Scholar 

  9. Y. Nambu, in Broken Symmetry: Selected Papers of Y. Nambu, ed. by T. Eguchi, K. Nishijima (World Scientific, NJ, 1995)

    Google Scholar 

  10. S. Ferrara (ed.), Supersymmetry, vols. 1, 2 (World Scientific, Singapore, 1987)

    Google Scholar 

  11. B. Riemann, Collected Papers, ed. by R. Narasimhan (Springer, Berlin, 1990) There are translations of Riemann’s talk in English. See M. Spivak, Differential Geometry, vol. II (Publish or Perish Inc, IL, 1979), pp. 132–134

    Google Scholar 

  12. P. Deligne, J. Morgan, in Notes on Supersymmetry (Following Joseph Bernstein). Quantum Fields and Strings: A Course for Mathematicians, vol. I (American Mathematical Society, RI, 1999), pp. 41–97

    Google Scholar 

  13. C. Carmeli, R. Fioresi, L. Caston, (with an appendix by I. Dimitrov), Mathematical Foundations of Supersymmetry (to appear)

    Google Scholar 

  14. B. Kostant, in Graded Manifolds, Graded Lie Theory, and Prequantization. Differential Geometrical Methods in Mathematical Physics. Lecture Notes in Mathematics, vol. 570 (Springer, Berlin, 1977), pp. 177–306

    Google Scholar 

  15. D.A. Leites, Introduction to the theory of supermanifolds. Russ. Math. Surv. 35(1), 1–64 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  16. D.S. Freed, Five Lectures on Supersymmetry (AMS, RI, 1991)

    Google Scholar 

  17. V.G. Kac, Lie superalgebras. Adv. Math. 26, 8–26 (1977)

    MATH  Google Scholar 

  18. V.G. Kac, in Representations of Classical Lie Superalgebras. Lecture Notes in Mathematics, vol. 676 (Springer, Berlin, 1978), pp. 597–626

    Google Scholar 

  19. I. Dimitrov, Lie Superalgebras. Appendix A, in [13]

    Google Scholar 

  20. H.P. Jakobsen, The full set of unitarizable highest weight modules of basic classical Lie superalgebras. Mem. Am. Math. Soc. 111, 532 (1994)

    MathSciNet  Google Scholar 

  21. Yu.I. Manin, Topics in Noncommutative Geometry (Princeton University Press, Princeton, 1991)

    MATH  Google Scholar 

  22. Yu.I. Manin, Gauge Field Theory and Complex Geometry (Springer, Berlin, 1988)

    MATH  Google Scholar 

  23. P. Deligne, Personal communication

    Google Scholar 

  24. J.A. DomĂ­nguez-PĂ©res, D. HernĂ¡ndez Ruiperez, C. Sancho de Salaz, J. Geom. Phys. 21, 199–217 (1997)

    Google Scholar 

  25. A.Y. Vaintrob, Deformations of complex superspaces and coherent sheaves on them. J. Soviet Math. 51, 2140–2188 (1990)

    Article  Google Scholar 

  26. R. Fioresi, F. Gavarini, Chevalley supergroups. Memoirs of the American Mathematical Society. See preprint arXiv: 0808.0785 (2008) (to appear)

    Google Scholar 

  27. A. Salam, J. Strathdee, Unitary representations of supergauge symmetries. Nucl. Phys. B80, 499–505 (1974)

    Article  MathSciNet  Google Scholar 

  28. C. Carmeli, G. Cassinelli, A. Toigo, V.S. Varadarajan, Unitary representations of super Lie groups and applications to the classification and multiplet structure of super particles. Comm. Math. Phys. 263, 217–258 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  29. H. Salmasian, Unitary representations of nilpotent super Lie groups. Comm. Math. Phys. 297, 189–227 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  30. P. Schneider, Continuous representation theory of p-adic Lie groups. in Proceedings of ICM Madrid 2006, vol. II, pp. 1261–1282

    Google Scholar 

Download references

Acknowledgements

I wish to thank Rita Fioresi, Marian Lledo, Alessio Marrani, and Jeff Rabin for reading earlier drafts of this article, correcting many errors, and suggesting major improvements.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to V. S. Varadarajan .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Varadarajan, V.S. (2011). Introduction. In: Ferrara, S., Fioresi, R., Varadarajan, V. (eds) Supersymmetry in Mathematics and Physics. Lecture Notes in Mathematics(), vol 2027. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21744-9_1

Download citation

Publish with us

Policies and ethics