  We classify all continuous tensor product systems of Hilbert spaces which are
``infinitely divisible" in the sense that they have an associated logarithmic
structure. These results are applied to the theory of E_0 semigroups to deduce
that every E_0 semigroup which possesses sufficiently many ``decomposable"
operators must be cocycle conjugate to a CCR flow. A *path space* is an
abstraction of the set of paths in a topological space, on which there is given
an associative rule of concatenation. A metric path space is a pair (P,g)
consisting of a path space P and a function g:P^2 --> complex numbers which
behaves as if it were the logarithm of a multiplicative inner product. The
logarithmic structures associated with infinitely divisible product systems are
such objects. The preceding results are based on a classification of metric
path spaces.
