2.7 Assorted topics2 Gauge-theoretic discretizations of gravity2.5 Proving reflection positivity

2.6 The measure

One can derive non-trivial conditions on the lattice measure by imposing the Slavnov-Taylor identities in a perturbative lattice calculation. Starting from the general form of the measure for Poincaré gravity,

  equation131

Menotti and Pelissetto [166] performed a one-loop calculation and found that the Slavnov-Taylor identity can be satisfied for a particular choice of N, tex2html_wrap_inline2325 (momentum expansion coefficients of f), and of the cosmological constant tex2html_wrap_inline2329 . The solution still depends on a real parameter tex2html_wrap_inline2331 (related to a residual non-invariance under rotations). This makes it difficult to draw any immediate conclusions on the structure of the full, non-perturbative measure.



2.7 Assorted topics2 Gauge-theoretic discretizations of gravity2.5 Proving reflection positivity

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