A look at quantum systems via p-adic 1-Lipschitz maps

In the talk, it will be argued that basic notions of quantum theory (wave function, observable, pure state, mixed state, etc.) can naturally be expressed in terms of functions whose domain and range are p-adic integers and which satisfy the p-adic Lipschitz condition with a constant 1 (briefly, the p-adic 1-Lipschitz maps). The latter maps constitute the class of all causal functions; the functions describe evolution of quantum systems in theories with a minimum scale lengths. In these terms it is possible to reveal how randomness emerges in quantum systems, how wave function collapses, etc. The approach is motivated by the ideas of I.V.Volovich and G.‘t Hooft and can be judged as a contribution to the p-adic mathematical physics initiated by V.S.Vladimirov in 1988. The talk is mostly based on the paper `Toward the (non-cellular) automata interpretation of quantum mechanics: Volovich postulates as a roadmap’, International Journal of Modern Physics A, Vol. 37, No. 20–21, 2243003 (2022) by Vladimir Anashin.