TY - JOUR
T1 - Physics in space-time with scale-dependent metrics
AU - Balankin, Alexander S.
N1 - Funding Information:
I thank Michael Shapiro Fishman and Rodolfo Camacho-Velázquez for useful and clarifying discussions. This work was supported by Mexican government under the research grants SENER-CONACYT No. 143927 .
PY - 2013/10/1
Y1 - 2013/10/1
N2 - We construct three-dimensional space Rγ3 with the scale-dependent metric and the corresponding Minkowski space-time Mγ,β4 with the scale-dependent fractal (DH) and spectral (DS) dimensions. The local derivatives based on scale-dependent metrics are defined and differential vector calculus in Rγ3 is developed. We state that Mγ,β4 provides a unified phenomenological framework for dimensional flow observed in quite different models of quantum gravity. Nevertheless, the main attention is focused on the special case of flat space-time M1/3,14 with the scale-dependent Cantor-dust-like distribution of admissible states, such that DH increases from DH=2 on the scale < l o to DH=4 in the infrared limit > lo, where lo is the characteristic length (e.g. the Planck length, or characteristic size of multi-fractal features in heterogeneous medium), whereas DS≡4 in all scales. Possible applications of approach based on the scale-dependent metric to systems of different nature are briefly discussed.
AB - We construct three-dimensional space Rγ3 with the scale-dependent metric and the corresponding Minkowski space-time Mγ,β4 with the scale-dependent fractal (DH) and spectral (DS) dimensions. The local derivatives based on scale-dependent metrics are defined and differential vector calculus in Rγ3 is developed. We state that Mγ,β4 provides a unified phenomenological framework for dimensional flow observed in quite different models of quantum gravity. Nevertheless, the main attention is focused on the special case of flat space-time M1/3,14 with the scale-dependent Cantor-dust-like distribution of admissible states, such that DH increases from DH=2 on the scale < l o to DH=4 in the infrared limit > lo, where lo is the characteristic length (e.g. the Planck length, or characteristic size of multi-fractal features in heterogeneous medium), whereas DS≡4 in all scales. Possible applications of approach based on the scale-dependent metric to systems of different nature are briefly discussed.
KW - Flat space-time
KW - Multi-fractal media
KW - Quantum gravity
KW - Scale-dependent metric
UR - http://www.scopus.com/inward/record.url?scp=84877737659&partnerID=8YFLogxK
U2 - 10.1016/j.physleta.2013.04.040
DO - 10.1016/j.physleta.2013.04.040
M3 - Artículo
AN - SCOPUS:84877737659
SN - 0375-9601
VL - 377
SP - 1606
EP - 1610
JO - Physics Letters, Section A: General, Atomic and Solid State Physics
JF - Physics Letters, Section A: General, Atomic and Solid State Physics
IS - 25-27
ER -