Defining some integrals in Regge calculus

Abstract

Regge calculus minisuperspace action in the connection representation has the form in which each term is linear over some field variable (scale of area-type variable with sign). We are interested in the result of performing integration over connections in the path integral. To find this function, we compute its moments, i. e. integrals with powers of that variable. Calculation proceeds through intermediate appearance of $\delta$-functions and integrating them out and leads to finite result for any power. The function of interest should therefore be exponentially suppressed at large areas and it really does being restored from moments. This gives for gravity a way of defining such nonabsolutely convergent integral as path integral.