  A set of Green functions ${\cal G}_{\alpha}(x-y), \alpha \in [0, 2 \pi [$,
for free scalar field theory is introduced, varying between the Hadamard Green
function $\Delta_1(x-y) \equiv \linebreak[2] \lsta{0} \hspace{-0.1cm} \{
\varphi(x), \varphi(y) \} \hspace{-0.1cm} \rsta{0}$ and the causal Green
function ${\cal G}_{\pi}(x-y) = i \Delta(x-y) \equiv [\varphi(x), \varphi(y)]$.
For every $\alpha \in [0, 2 \pi [$ a path-integral representation for ${\cal
G}_{\alpha}$ is obtained both in the configuration space and in the phase space
of the classical relativistic particle. Especially setting $\alpha = \pi$ a
sum-over-histories representation for the causal Green function is obtained.
Furthermore using BRST theory an alternative path-integral representation for
${\cal G}_{\alpha}$ is presented. From these path integral representations the
composition laws for the ${\cal G}_{\alpha}$'s are derived using a modified
path decomposition expansion.

High Energy Physics - Theory