摘要We argue that in the generalized uncertainty principle (GUP) model, the parameter β0 whose square root, multiplied by Planck length ℓp, approximates the minimum measurable distance, varies with energy scales. Since the minimal measurable length and extra dimensions are both suggested by quantum gravity theories, we investigate the models based on the GUP and one extra dimension, compactified with radius ρ. We obtain an inspiring relation √β0 ℓp/ρ∼ O(1). This relation is also consistent with the predictions at Planck scale and the usual quantum mechanics scale. We also estimate the application range of the GUP model. It turns out that the minimum measurable length is exactly the compactification radius of the extra dimension.
Abstract：We argue that in the generalized uncertainty principle (GUP) model, the parameter β0 whose square root, multiplied by Planck length ℓp, approximates the minimum measurable distance, varies with energy scales. Since the minimal measurable length and extra dimensions are both suggested by quantum gravity theories, we investigate the models based on the GUP and one extra dimension, compactified with radius ρ. We obtain an inspiring relation √β0 ℓp/ρ∼ O(1). This relation is also consistent with the predictions at Planck scale and the usual quantum mechanics scale. We also estimate the application range of the GUP model. It turns out that the minimum measurable length is exactly the compactification radius of the extra dimension.
MU Ben-Rong;WU Hou-Wen**;YANG Hai-Tang
. Generalized Uncertainty Principle in the Presence of Extra Dimensions[J]. 中国物理快报, 2011, 28(9): 91101-091101.
MU Ben-Rong, WU Hou-Wen**, YANG Hai-Tang
. Generalized Uncertainty Principle in the Presence of Extra Dimensions. Chin. Phys. Lett., 2011, 28(9): 91101-091101.
[1] Veneziano G 1986 Europhys. Lett. 2 199
[2] Gross D J and Mende P F 1988 Nucl. Phys. B 303 407
[3] Amati D, Ciafaloni M and Veneziano G 1989 Phys. Lett. B 216 41
[4] Konishi K, Paffuti G and Provero P 1990 Phys. Lett. B 234 276
[5] Guida R, Konishi K and Provero P 1991 Mod. Phys. Lett. A 6 1487
[6] Maggiore M 1993 Phys. Lett. B 304 65
[7] Garay L J 1995 Int. J. Mod. Phys. A 10 145
[8] Scardigli F 1999 Phys. Lett. B 452 39
[9] Kempf A, Mangano G and Mann R B 1995 Phys. Rev. D 52 1108
[10] Kempf A 1997 J. Phys. A 30 2093
[11] Brau F 1999 J. Phys. A 32 7691
[12] Brau F and Buisseret F 2006 Phys. Rev. D 74 036002
[13] Chang L N, Minic D, Okamura N and Takeuchi T 2002 Phys. Rev. D 65 125027
[14] Dadic I, Jonke L and Meljanac S 2003 Phys. Rev. D 67 087701
[15] Nozari K and Azizi T 2006 Gen. Rel. Grav. 38 735
[16] Stetsko M M Tkachuk V M 2006 e-print
[17] Stetsko M M 2006 Phys. Rev. A 74 062105
[18] Benczik S Z 2007 PhD Dissertation (Blacksburg: Virginia Polytechnic Institute and State University)
[19] Battisti M V and Montani G 2007 Phys. Lett. B 656 96
[20] Battisti M V and Montani G 2008 Phys. Rev. D 77 023518
[21] Battisti M V 2011 Phys. Rev. D (submitted) [arXiv: 0805.1178]
[22] Das S and Vagenas E C 2008 Phys. Rev. Lett. 101 221301
[23] Ali A F, Das S and Vagenas E C 2009 Phys. Lett. B 678 497
[24] Antoniadis I 1990 Phys. Lett. B 246 377
[25] Arkani-Hamed N Dimopoulos S and Dvali G R 1998 Phys. Lett. B 429 263
[26] Antoniadis I, Arkani-Hamed N, Dimopoulos S and Dvali G R 1998 Phys. Lett. B 436 257
[27] Randall L and Sundrum R 1999 Phys. Rev. Lett. 83 3370
[28] Randall L and Sundrum R 1999 Phys. Rev. Lett. 83 4690
[29] Dvali G R, Gabadadze G and Porrati M 2000 Phys. Lett. B 485 208
[30] Appelquist T, Cheng H C and Dobrescu B A 2001 Phys. Rev. D 64 035002
[31] Cremades D, Ibanez L E and Marchesano F 2002 Nucl. Phys. B 643 93
[32] Kokorelis C 2004 Nucl. Phys. B 677 115
[33] Shifman M 2010 Int. J. Mod. Phys. A 25 199
[34] Hossenfelder S, Bleicher M, Hofmann S, Ruppert J, Scherer S and Stoecker H 2003 Phys. Lett. B 575 85
[35] Hossenfelder S 2004 Phys. Lett. B 598 92
[36] Hossenfelder S 2004 Phys. Rev. D 70 105003
[37] Hossenfelder S 2005 Czech. J. Phys. B 55 809
[38] Harbach U and Hossenfelder S 2006 Phys. Lett. B 632 379
[39] Scardigli F and Casadio R 2003 Class. Quant. Grav. 20 3915
[40] Scardigli F and Casadio R 2009 Int. J. Mod. Phys. D 18 319
[41] Wang P, Wu H and Yang H 2011 Spectra of harmonic oscillators with GUP and extra dimensions (in praration)
2011, Vol. 28 
