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As well known, spacelike proton form factors expressed in the Breit frame maybe interpreted as the Fourier transform of static space distributions ofelectric charge and current. In particular, the electric form factor is simplythe Fourier transform of the charge distribution $F(q)=\int e^{i\vec q \cdot\vec r} \rho(r)d^3r$. We don't have an intuitive interpretation of the samelevel of simplicity for the proton timelike form factor appearing in thereactions $e^+e^-\leftrightarrow \bar{p}p$. However, one may suggest that inthe center of mass (CM) frame, where $q_\mu x^\mu =qt$, a timelike electricform factor is the Fourier transform $F(q) =\int e^{iqt} R(t)dt$ of a function$R(t)$ expressing how the electric properties of the forming (or annihilating)proton-antiproton pair evolve in time. Here we analyze in depth this idea, showthat the functions $\rho(r)$ and $R(t)$ can be formally written as the time andspace integrals of a unique correlation function depending on both time andspace coordinates.

The fourth dimension of the nucleon structure: spacetime analysis of the timelike electromagnetic proton form factors