  The saddle points of a conventional Feynman path integral are not entangled,
since they comprise a sequence of classical field configurations. We combine
insights from field theory and tensor networks by constructing a Feynman path
integral over a sequence of matrix product states. The paths that dominate this
path integral include some degree of entanglement. This new feature allows
several insights and applications: i. A Ginzburg-Landau description of
deconfined phase transitions. ii. The emergence of new classical collective
variables in states that are not adiabatically continuous with product states.
iii. Features that are captured in product-state field theories by
proliferation of instantons are encoded in perturbative fluctuations about
entangled saddles. We develop a general formalism for such path integrals and a
couple of simple examples to illustrate their utility.
