HPO formalism

The History Projection Operator (HPO) formalism is an approach to temporal quantum logic developed by Chris Isham. It deals with the logical structure of quantum mechanical propositions asserted at different points in time.

In standard quantum mechanics a physical system is associated with a Hilbert space ${\displaystyle {\mathcal {H}}}$. States of the system at a fixed time are represented by normalised vectors in the space and physical observables are represented by Hermitian operators on ${\displaystyle {\mathcal {H}}}$.

A physical proposition ${\displaystyle \,P}$ about the system at a fixed time can be represented by a projection operator ${\displaystyle {\hat {P}}}$ on ${\displaystyle {\mathcal {H}}}$ (See quantum logic). This representation links together the lattice operations in the lattice of logical propositions and the lattice of projection operators on a Hilbert space (See quantum logic).

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