p -adic path integrals
E. I. Zelenov
Source abstract
The definition of a path integral is proposed. The method suggested is analogous to Lagrange’s formulation of a path integral used in ordinary quantum mechanics. The notation of linear order on the set of p-adic number, p-adic segment, p-adic Lagrangian, integral of p-adic function of one variable and classical action are introduced. It is proven that if the action is stationary at some trajectory then the Euler–Lagrange equations are satisfied on this trajectory. A finite approximation of a path integral is constructed and the kernel of the operator of evolution is calculated for the case of p-adic harmonic oscillator.
Evidence graph
No public relationships recorded yet.
Integrity note: This page is a factual metadata record created by deterministic ingestion. It is not a claim that the work moves a mathematical frontier or has been independently verified.