# p-ADIC AND ADELIC MINISUPERSPACE QUANTUM COSMOLOGY

@article{Djordjevic2002pADICAA, title={p-ADIC AND ADELIC MINISUPERSPACE QUANTUM COSMOLOGY}, author={Goran S. Djordjevic and Branko Dragovich and Lj. Ne{\vs}i{\'c} and Igor V. Volovich}, journal={International Journal of Modern Physics A}, year={2002}, volume={17}, pages={1413-1433} }

We consider the formulation and some elaboration of p-adic and adelic quantum cosmology. The adelic generalization of the Hartle–Hawking proposal does not work in models with matter fields. p-adic and adelic minisuperspace quantum cosmology is well defined as an ordinary application of p-adic and adelic quantum mechanics. It is illustrated by a few cosmological models in one, two and three minisuperspace dimensions. As a result of p-adic quantum effects and the adelic approach, these models… Expand

#### 31 Citations

p-Adic and Adelic Quantum Mechanics

- Physics
- 2003

p-Adic mathematical physics emerged as a result of efforts to find a non-Archimedean approach to the spacetime and string dynamics at the Planck scale. One of its main achievements is a successful… Expand

Towards p-Adic Matter in the Universe

- Physics, Mathematics
- 2013

Starting from p-adic string theory with tachyons, we introduce a new kind of non-tachyonic matter which may play an important role in evolution of the Universe. This matter retains nonlocal and… Expand

Signature change in p-adic and noncommutative FRW cosmology

- Physics
- 2014

The significant matter for the construction of the so-called no-boundary proposal is the assumption of signature transition, which has been a way to deal with the problem of initial conditions of the… Expand

The p-adic sector of the adelic string

- Mathematics, Physics
- 2010

We study the construction of Lagrangians that can be considered the Lagrangians of the p-adic sector of an adelic open scalar string. Such Lagrangians are closely related to the Lagrangian for a… Expand

Path integrals for quadratic lagrangians on p-adic and adelic spaces

- Mathematics, Physics
- 2010

Feynman’s path integrals in ordinary, p-adic and adelic quantum mechanics are considered. The corresponding probability amplitudes K(x″, t″; x′, t′) for two-dimensional systems with quadratic… Expand

Towards effective Lagrangians for adelic strings

- Physics, Mathematics
- 2009

p-Adic strings are important objects of string theory, as well as of p-adic mathematical physics and nonlocal cosmology. By a concept of adelic string one can unify and simultaneously study various… Expand

On Adelic Modelling in p-Adic Mathematical Physics

- 2011

Adeles are infinite sequences which contain real and p-adic numbers for all primes p. They unify real and p-adic numbers, giving possibility to trait them simultaneously at an equal footing. Adelic… Expand

Two-oscillator Kantowski–Sachs model of the Schwarzschild black hole interior

- Physics
- 2015

In this paper the interior of the Schwarzschild black hole, which is presented as a vacuum, homogeneous and anisotropic Kantowski–Sachs minisuperspace cosmological model, is considered. Lagrangian of… Expand

D ec 2 00 5 p-Adic and Adelic Superanalysis

- 2005

After a brief review ofp-adic numbers, adeles and their functions, we consider real,p-adic and adelic superalgebras, superspaces and superanal yses. A concrete illustration is given by means of the… Expand

p-Adic mathematical physics: the first 30 years

- Mathematics, Physics
- 2017

A brief review of main achievements in some selected topics of p-adic mathematical physics and its applications, especially in the last decade, mainly paid to developments with promising future prospects. Expand

#### References

SHOWING 1-10 OF 64 REFERENCES

p-ADIC AND ADELIC FREE RELATIVISTIC PARTICLE

- Physics, Mathematics
- 1999

We consider spectral problem for a free relativistic particle in p-adic and adelic quantum mechanics. In particular, we found p-adic and adelic eigenfunctions. Within adelic approach there exist… Expand

Quantum mechanics on p-adic fields

- Mathematics
- 1989

A formulation of quantum mechanics on p‐adic number fields is presented. Quantum amplitudes are taken as complex functions of p‐adic variables and it is shown how the Weyl approach to quantum… Expand

Adelic Harmonic Oscillator

- Physics, Mathematics
- 1995

Using the Weyl quantization we formulate one-dimensional adelic quantum mechanics, which unifies and treats ordinary and p-adic quantum mechanics on an equal footing. As an illustration the… Expand

p-adic quantum mechanics

- Physics
- 1989

An extension of the formalism of quantum mechanics to the case where the canonical variables are valued in a field ofp-adic numbers is considered. In particular the free particle and the harmonic… Expand

THE WAVE FUNCTION OF THE UNIVERSE AND p-ADIC GRAVITY

- Physics
- 1991

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… Expand

p-adic string

- Physics
- 1987

The hypothesis of the possible p-adic structure of spacetime is considered. The p-adic Veneziano amplitude is proposed and the main properties of the p-adic string theory are discussed. The analogous… Expand

p-Adic and adelic harmonic oscillator with a time-dependent frequency

- Physics, Mathematics
- 2000

The classical and quantum formalism for a p-adic and adelic harmonic oscillator with a time-dependent frequency is developed, and general formulas are obtained for the main theoretical quantities. In… Expand

Quantum Gravity In De Sitter Space

- Physics
- 2001

We discuss some general properties of quantum gravity in De Sitter space. It has been argued that the Hilbert space is of finite dimension. This suggests a macroscopic argument that General… Expand

Path-integral quantum cosmology: A class of exactly soluble scalar-field minisuperspace models with exponential potentials.

- Physics, Medicine
- Physical review. D, Particles and fields
- 1991

The nature of the geometries corresponding to the saddle points of the no-boundary amplitude of the minisuperspace model are discussed, and the set of classical solutions this proposal picks out in the classical limit is identified. Expand

Minisuperspaces with conformally and minimally coupled scalar fields

- Physics
- 1991

One may perform a local field redefinition to transform between gravity minimally coupled to a free scalar field and gravity conformally coupled. However, the allowed field values differ in the two… Expand