Using a relationship between the occupation field and connected Feynman diagrams, the author obtains \(L^ p\)-estimates for the renormalization of the occupation field \(\vdots T^ n\vdots\) for a two-dimensional Brownian motion X. Furthermore, a measure on the space of continuous sample paths \(dQ=Z^{-1}\exp (-\vdots T^ n\vdots_{\lambda})dP\) is obtained where dP is the distribution of X, Z is a normalization constant, and \(\lambda\) represents a space cutoff. This extends e.g. certain results of \textit{E. B. Dynkin} [J. Funct. Anal. 58, 20-52 (1984; Zbl 0552.60075)] and the first author [ibid. 80, No.2, 308-331 (1988; Zbl 0656.60088)].