  To represent the two-dimensional $N$-body delta-Bose gas for any integer
$N\geq 2$, we construct an It\^{o} diffusion satisfying the strong Markov
property and establish an associated Feynman-Kac-type formula. Among several
properties, the diffusion is singular to the Brownian motion for showing almost
sure contacts of particles and has a supercritical drift coefficient in the
sense of a Ladyzhenskaya-Prodi-Serrin-type condition. Despite the
supercriticality, the construction of the diffusion process and the relevant
distributional properties for the Feynman-Kac-type formula are obtained by
locally transforming the relative motions in two-body interactions and the
necessary free motions. The central mechanism making this reduction to two-body
interaction possible is the "no triple contacts" of particles, observed earlier
in the functional integrals of the two-dimensional delta-Bose gas and now
extended to the stochastic process level.
