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In quantum mechanics, the measureable quantities of a given theory arepredicted by performing a weighted sum over possibilities. We show how toarrange the possibilities into bundles such that the associated subsums can beviewed as well-defined theories on their own right. These bundles aresubmani$\textit{folds}$ of $\textit{possi}$bilities which we call possifolds.We collect and prove some basic facts about possifolds. Especially, we showthat possifolds are ensembles of what in a certain broadly defined sense thatwe explain can be regarded as soliton excitations (soliton-possifoldcorrespondence). We provide an outlook on some applications. Among otherthings, we illustrate the use of the developed framework for the example of theLieb-Liniger model. It describes non-relativistic bosons with an attractiveinteraction. We derive a dual theory describing the lowest-lying energyexcitation modes. While the standard Bogoliubov-approximation breaks down atthe critical point, our derived summation prescription stays regular. In theBogoliubov-limit we observe the summation to possess an enhanced symmetry atthis point while the summation cannot be ignored there. We finally provide aglimpse on the restrictions black hole physics implies in this context for thegravitational path integral.

Framework for the Quantum Mechanical Sum of Possibilities and Meaning for Field Theory and Gravity