Skip to main content
SpringerLink
Log in

Towards a q-Deformed Supersymmetric Field Theory

  • Chapter
Book cover Quantum Field Theory

  • 2342 Accesses

Abstract

This article intends to show the possibility of building noncommutative, q-deformed structures in a way that is analog to the commutative case. Especially, some aspects concerning q-deformed superspaces and q-deformed superalgebras are considered.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover 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. W. Heisenberg, 1930 Z. Phys. 64 4 & 1938 Ann. Phys. 32 20.

    ADS  Google Scholar 

  2. H.S. Snyder, Quantized space-time, Phys. Rev. 71 (1947) 38–41.

    Article  MATH  ADS  MathSciNet  Google Scholar 

  3. A. Einstein Out of My Later Years

    Google Scholar 

  4. H. Grosse, C. Klimčik, and P. Prešnajder, Towards finite quantum field theory in non-commutative geometry, 1996 Int. J. Theor. Phys. 35 231 [hep-th/9505175]

    Article  MATH  Google Scholar 

  5. S. Majid, On the q-regularisation, 1990 Int. J. Mod. Phys. A 5 4689

    Article  MATH  ADS  MathSciNet  Google Scholar 

  6. R. Oeckl, Braided Quantum Field Theory, 2001 Commun. Math. Phys. 217 451

    Article  MATH  ADS  MathSciNet  Google Scholar 

  7. M. Chaichian, A.P. Demichev, Phys. Lett. B 320 273 (1994) [hep-th/9310001]

    Article  ADS  MathSciNet  Google Scholar 

  8. C. Blohmann, Free q-deformed relativistic wave equations by representation theory, 2003 Eur. Phys. J. C 30 435 [hep-th/0111172]

    Article  MATH  ADS  MathSciNet  Google Scholar 

  9. M. Fichtmüller, A. Lorek, and J. Wess, q-deformed Phase Space and its Lattice Structure, 1996 Z. Phys. C 71 533 [hep-th/9511106]; J. Wess, q-deformed phase space and its lattice structure, 1997 Int. J. Mod. Phys. A 12 4997

    ADS  MathSciNet  Google Scholar 

  10. B.L. Cerchiai and J. Wess, q-Deformed Minkowski Space based on a q-Lorentz Algebra, 1998 Eur. Phys. J. C 5 553 [math.QA/9801104]

    ADS  MathSciNet  Google Scholar 

  11. D. Mikulovic, A. Schmidt and H. Wachter, Grassmann variables on quantum spaces, Eur. Phys. J. C 45 (2006) 529, [hep-th/0407273].

    Article  ADS  Google Scholar 

  12. A. Schmidt and H. Wachter, Superanalysis on quantum spaces, JHEP 0601 (2006) 84, [hep-th/0411180].

    Article  ADS  MathSciNet  Google Scholar 

  13. A. Schmidt and H. Wachter, q-Deformed quantum Lie algebras, J. Geom. Phys. 56 (2006), [mat-ph/0500932].

    Google Scholar 

  14. A. Schmidt, H. Wachter q-Deformed Superalgebras, preprint [hep-th/0705.1683].

    Google Scholar 

  15. J. Wess, q-deformed Heisenberg Algebras, in H. Gausterer, H. Grosse and L. Pittner, Eds., Proceedings of the 38. Internationale Universitätswochen für Kern-und Teilchen physik, no. 543 in Lect. Notes in Phys., Springer-Verlag, Schladming (2000), math-phy/9910013.

    Google Scholar 

  16. H. Wachter Towards a q-Deformed Quantum Field Theory, Printed in this volume.

    Google Scholar 

  17. H. Wachter, Analysis on q-deformed quantum spaces, Int. J. Mod. Phys. A 22 (2007) 95.

    Article  MATH  ADS  MathSciNet  Google Scholar 

  18. S. L. Woronowicz, Compact matrix pseudogroups, Commun. Math. Phys. 111 (1987) 613.

    Article  MATH  ADS  MathSciNet  Google Scholar 

  19. N. Yu. Reshetikhin, L. A. Takhtadzhyan and L. D. Faddeev, Quantization of Lie Groups and Lie Algebras, Leningrad Math. J. 1 (1990) 193.

    MATH  MathSciNet  Google Scholar 

  20. V. G. Drinfeld, Hopf algebras and the quantum Yang-Baxter equation, Sov. Math. Dokl. 32 (1985) 254.

    Google Scholar 

  21. M. Jimbo, A q-analogue of U(g) and the Yang-Baxter equation, Lett. Math. Phys. 10 (1985) 63.

    Article  MATH  ADS  MathSciNet  Google Scholar 

  22. V. G. Drinfeld, Quantum groups, in A. M. Gleason, ed., Proceedings of the International Congress of Mathematicians, Amer. Math. Soc., 798 (1986).

    Google Scholar 

  23. A. Lorek, W. Weich and J. Wess, Non-commutative Euclidean and Minkowski Structures, Z. Phys. C 76 (1997) 375, [q-alg/9702025].

    Article  MathSciNet  Google Scholar 

  24. P. P. Kulish and N. Yu. Reshetikin, Quantum linear problem for the Sine-Gordon equation and higher representations, J. Sov. Math. 23 (1983) 2345.

    Article  Google Scholar 

  25. S. Majid, Foundations of Quantum Group Theory, University Press, Cambridge (1995).

    Book  MATH  Google Scholar 

  26. M. Chaichian and A. P. Demichev, Introduction to Quantum Groups, World Scientific, Singapore (1996).

    Book  MATH  Google Scholar 

  27. A. Klimyk, K. Schmüdgen, Quantum Groups and their Representations, Springer-Verlag, 1997.

    Google Scholar 

  28. P. Schupp, P. Watts and B. Zumino, Bicovariant Quantum Algebras and Quantum Lie algebras, Commun. Math. Phys. 157 (1993) 305.

    Article  MATH  ADS  MathSciNet  Google Scholar 

  29. S. Majid, Quantum and Braided Lie algebras, J. Geom. Phys. 13 (1994) 307.

    Article  MATH  ADS  MathSciNet  Google Scholar 

  30. A. Sudbery, Quantum differential calculus and lie algebras, Int. J. Mod. Phys. A (1993) 228.

    Google Scholar 

  31. L.C. Biedenharn, M. Tartini, On q-Tensor Operators for Quantum Groups, Lett. Math. Phys. 20 (1990) 271–278.

    Article  MATH  ADS  MathSciNet  Google Scholar 

  32. Yu. I. Manin, Quantum Groups and Non-Commutative Geometry, Centre de Recherche Mathématiques, Montreal (1988).

    Google Scholar 

  33. S. Majid, Free braided differential calculus, braided binomial theorem and the braided exponential map, 1993 J. Mat. Phys. 34 4843.

    Article  MATH  ADS  MathSciNet  Google Scholar 

  34. S. Majid, Introduction to Braided Geometry and q-Minkowski Space, Preprint, 1994 [hep-th/9410241]

    Google Scholar 

  35. C. Bauer and H. Wachter, Operator representations on quantum spaces, 2003 Eur. Phys. J. C 31 261 [math-ph/0201023]

    Article  MATH  ADS  MathSciNet  Google Scholar 

  36. A. Schmidt and H. Wachter, Spinor calculus for q-deformed quantum spaces I, preprint, [hep-th/0705.1640].

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Arnold-Sommerfeld-Center, Theresienstr. 37, D-80333, München

    Alexander Schmidt

Authors
  1. Alexander Schmidt
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Max-Planck-Institut für Mathematik in den Naturwissenschaften, Inselstrasse 22-26, D-04103, Leipzig, Germany

    Bertfried Fauser , Jürgen Tolksdorf  & Eberhard Zeidler ,  & 

Additional information

In memory of Julius Wess.

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Birkhäuser Verlag Basel/Switzerland

About this chapter

Cite this chapter

Schmidt, A. (2009). Towards a q-Deformed Supersymmetric Field Theory. In: Fauser, B., Tolksdorf, J., Zeidler, E. (eds) Quantum Field Theory. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8736-5_16

Download citation

Publish with us

Policies and ethics

Search

Navigation