B. Three Basic Formulae

One needs only three basic formulae in order to derive the main results reported in this paper: one is the extension of the Gaussian integral to a $D$-component vector variable, and the other two are representations for the Dirac delta-function.

Generalized Gaussian Integral:

$$\int d{\bf X} \exp\left(-{1\over 2} X^i A_{ij} X^j + B... ...{\bf B} \cdot {\bf A}^{-1} \cdot \vec{\bf B}/2 \right)$$ (59)

where

$${\bf A} = \left( A _{ij} \right) \quad {\rm and} \quad \vec{\bf B} = \left( B _{i} \right)$$ (60)

Dirac-delta representations

a) Functional Fourier Transform:

$$\delta[\vec{\bf X}(\lambda)]=({\rm {}const.})\times \int [{\... ... \vec{\bf P} (\lambda) \cdot \vec{\bf X} (\lambda) \right)$$ (61)

b) Gaussian Representation:

$$\delta^D(x)\equiv \lim_{\epsilon\rightarrow 0} \left( {1\over\pi\epsilon} \right)^{D/2} \exp\left(-x^2/\epsilon \right)$$ (62)