Non-local imprints of gravity on quantum theory

During the last two decades or so much effort has been devoted to discussion of quantum mechanics (QM) that in some way incorporates notion a minimum length. This upsurge research prompted by modified uncertainty relation brought about framework string theory. In general, implementation length QM can be done either modification position and momentum operators restriction their domains. former case we have called soccer-ball problem when naive classical limit appears drastically different from usual one. Starting with latter possibility, an alternative approach was suggested form band-limited QM. However, applying cutoff wave-function, one faces incompatibility Schrödinger equation. One overcome this natural fashion appropriately modifying But takes place for boundary conditions as well. Such wave-function cannot any more finite support coordinate space it simply follows Paley–Wiener theorem. Treating, instance, simplest quantum-mechanical particle infinite potential well, no longer impose box conditions. such cases, further theory is order. We propose non-local QM, which close ties but does not require hard cutoff. model, easily work out corrections various processes discuss semi-classical