2.8 Summary2 Gauge-theoretic discretizations of gravity2.6 The measure

2.7 Assorted topics

Caselle et al [70] proposed a lattice action that is genuinely Poincaré-invariant, at the price of introducing additional lattice ``coordinate variables''. They also suggested a compact O (5)-formulation which reduces to the Poincaré form in the limit as the length of some preferred O (5)-vector is taken to infinity, as well as a super-version involving the graded Poincaré group. The same authors in [69] put forward an argument for why doubling should appear in general gravity plus matter systems.

Reisenberger [175] has recently suggested a gauge-theoretic path integral based on the Plebanski action for Euclidean gravity. He discretizes the theory on a simplicial or hypercubic lattice with group- and algebra-valued fields. A metricity constraint needs to be imposed on the basic spin-1 fields, which it turns out is difficult to treat exactly.



2.8 Summary2 Gauge-theoretic discretizations of gravity2.6 The measure

image Discrete Approaches to Quantum Gravity in Four Dimensions
Renate Loll
http://www.livingreviews.org/lrr-1998-13
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