Skip to main content

On Geometry and Physics of Staggered Lattice Fermions

  • Chapter
  • 718 Accesses

Part of the book series: NATO ASI Series ((ASIC,volume 183))

Abstract

This report contains:

  1. 1.

    Introduction.

  2. 2.

    The Problem of Lattice Fermions.

  3. 3.

    Relation between Dirac Fields and Differential Forms.

  4. 4.

    Dirac Kaehler Equation and Clifford Product on a Cubic Lattice.

  5. 5.

    The Symmetry of the Dirac Kaehler Equation on the Lattice.

  6. 6.

    A Physics Problem.

  7. 7.

    Summary and Outlook.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   219.99
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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. E. Kaehler: Rend. Mat. Ser. V, 21 (1962) 425.

    Google Scholar 

  2. P. Becher, H. Joos: Z. Phys.C-P articles and Fields 15 (1982) 343.

    Article  MathSciNet  Google Scholar 

  3. M. Goeckeler, H. Joos: Progress in Gauge Field Theory, (Cargese 83) p. 247. G. t’Hooft et.al. (ed.) 1984 Plenum Press New York.

    Google Scholar 

  4. P. Becher: Proceedings of the Johns Hopkins Workshop on Current Problems in Particle Theory 7, p. 13. G. Domokos, S. Kovesi-Domokos (ed.), World Scientifique Publishing Co. 1983 Singapore.

    Google Scholar 

  5. L. Susskind: Phys. Rev. D16 (1976) 3031.

    Google Scholar 

  6. P. Becher, M. Boehm, H. Joos: ‘Gauge Theories of the Strong and Electroweak Interactions’. John Wiley and Sons 1984. (B.G. Teubner 1981).

    Google Scholar 

  7. C. Itzikson, J.-B. Zuber: Quantum Field Theory, McGraw-Hill, New York, 1980.

    Google Scholar 

  8. K. Osterwalder, R. Schrader: Comm. Math. Phys. 42 (1975) 281.

    Article  MathSciNet  MATH  Google Scholar 

  9. K.G. Wilson: Phys. Rev. D10 (1974) 2445.

    Google Scholar 

  10. L.H. Karsten, J. Smit: Nucl. Phys. 183 (1981) 103.

    Article  Google Scholar 

  11. A. Chodos, J. B. Healy: Nucl. Phys. 127 (1977) 426. H.S. Charatchandra, H.J. Thun, P. Weisz: Nucl. Phys. 192 (1981) 205.

    Article  Google Scholar 

  12. H. B. Nielsen, N. Ninomya: Nucl. Phys. 185 (1980) 20, 193 (1981) 173.

    Article  Google Scholar 

  13. D. Friedan: Comm. Math. Phys. 85 (1982) 482.

    Article  MathSciNet  Google Scholar 

  14. M. F. Atiyah, W.K. Patodi, I.M. Singer: Math.Cambr. Philosoph. Soc. 79 (1976) 71.

    Article  MathSciNet  MATH  Google Scholar 

  15. K.G. Wilson: New Phenomena in Sub-Nuclear Physics. A. Zichichi (ed.), Plenum Press New York, 1977.

    Google Scholar 

  16. A.K. Common: ‘The reduction of the Dirac Kaehler Equation to the Dirac equation’, University of Kent (preprint 1983)

    Google Scholar 

  17. P. Lounesto: Contributionto this Proceedings.

    Google Scholar 

  18. W. Graf: Ann. Inst. H. Poincare. Sect. A29 (1978) 85.

    MathSciNet  Google Scholar 

  19. I.M. Singer, J.A. Thorpe: Lecture Notes on Elementary Topology and Geometry, Springer, New York 1967.

    MATH  Google Scholar 

  20. J.M. Rabin: Nucl. Phys. B201 (1982) 315.

    Article  MathSciNet  Google Scholar 

  21. N. Salingaros: J. Math. Phys. 22 (1981) 226, 23 (1982) 1. H.W. Braden: J. Math. Phys. 26 (1985) 613. We suggest to call this group K4 which does not have a generally accepted name (H.W. Braden) in honour of this workshop: ‘Kent Group’.

    Article  MathSciNet  MATH  Google Scholar 

  22. M. Schaefer: ‘Die Gitterfermiongruppe und ihre Darstellungen’, Diplomarbeit Hamburg 1985.

    Google Scholar 

  23. H. Joos, M. Schaefer: ‘The Representation Theory of the Symmetry Group of Lattice Fermions as a Basis for Kinematics in Lattice QCD’. (in preparation)

    Google Scholar 

  24. H. Brown, R. Buelow, J. Neubueser, H. Wondrascheck, H. Zassenhaus: Cristallographic Groups of Four-Dimensional Space. J. Wiley and Sons, (New York) 1978.

    Google Scholar 

  25. E.P. Wigner: Ann.Math, 40 (1939) 149.

    Article  MathSciNet  Google Scholar 

  26. G. W. Mackey:, Acta Math. 99 (1958) 365. ‘The Theory of Group Represenations’,(Chicago mimeographed Lecture Notes).

    Article  MathSciNet  Google Scholar 

  27. P. Becher, H. Joos: Lett. Nuovo Cim. 38 (1983) 293.

    Article  Google Scholar 

  28. O. Napoli: Phys. Lett. B183 145. P. Mitra, P. Weisz: Phys. Lett 126B (1983) 355.

    Google Scholar 

  29. F.A. Berezin: The Method of Second Quantization, Academic Press, New York, 1966.

    MATH  Google Scholar 

  30. H. Kluber-Stern, A. Morel, B. Peterson: Nucl. Phys. B215 (1983) 527.

    Article  Google Scholar 

  31. O. Martin: ‘Large N Gauge Theory at Strong Coupling with Chiral Fermions’, PhD Thesis Caltech. 68–1048. Phys. Lett. 114 (1982) 152.

    Google Scholar 

  32. M. F. L. Golterman, J. Smit: Nucl. Phys. B245 (1984) 61.

    Article  Google Scholar 

  33. M. Mehamid, private communication.

    Google Scholar 

  34. J. P. Gilchrist, G. Schierholz, H. Schneider, M. Teper: Phys. Lett. 136B (1984), Nucl. Phys. B248 (1984) 29. and literature quoted there.

    Google Scholar 

  35. T. Banks et.al.: Phys. Rev. Dl5 (1977) 1111.

    Google Scholar 

  36. D. Hestenes: Found. Phys. 12 (1982) 153. See also: Contribution to this Proceedings.

    Article  MathSciNet  Google Scholar 

  37. See especially the contributions by D. Hestenes, and R.W. Tucker.

    Google Scholar 

  38. M.F. Atiyah, I.M. Singer: Ann. Math. 87 (1968) 485, 546; 93(1971)1, 119, 139. E.F. Corrigan, D.B. Fairlie, S. Temple ton, P. Goddard: Nucl. Phys. B140 (1978) 31. R. Jackiw, C. Rebbi: Phys. Rev. D16 (1977) 1052.

    Google Scholar 

  39. M. Luescher: Comm. Math. Phys. 85 (1982) 29. I. A. Fox, M.L.Laursen, G.Schierholz: Phys. Rev. Lett. 54 (1985) 749. I.A.Fox et. al., M.Goeckeler: Phys. Lett. 158B (1985) 332.

    Google Scholar 

  40. J. Cheeger, W. Mueller, R. Schrader: ‘Lattice Gravity or Riemann Structure on Piecewise Linear Spaces’, in Unified Theories of Elementary Particle, P. Breitenlohner, H.P. Duerr (ed.). Springer Verlag (Berlin, Heidelberg, New York), 1982.

    Google Scholar 

  41. T. Banks, Y. Dothan, D. Horn: Phys. Lett. 117B (1982) 413.

    MathSciNet  Google Scholar 

  42. J. Krueger: Klassische Loesungen der Dirac Kaehler Gleichung, (Diplomarbeit Hamburg 1985)

    Google Scholar 

  43. J. Wess, J. Bagger: Supersymmetry and Supergravity, Princeton University Press 1982.

    Google Scholar 

  44. C. G. Callan, R. Dashen, D.J. Gross. Phys. Rev. D17 (1978) 2717. C. Vafa, E. Witten: Comm. Math. Phys. 95 (1984) 257.

    Google Scholar 

  45. H. Joos: Revista Brasileira de Fisica, M. Schoenberg Vol. 1984, p.169.

    Google Scholar 

  46. S. Elitzur, E. Rabinovici, A. Schwimmer: Phys. Lett. 119B (1982) 165. H. Aratyn, A. H. Zimerman: Phys. Lett. 137B (1984) 392, Z. Phys. C. — Particles and Fields C27 (1985) 536.

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1986 D. Reidel Publishing Company

About this chapter

Cite this chapter

Joos, H. (1986). On Geometry and Physics of Staggered Lattice Fermions. In: Chisholm, J.S.R., Common, A.K. (eds) Clifford Algebras and Their Applications in Mathematical Physics. NATO ASI Series, vol 183. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-4728-3_35

Download citation

  • DOI: https://doi.org/10.1007/978-94-009-4728-3_35

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-8602-8

  • Online ISBN: 978-94-009-4728-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics