Research PapersNo Access

A CYCLIC INTEGRAL ON κ-MINKOWSKI NONCOMMUTATIVE SPACE–TIME

School of Mathematics, Cardiff University, Senghennydd Road, Cardiff, CF24 4AG, Wales, UK

Dipartimento di Fisica, Università di Roma "La Sapienza" and INFN Sez. Roma1, P.le Moro 2, 00185 Roma, Italy

Institute of Field Physics, Department of Physics and Astronomy, University of North Carolina, Chapel Hill, NC 27599-3255, USA

Search for more papers by this author

, and

FRANCESCO D'ANDREA

Mathematical Physics Sector, International School for Advanced Studies (SISSA), Via Beirut 2-4, Trieste, Italy

Search for more papers by this author

https://doi.org/10.1142/S0217751X06031077Cited by:19

Abstract

We examine some alternative possibilities for an action functional for κ-Minkowski noncommutative space–time. Early works on κ-Minkowski focused on κ-Poincaré covariance and the dependence of the action functional on the choice of Weyl map, renouncing to invariance under cyclic permutations of the factors composing the argument of the action functional. It has been recently suggested, focusing on a specific choice of Weyl map and setting aside the issue of κ-Poincaré covariance of the action functional, that a cyclicity-inducing measure could be introduced in implicit form. We provide an explicit formula for (and derivation of) a choice of measure which indeed ensures cyclicity of the action functional. The same choice of measure is applicable to all the most used choices of Weyl map, but we find that this "cyclicity-inducing measure" is not invariant under κ-Poincaré transformations. We also notice that the cyclicity-inducing measure can be straightforwardly derived using a map which connects the κ-Minkowski space–time coordinates and the space–time coordinates of a "canonical" noncommutative space–time, with coordinate-independent commutators.

Keywords:

References

H. S. Snyder, Phys. Rev. 71, 38 (1947), DOI: 10.1103/PhysRev.71.38. Crossref, ISI, ADS, Google Scholar
J. Madoreet al., Eur. Phys. J. C 16, 161 (2000), DOI: 10.1007/s100520050012. Crossref, ISI, ADS, Google Scholar
B. L. Cerchiai and J. Wess, Eur. Phys. J. C 5, 553 (1998), DOI: 10.1007/s100520050300. Crossref, ISI, ADS, Google Scholar
S. Doplicher, K. Fredenhagen and J. E. Roberts, Phys. Lett. B 331, 39 (1994), DOI: 10.1016/0370-2693(94)90940-7. Crossref, ISI, ADS, Google Scholar
G. Amelino-Camelia, Phys. Lett. B 392, 283 (1997), DOI: 10.1016/S0370-2693(96)01565-1. Crossref, ISI, ADS, Google Scholar
N. R. Douglas and N. A. Nekrasov, Rev. Mod. Phys. 73, 977 (2001), DOI: 10.1103/RevModPhys.73.977. Crossref, ISI, ADS, Google Scholar
B. L. Cerchiai, J. High Energy Phys. 0306, 056 (2003), DOI: 10.1088/1126-6708/2003/06/056. ADS, Google Scholar
O. Bertolami and L. Guisado, J. High Energy Phys. 0312, 013 (2003), DOI: 10.1088/1126-6708/2003/12/013. ADS, Google Scholar
G. Amelino-Camelia, L. Smolin and A. Starodubtsev, Class. Quantum Grav. 21, 3095 (2004), DOI: 10.1088/0264-9381/21/13/002. Crossref, ISI, ADS, Google Scholar
L. Freidel, J. Kowalski-Glikman and L. Smolin, hep-th/0307085 . Google Scholar
O. Ogievetskyet al., Commun. Math. Phys. 150, 495 (1992), DOI: 10.1007/BF02096958. Crossref, ISI, ADS, Google Scholar
P. Kosinski, J. Lukierski and P. Maslanka, Czech. J. Phys. 50, 1283 (2000), DOI: 10.1023/A:1022821310096. Crossref, ISI, ADS, Google Scholar
G. Amelino-Camelia and S. Majid, Int. J. Mod. Phys. A 15, 4301 (2000), DOI: 10.1016/S0217-751X(00)00277-7. ISI, ADS, Google Scholar
G. Amelino-Camelia and M. Arzano, Phys. Rev. D 65, 084044 (2002), DOI: 10.1103/PhysRevD.65.084044. Crossref, ISI, Google Scholar
A. Agostini, G. Amelino-Camelia and F. D'Andrea, hep-th/0306013 . Google Scholar
S. Majid and H. Ruegg, Phys. Lett. B 334, 348 (1994), DOI: 10.1016/0370-2693(94)90699-8. Crossref, ISI, ADS, Google Scholar
J. Lukierski, H. Ruegg and W. J. Zakrzewski, Ann. Phys. 243, 90 (1995), DOI: 10.1006/aphy.1995.1092. Crossref, ISI, ADS, Google Scholar
J. Kowalski-Glikman and S. Nowak, hep-th/0204245 . Google Scholar
M. Dimitrijevicet al., Eur. Phys. J. C 31, 129 (2003), DOI: 10.1140/epjc/s2003-01309-y. Crossref, ISI, ADS, Google Scholar
W. Behr and A. Sykora, Nucl. Phys. B 698, 473 (2004), DOI: 10.1016/j.nuclphysb.2004.07.024. Crossref, ISI, ADS, Google Scholar
F. Bayenet al., Lett. Math. Phys. 1, 521 (1977), DOI: 10.1007/BF00399745. Crossref, ISI, ADS, Google Scholar
F. Bayenet al., Ann. Phys. 111, 61 (1978), DOI: 10.1016/0003-4916(78)90224-5. Crossref, ISI, ADS, Google Scholar
P. Schupp, P. Watts and B. Zumino, Commun. Math. Phys. 157, 305 (1993), DOI: 10.1007/BF02099762. Crossref, ISI, ADS, Google Scholar
S. Gutt, math.DG/0003107 . Google Scholar
J. Moyal, Proc. Camb. Phil. Soc. 45, 99 (1949). Crossref, ISI, ADS, Google Scholar
H. Weyl, Z. Phys. 46, 1 (1927), DOI: 10.1007/BF02055756. Crossref, ADS, Google Scholar
A. Agostini, F. Lizzi and A. Zampini, Mod. Phys. Lett. A 17, 2105 (2002), DOI: 10.1142/S021773230200871X. Link, ISI, ADS, Google Scholar
P. Kosinskiet al., Czech. J. Phys. 48, 1407 (1998), DOI: 10.1023/A:1021661323795. Crossref, ISI, ADS, Google Scholar
S. Majid and R. Oeckl, Commun. Math. Phys. 205, 617 (1999), DOI: 10.1007/s002200050692. Crossref, ISI, ADS, Google Scholar
P. Kosinski, J. Lukierski and P. Maslanka, Nucl. Phys. B (Proc. Suppl.) 102 & 103, 161 (2001). ISI, Google Scholar
G. Amelino-Camelia, Lect. Notes Phys. 541 (2000) p. 1. Google Scholar
G. Amelino-Camelia, F. D'Andrea and G. Mandanici, J. Cosmol. Astropart. Phys. 0309, 006 (2003). ADS, Google Scholar

You currently do not have access to the full text article.
Recommend the journal to your library today!

Vol. 21, No. 15

Metrics

History

Received 10 November 2004

Revised 15 November 2005

Keywords

PDF download

System Upgrade on Tue, Oct 25th, 2022 at 2am (EDT)

A CYCLIC INTEGRAL ON κ-MINKOWSKI NONCOMMUTATIVE SPACE–TIME

Abstract

References

Recommended