Vol. 1, No 3, 1996 pp.
237 - 239
UDC
530.1
ON p-ADIC MODELS OF THE UNIVERSE
B. Dragović1, Lj. Nešić2
1 Institute of Physics, P.O. Box 57, 11001 Belgrade, Yugoslavia
E-mail: dragovic@shiva.phy.bg.ac.yu
2 Department of Physics, University of Niš, P.O.Box 91, 18001 Niš, Yugoslavia
University of Niš, P.O. Box 92, 18000 Niš, Yugoslavia
E-mail: nesiclj@archimed.filfak.ni.ac.yu
Abstract.
p-Adic generalization of ordinary minisuperspace cosmological models, i.e. their formulation over fields of p-adic numbers Qp, is considered. To obtain the wave function of the ground state of the universe, we use the "no-boundary" proposal of Hartle and Hawking. In this proposal wave function for the spatially closed universe is given by Feynman's path integral method over histories. It corresponds to an amplitude of transition from "nothing" to 3-dimensional hypersurface over all compact 4-metrics connecting these two 3-space states. Integration over compact real metrics extrapolates to all corresponding p-adic compact metrics. p-Adic wave functions are obtained for the following models of the universe: the de Sitter model, a model with cosmological constant in 3 dimensions, and a model with a homogeneous scalar field.
O p-ADIČNIM MODELIMA VASIONE
Razmatrana je p-adična generalizacija minisuperprostornih kosmoloških modela standardne kvantne kosmologije (kosmologije nad poljem realnih brojeva R), odnosno njihovog formulisanja nad p-adičnim poljima brojeva Qp. Za dobijanje talasne funkcije osnovnog stanja vasione korišćen je Hartl-Hokingov prilaz po kome se talasna funkcija vasione dobija pomoću Fejnmanovog metoda integracije po "istorijama". Ona odgovara amplitudi prelaza iz "ničega" u 3-dimenzionu hiperpovrš preko svih kompaktnih 4-metrika koje povezuju ova dva stanja 3-prostora. Integracija po kompaktnim realnim metrikama je generalizovana na odgovarajuće p-adične kompaktne metrike. Dobijena je p-adična talasna funkcija za sledeće modele vasione: de Siterov model, model sa kosmološkom konstantom u 3 dimenzije, i jedan model sa homogenim skalarnim poljem.
