Dynamical
Triangulation Approach to Regge Calculus| Dynamical
Triangulation Approach to Regge Calculus |
In General
* Idea: Fix the edge lengths and vary the triangulation by adding/removing
simplices with well-defined moves.
* Motivation: Supposed to be ergodic in the space of geometries, and
one
expects to be able to get many more.
* Drawbacks: Recovery of
the Einstein-Hilbert action is more problematic, since diffeomorphism invariance
is
lost.
* Action (4D): Given by I =
2
N2 – 10 
N4,
with
= arcos(1/5), Nn = number
of n-simplices.
* 2D: Dynamical triangulations
are equivalent to matrix models.
* Phase transition: As
one changes the curvature (Newton) coupling, between an elongated and a crumpled
phase.
References
@ General: Godfrey & Gross PRD(91)
[more than 2D]; Ambjørn & Jurkiewicz PLB(92);
Nabutovsky & Ben-Av CMP(93)
[4D, non-computability]; Ambjørn
CQG(95)
[2D]; Ambjørn et al LNP-ht/96;
Schleich & Witt gq/96-in
[quantum]; Bialas et al NPPS(98)gq/97.
@ 3D: Carfora & Marzuoli IJMPA(93)
[and Reidemeister torsion]; Egawa & Tsuda PLB(98)
[random surfaces].
@ Random surfaces: David et al NPB(87)
[critical exponents]; Migdal JGP(88).
@ Related topics: Renken NPB(97)hl/96 [renormalization
group]; Catterall et
al PLB(98)
[singular geometries]; Henson CQG(09)-a0907 [coarse-graining].
@ Phase structure, transitions: Agishtein & Migdal NPB(92),
MPLA(92);
Varsted NPB(94)
[and continuum limit]; Brügmann & Marinari JMP(95)
[no exponential bound]; de
Bakker PLB(96)
[phase transition, first-order]; Renken et al NPB(98),
Warner et al PLB(98)
[3D]; Warner & Catterall PLB(00)hl [4D,
with boundary].
@ Euclidean:
Brügmann PRD(93),
& Marinari
PRL(95) [4D,
measure]; Ambjørn et al JMP(95)ht [2D];
Veselov & Zubkov PLB(04)
[10D].
Lorentzian / Causal Dynamical Triangulations > s.a. Potts
Model [coupled to gravity].
@ Reviews: Ambjørn et al CP(06)ht/05,
in(09)ht/06;
Alpert SA(07)feb; Loll CQG(08)-a0711;
Ambjørn et al SA(08)jul, a0906-ln.
@ General references: Markopoulou & Smolin NPB(06)ht/04 [varying
lapse]; Benedetti a0707-PhD
[analytical]; Zohren PhD(08)-a0905;
Durhuus et al a0908 [spectral dimension].
@ 2D:
Ansari & Markopoulou NPB(05)ht [as
a spin system]; Loll et al AIP(06)ht [sum
over topologies]; Zohren MS(05)ht/06
[analytic results, rev]; Benedetti & Loll GRG(07)gq/06 [counting
graphs, and matter behavior]; Ambjørn et al JHEP(07)-a0709 [with
partial lifting of causality constraint] Ambjørn et al PLB(08)
[matrix model representation]; Westra a0810-PhD
[and topology change]; Benedetti & Henson PLB(09)-a0812 [matrix
model]; > s.a. cosmological
constant
problem, topology change.
@ 3D: Ambjørn et al NPB(01)ht [and
4D]; Ambjørn et al NPPS(02)hl;
Dittrich & Loll PRD(02);
Konopka PRD(06)ht/05 [varying
lapse]; Benedetti et al PRD(07)-a0704 [continuum
limit and Hamiltonian]; Benedetti & Henson a0911 [de Sitter as semiclassical
ground state].
@ 4D: Ambjørn et al PRL(04)ht;
Ambjørn
et al PRL(08)-a0712,
PRD(08)-a0807 [quantum
de Sitter universe].
main page – abbreviations – journals – comments – other
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send feedback and suggestions to bombelli at olemiss.edu – modified 2
nov
2009