Duality and Zero-Point Length of Spacetime

The action for a relativistic free particle of mass $m$ receives a contribution $\ensuremath{-}mds$ from a path of infinitesimal length $\mathrm{ds}$. Using this action in a path integral, one can obtain the Feynman propagator for a spinless particle of mass $m$. Assuming that the path integral amplitude is invariant under the ``duality'' transformation $\mathrm{ds}\ensuremath{\rightarrow}{L}_{P}^{2}/\mathrm{ds}$, one can calculate the modified Feynman propagator. I show that this propagator is the same as the one obtained by assuming that quantum effects of gravity lead to modification of the spacetime interval $(x\ensuremath{-}y{)}^{2}$ to $(x\ensuremath{-}y{)}^{2}{+L}_{P}^{2}$. The implications of this result are discussed.

Перевод пока недоступен