7 problems

The $p$-adic setting uses a non-Archimedean spacetime, meaning that spacetime is modeled over a field with a non-Archimedean absolute value. Volovich's conjecture. Spacetime has a…

The $p$-adic numbers $Q_p$ and the real numbers $R$ are number fields used here to formulate corresponding path integrals for quadratic Lagrangians. Volovich's conjecture. Fundamen…

Let space-time be the geometric arena of physical theories, and let $p$-adic geometry refer to geometry over a field of $p$-adic numbers. Space-time conjecture. It is conjectured t…

Let the space-filling brane be the unstable D-brane supporting the usual open bosonic string fields, and let $p2$-branes denote the corresponding branes on the $p$-adic branches, w…

The $p$-adic amplitudes depend on the prime parameter $p$, and the Gerasimov–Shatashvili Lagrangian is the Archimedean theory obtained through the $p\to1$ limit. The four-point and…

The $p$-adic BTZ background is obtained as a genus-$1$ quotient geometry, with boundary qubits whose reduced-state entanglement entropy is compared with the length of bulk geodesic…

Vladimirov–Volovich conjecture. Spacetime has a non-Archimedean nature at the Planck scale.