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

Djordjević, Goran S.; Nešić, Ljubiša; Radovancevic, Darko

doi:10.1007/s10714-016-2102-x

Cited by 3 publications

(1 citation statement)

References 41 publications

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“…Adelic quantum cosmology, as application of adelic quantum mechanics to minisuperspace cosmological models, was initiated by Dragovich [93] and has been considered in several papers, see, e.g. [94,65,64,66,67,68]. As a result of p-adic effects and adelic approach to the wave function of the universe one obtains that spacetime exhibits discreteness at the Planck scale.…”

Section: 2mentioning

confidence: 99%

p-Adic mathematical physics: the first 30 years

Драгович

Khrennikov

Козырев

et al. 2017

P-Adic Num Ultrametr Anal Appl

135

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p-Adic mathematical physics is a branch of modern mathematical physics based on the application of p-adic mathematical methods in modeling physical and related phenomena. It emerged in 1987 as a result of efforts to find a non-Archimedean approach to the spacetime and string dynamics at the Planck scale, but then was extended to many other areas including biology. This paper contains a brief review of main achievements in some selected topics of p-adic mathematical physics and its applications, especially in the last decade. Attention is mainly paid to developments with promising future prospects.

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Section: 2mentioning

confidence: 99%

p-Adic mathematical physics: the first 30 years

Драгович

Khrennikov

Козырев

et al. 2017

P-Adic Num Ultrametr Anal Appl

135

View full text Add to dashboard Cite

show abstract

Gravitational decoupling in cosmology

Cedeño

Contreras

2020

Physics of the Dark Universe

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Quantum mechanics on a p-adic Hilbert space: Foundations and prospects

Aniello,

Mancini,

Parisi

2024

Int. J. Geom. Methods Mod. Phys.

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We review some recent results on the mathematical foundations of a quantum theory over a scalar field that is a quadratic extension of the non-Archimedean field of [Formula: see text]-adic numbers. In our approach, we are inspired by the idea — first postulated in [I. V. Volovich, [Formula: see text]-adic string, Class. Quantum Grav. 4 (1987) L83–L87] — that space, below a suitably small scale, does not behave as a continuum and, accordingly, should be modeled as a totally disconnected metrizable topological space, ruled by a metric satisfying the strong triangle inequality. The first step of our construction is a suitable definition of a [Formula: see text]-adic Hilbert space. Next, after introducing all necessary mathematical tools — in particular, various classes of linear operators in a [Formula: see text]-adic Hilbert space — we consider an algebraic definition of physical states in [Formula: see text]-adic quantum mechanics. The corresponding observables, whose definition completes the statistical interpretation of the theory, are introduced as SOVMs, a [Formula: see text]-adic counterpart of the POVMs associated with a standard quantum system over the complex numbers. Interestingly, it turns out that the typical convex geometry of the space of states of a standard quantum system is replaced, in the [Formula: see text]-adic setting, with an affine geometry; therefore, a symmetry transformation of a [Formula: see text]-adic quantum system may be defined as a map preserving this affine geometry. We argue that, as a consequence, the group of all symmetry transformations of a [Formula: see text]-adic quantum system has a richer structure with respect to the case of standard quantum mechanics over the complex numbers.

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

Cited by 3 publications

References 41 publications

p-Adic mathematical physics: the first 30 years

p-Adic mathematical physics: the first 30 years

Gravitational decoupling in cosmology

Quantum mechanics on a p-adic Hilbert space: Foundations and prospects

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