Abstract
This is a concise overview of the construction of Yang-Mills theories with realistic gauge groups on noncommutative generalizations of space-time and of the construction of the noncommutative standard model. We discuss the relevant mathematical tools including tensor products, indicate some exciting physical consequences and conclude with a short-list of challenging open problems.
That is the limit from accelerator experiments [2,3,4,5]. Much higher limits exist for low-energy physics [6]; these should, however, be interpreted with care. See also [7].
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References
H. S. Snyder, “Quantized Space-Time,” Phys. Rev. 71, 38 (1947).
H. Arfaei and M. H. Yavartanoo, arXiv:hep-th/0010244.
J. L. Hewett, F. J. Petriello and T. G. Rizzo, Phys. Rev. D 64, 075012 (2001).
I. Hinchliffe and N. Kersting, Phys. Rev. D 64, 116007 (2001).
W. Behr, N. G. Deshpande, G. Duplancic, P. Schupp, J. Trampetic and J. Wess, arXiv:hep-ph/0202121.
C. E. Carlson, C. D. Carone and R. F. Lebed, Phys. Lett. B 518, 201 (2001).
I. Hinchliffe and N. Kersting, arXiv:hep-ph/0205040.
A. Connes, Non-commutative geometry (Academic Press, London 1994).
J. Madore, An Introduction to Noncommutative Differential Geometry and its Physical Applications, 2nd edn. (Cambridge University Press 1999).
J. Madore, S. Schraml, P. Schupp and J. Wess, Eur. Phys. J. C 16, 161 (2000).
B. Jurco, S. Schraml, P. Schupp and J. Wess, Eur. Phys. J. C 17, 521 (2000).
B. Jurco, P. Schupp and J. Wess, Nucl. Phys. B 604, 148 (2001).
B. Jurco, L. Moller, S. Schraml, P. Schupp and J. Wess, Eur. Phys. J. C 21, 383 (2001).
P. Schupp, hep-th/0111038.
J. Madore, Class. and Quant. Grav. 9, 69 (1992).
B. L. Cerchiai and J. Wess, Eur. Phys. J. C 5, 553 (1998).
F. Bayen, M. Flato, C. Fronsdal, A. Lichnerowicz, D. Sternheimer, Ann. Phys. 111, 61 (1978).
N. Seiberg and E. Witten, J. High Energy Phys. 9909, 032 (1999).
R. Stora, privat communication.
D. Brace, B. L. Cerchiai, A. F. Pasqua, U. Varadarajan and B. Zumino, J. High Energy Phys. 0106, 047 (2001); D. Brace, B. L. Cerchiai and B. Zumino, hepth/0107225.
G. Barnich, F. Brandt and M. Grigoriev, hep-th/0206003.
B. Jurco, P. Schupp and J. Wess, Lett. Math. Phys. (to appear), hep-th/0106110.
A. A. Bichl, J. M. Grimstrup, L. Popp, M. Schweda and R. Wulkenhaar, hepth/0102103.
H. Dorn and C. Sieg, hep-th/0205286.
M. Hayakawa, hep-th/9912167.
X. Calmet, B. Jurco, P. Schupp, J. Wess and M. Wohlgenannt, Eur. Phys. J. C 23, 363 (2002).
P. Aschieri, B. Jurco, P. Schupp and J. Wess, hep-th/0205214.
N. G. Deshpande and X. G. He, Phys. Lett. B 533, 116 (2002).
D. Bahns, S. Doplicher, K. Fredenhagen and G. Piacitelli, Phys. Lett. B 533, 178 (2002).
A. Bichl, J. Grimstrup, H. Grosse, L. Popp, M. Schweda and R. Wulkenhaar, J. High Energy Phys. 0106, 013 (2001); R. Wulkenhaar, J. High Energy Phys. 0203, 024 (2002).
J. M. Grimstrup and R. Wulkenhaar, hep-th/0205153.
E. O. Iltan, hep-ph/0204332; hep-ph/0204129.
Z. Chang and Z. z. Xing, hep-ph/0204255.
M. Chaichian, P. Presnajder, M. M. Sheikh-Jabbari and A. Tureanu, hepth/0107055.
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© 2003 Springer-VerlagBerlin Heidelber
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Schupp, P. (2003). Particle Physics on Noncommutative Space-Time. In: Trampetić, J., Wess, J. (eds) Particle Physics in the New Millennium. Lecture Notes in Physics, vol 616. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36539-7_22
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DOI: https://doi.org/10.1007/3-540-36539-7_22
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