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

VL - 1998

JO - Journal of High Energy Physics (Online)

JF - Journal of High Energy Physics (Online)

SN - 1126-6708

IS - 4

M1 - 016

ER -