On path integration on noncommutative geometries

• Autorzy: Achim Kempf
• Języki publikacji: EN

Abstrakty

EN

We discuss a recent approach to quantum field theoretical path integration on noncommutative geometries which imply UV/IR regularising finite minimal uncertainties in positions and/or momenta. One class of such noncommutative geometries arise as `momentum spaces' over curved spaces, for which we can now give the full set of commutation relations in coordinate free form, based on the Synge world function.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 1997
• Tom: 40
• Numer: 1
• Strony: 379-386

Daty

wydano

1997

Twórcy

autor

Achim Kempf

• Department of Applied Mathematics, & Theoretical Physics, and Corpus Christi College in the University of Cambridge, Silver Street, Cambridge CB3 9EW, U.K.

Bibliografia

• [1] A. Connes, Noncommutative geometry, AP (1994).
• [2] P. K. Townsend, Phys. Rev. D, Vol. 15, No 10 2795-2801 (1976).
• [3] D. Amati, M. Cialfaloni, G. Veneziano, Phys. Lett. B 216, 41 (1989).
• [4] M. Maggiore, Phys. Lett. B 319, 83 (1993).
• [5] L. J. Garay, Int. J. Mod. Phys. A10: 145 (1995).
• [6] A. Kempf, Lett. Math. Phys. 26: 1-12 (1992).
• [7] A. Kempf, J. Math. Phys., Vol. 34, No. 3, 969-987 (1993) .
• [8] A. Kempf, Proc. XXII DGM Conf. Sept. 93 Ixtapa (Mexico), Adv. Appl. Cliff. Alg. (Proc. Suppl. ) (S1) (1994).
• [9] A. Kempf, J. Math. Phys. 35 (9): 4483 (1994).
• [10] A. Kempf, Preprint DAMTP/94-33, hep-th/9405067, rev. version.
• [11] A. Kempf, Czech. J. Phys. (Proc. Suppl. ) 44, 11-12: 1041 (1994).
• [12] A. Kempf, G. Mangano, R. B. Mann, Phys. Rev. D52: 1108-1118 (1995).
• [13] A. Kempf, H. Hinrichsen, DAMTP/95-50, hep-th/9510144.
• [14] A. Kempf, G. Mangano, in preparation.
• [15] M. Arik, D. D. Coon, J. Math. Phys. 17: 524 (1975).
• [16] W. Pusz, S. Woronowicz, Rep. Math. Phys. 27, 231 (1989).
• [17] I. M. Burban, A. U. Klimyk, Lett. Math. Phys. 29, No1: 13 (1993).
• [18] R. P. Feynman, Dirac Memorial Lecture, `The reason for antiparticles' CUP (1987)
• [19] C. W. Misner, K. S. Thorne, J. A. Wheeler, Gravitation, p. 285 Freeman & Co (1973).
• [20] Y. Yamashita, Gen. Rel. Grav., 16: 99 (1984).
• [21] N. D. Birrell, P. C. W. Davies, Quantum fields in curved space, CUP (1982).
• [22] B. S. DeWitt, The Dynamical Theory of Groups and Fields, Gordon & Breach (1965).
• [23] S. A. Fulling, Aspects of Quantum Field Theory in Curved Space-Time, CUP (1989).
• [24] S. Doplicher, K. Fredenhagen, J. E. Roberts, Comm. Math. Phys. 172: 187 (1995).