  Several stochastic processes related to transient L\'evy processes with
potential densities $u(x,y)=u(y-x)$, that need not be symmetric nor bounded on
the diagonal, are defined and studied.
  They are real valued processes on a space of measures $V$ endowed with a
metric $d$. Sufficient conditions are obtained for the continuity of these
processes on $(V,d)$. The processes include $n$-fold self-intersection local
times of transient L\'evy processes and permanental chaoses, which are `loop
soup $n$-fold self-intersection local times' constructed from the loop soup of
the L\'evy process. Loop soups are also used to define permanental Wick powers,
which generalizes standard Wick powers, a class of $n$-th order Gaussian
chaoses. Dynkin type isomorphism theorems are obtained that relate the various
processes.
  Poisson chaos processes are defined and permanental Wick powers are shown to
have a Poisson chaos decomposition. Additional properties of Poisson chaos
processes are studied and a martingale extension is obtained for many of the
processes described above.
