TY - JOUR
T1 - The Concept of Time in 2D Quantum Gravity
AU - Ambjørn, Jan
AU - Anagnostopoulos, K.N.
AU - Jurkiewicz, Jerzy
AU - Kristjansen, Charlotte Fløe
N1 - NBI98
PY - 1998/4/1
Y1 - 1998/4/1
N2 - We show that the "time" ts defined via spin clusters in the Ising model coupled to 2d gravity leads to a fractal dimension dh(s) = 6 of space-time at the critical point, as advocated by Ishibashi and Kawai. In the unmagnetized phase, however, this definition of Hausdorff dimension breaks down. Numerical measurements are consistent with these results. The same definition leads to dh(s) = 16 at the critical point when applied to flat space. The fractal dimension dh(s) is in disagreement with both analytical prediction and numerical determination of the fractal dimension dh(g), which is based on the use of the geodesic distance tg as "proper time". There seems to be no simple relation of the kind ts = t9dh(g)/dh(s) as expected by dimensional reasons.
AB - We show that the "time" ts defined via spin clusters in the Ising model coupled to 2d gravity leads to a fractal dimension dh(s) = 6 of space-time at the critical point, as advocated by Ishibashi and Kawai. In the unmagnetized phase, however, this definition of Hausdorff dimension breaks down. Numerical measurements are consistent with these results. The same definition leads to dh(s) = 16 at the critical point when applied to flat space. The fractal dimension dh(s) is in disagreement with both analytical prediction and numerical determination of the fractal dimension dh(g), which is based on the use of the geodesic distance tg as "proper time". There seems to be no simple relation of the kind ts = t9dh(g)/dh(s) as expected by dimensional reasons.
U2 - 10.1088/1126-6708/1998/04/016
DO - 10.1088/1126-6708/1998/04/016
M3 - Journal article
SN - 1126-6708
VL - 1998
JO - Journal of High Energy Physics (Online)
JF - Journal of High Energy Physics (Online)
IS - 4
M1 - 016
ER -