  The standard way to construct a path integral is to use a Legendre
transformation to find the hamiltonian, to repeatedly insert complete sets of
states into the time-evolution operator, and then to integrate over the
momenta. This procedure is simple when the action is quadratic in its time
derivatives, but in most other cases Legendre's transformation is intractable,
and the hamiltonian is unknown. This paper shows how to construct path
integrals when one can't find the hamiltonian because the first time
derivatives of the fields occur in ways that make a Legendre transformation
intractable; it focuses on scalar fields and does not discuss higher-derivative
theories or those in which some fields lack time derivatives.
