3.11 Coupling to scalar matter

The coupling of Regge gravity to scalar matter was investigated by Hamber and Williams [120116] for λ = 1, a = 0.005, and various k-values. They considered a single, massive scalar field, with an action contribution
1 ∑ ( ϕi − ϕj )2 m2 ∑ 2 Sϕ = 2- Vij --l---- + -2- Viϕi, (20 ) <ij> ij i
where V i, V ij denote the 4-volumes associated with the vertices and edges. Most data were obtained on the 44-lattice, with the measure (1∕30) Vl ldl. The inclusion of the scalar field leads to a slight decrease in the average volume and edge length, as well as a very slight decrease in |ℛ |. They again performed a fit for ℛ according to (17View Equation) and found that the critical exponent and the location of kc were almost unchanged.
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