THE WAVE FUNCTION OF THE UNIVERSE AND p-ADIC GRAVITY

Abstract

A new approach to the wave function of the universe is suggested. The key idea is to take into account fluctuating number fields and present the wave function in the form of a Euler product. For this purpose we define a p-adic generalization of both classical and quantum gravitational theory. Elements of p-adic differential geometry are described. The action and gravitation field equations over the p-adic number field are investigated. p-adic analogs of some known solutions to the Einstein equations are presented. It follows that in quantum cosmology one should consider summation only over algebraic manifolds. The correspondence principle with the standard approach is considered.

Classification of p-adic 6-dimensional filiform Leibniz algebras by solutions of x q = a

“…In [5], we have shown the following: = 3: Any ∈ Q 3 has the form = εδ 3 , where ε ∈ {1 4 5}, δ ∈ {1 3 9}. = which again can be reduced to the previous equation.…”

“…Since 12 = 11 5 , 13 = 11 5 , 14 = 11 5 for some ∈ Q 5 and 4 = 5 3 , 12 = 5 3 , 36 = 5 3 for some ∈ Q 3 , we will omit 4 12 36 in E 3 3 and 12 13 14 in E 5 5 .…”

“…However, with time numerous applications of these numbers to theoretical physics [2,3,6,9,22], to quantum mechanics [14,19], to -adic-valued physical observables [14] were proposed, see also [15,27].…”

Existence of p-adic quasi Gibbs measure for countable state Potts model on the Cayley tree

“…Interest in the physics of non-Archimedean quantum models [1][2][3][4][5] is based on the idea that the structure of space-time for very short distances might conveniently be described in terms of non-Archimedean numbers. One of the ways to describe this violation of the Archimedean axiom, is the using p-adic analysis.…”

Profinite and finite groups associated with loop and diffeomorphism groups of non‐Archimedean manifolds

“…The importance of such groups in the non-Archimedean functional analysis, representation theory, and mathematical physics is clear (see [1,8,10,11,14,18,19]). This paper is devoted to one aspect of such groups: their structure from the point of view of the p-adic compactification (see also about Banaschewski compactification in [18]).…”