p-ADIC AND ADELIC MINISUPERSPACE QUANTUM COSMOLOGY

Abstract

1. Abstract p-Adic and adelic generalization of ordinary quantum cosmology is considered. In [1], we have calculated p-adic wave functions for some minisuperspace cosmological models according to the "no-boundary" Hartle-Hawking proposal. In this article, applying p-adic and adelic quantum mechanics, we show existence of the corresponding vacuum eigenstates. Adelic wave function contains some information on discrete structure of space-time at the Planck scale.

On classical and quantum dynamics of tachyon-like fields and their cosmological implications

“…Since quantum cosmology is used to describe the evolution of the universe in a very early stage, i.e. it is related to the Planck scale phenomena, then it is reasonable to consider various geometries, in particular the nonarchimedean one, which is closely connected to p-adic numbers and their application [25,26].…”

“…Conditions on the parameters of the theory also arise as well [9,27]. Now, the adelic ground states is of the form [26] …”

$p$-Адический сектор адельной струны

“…Также была сформулиро-вана адельная квантовая механика [12], причем была найдена связь между адель-ным вакуумным состоянием гармонического осциллятора и дзета-функцией Римана. Адельный анализ был успешно применен к фейнмановскому интегралу по траек-ториям [13], квантовой космологии [14], суммированию расходящихся рядов [15] и динамическим системам [16].…”

Quantum cosmology and tachyons

“…It is a strong motivation to study a class of exactly solvable quantum mechanical models and apply them in the frame of quantum cosmology. For the review and detailed discussion see [2,16]. The nonarchimedean and noncommutative cosmological quantum models with extra dimensions and an accelerating phase have been considered [17], as well as the relevant models and techniques in pure quantum mechanical context [18,19,20,21].…”