  We derive the asymptotic expansions of the wave function of three particles
having equal mass with finite-range interactions and infinite or zero
two-dimensional scattering length colliding at zero energy and zero orbital
angular momentum, from which a three-body parameter $D$ is defined. The
dimension of $D$ is length squared, and we call $D$ three-body scattering area.
We find that the ground state energy per particle of a zero-temperature dilute
Bose gas with these interactions is approximately $\frac{\hbar^2 D
}{6m}\rho^2$, where $\rho$ is the number density of the bosons, $m$ is the mass
of each boson, and $\hbar$ is Planck's constant over $2\pi$. Such a Bose gas is
stable at $D\geq 0$ in the thermodynamic limit, and metastable at $D<0$ in the
harmonic trap if the number of bosons is less than $N_{cr}\approx 3.6413
\sqrt{\frac{\hbar}{m\omega |D|}}$, where $\omega$ is the angular frequency of
the harmonic trap. If the two-body interaction supports bound states, $D$
typically acquires a negative imaginary part, and we find the relation between
this imaginary part and the amplitudes of the pair-boson production processes.
We derive a formula for the three-body recombination rate constant of the
many-boson system in terms of the imaginary part of $D$.
