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Two long-standing problems in the construction of coherent state pathintegrals, the unwarranted assumption of path continuity and the ambiguousdefinition of the Hamiltonian symbol, are rigorously solved. To this end thefully controlled dual representation familiar from lattice quantum fieldtheories is introduced. Dualization allows for both the step-by-step check inthe construction of discrete path integrals and for the identification of theHamiltonian and Berry phase part of the action, thus making both discrete andcontinuous path integrals consistently defined. Once the correct action isconstructed, we are able to follow the transition to the continuum for thepolar form of general Bose-Hubbard models and to provide an exact form of thepath integral for general spin systems, where previous works showed its failurefor all standard choices of operator ordering.

Rigorous construction of coherent state path integrals through dualization