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We argue that under very general conditions, there is a significantcomplication in amplitudes for spacetimes regions constructed from pathintegrals. This is the fact that the concrete implementation of therestrictions on paths over an interval of time corresponds, in an operatorlanguage, to sharp monitoring at every moment of time in the given timeinterval. Such processes suffer from the quantum Zeno effect -- the continualmonitoring of a quantum system in a Hilbert subspace prevents its state fromleaving that subspace. As a consequence, path integral amplitudes defined inthis seemingly obvious way have physically and intuitively unreasonableproperties and in particular, no sensible classical limit. In this paper wedescribe this frequently-occurring but little-appreciated phenomenon in somedetail, showing clearly the connection with the quantum Zeno effect. We thenshow that it may be avoided by implementing the restriction on paths in thepath integral in a "softer" way. The resulting amplitudes then involve a newcoarse graining parameter, which may be taken to be a timescale $\eps$,describing the softening of the restrictions on the paths. We argue that thecomplications arising from the Zeno effect are then negligible as long as $\eps>> 1/ E$, where $E$ is the energy scale of the incoming state. Our criticismsof path integral constructions largely apply to approaches to quantum theorysuch as the decoherent histories approach or quantum measure theory, which donot specifically involve measurements. We address some criticisms of ourapproach by Sokolovksi, concerning the relevance of our results tomeasurement-based models.

Amplitudes for Spacetime Regions and the Quantum Zeno Effect: Pitfalls of Standard Path Integral Constructions