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12 pages, 249 KiB

Open AccessArticle

On the Choice of Variable for Quantization of Conformal GR

by A. B. Arbuzov and A. A. Nikitenko

Universe 2024, 10(7), 294; https://doi.org/10.3390/universe10070294 - 13 Jul 2024

Viewed by 569

Abstract

The possibility of using spin connection components as basic quantization variables of a conformal version of general relativity is studied. The considered model contains gravitational degrees of freedom and a scalar dilaton field. The standard tetrad formalism is applied. Properties of spin connections [...] Read more.

The possibility of using spin connection components as basic quantization variables of a conformal version of general relativity is studied. The considered model contains gravitational degrees of freedom and a scalar dilaton field. The standard tetrad formalism is applied. Properties of spin connections in this model are analyzed. Secondary quantization of the chosen variables is performed. The gravitational part of the model action turns out to be quadratic with respect to the spin connections. So at the quantum level, the model looks trivial, i.e., without quantum self-interactions. Meanwhile the correspondence to general relativity is preserved at the classical level. Full article

(This article belongs to the Special Issue Quantum Physics including Gravity: Highlights and Novelties)

9 pages, 253 KiB

Open AccessCommunication

Quantized p-Form Gauge Field in D-Dimensional de Sitter Spacetime

by Emanuel W. D. Dantas, Geová Alencar, Ilde Guedes and Milko Estrada

Universe 2024, 10(7), 281; https://doi.org/10.3390/universe10070281 - 28 Jun 2024

Viewed by 765

Abstract

In this work, we utilize the dynamic invariant method to obtain a solution for the time-dependent Schrödinger equation, aiming to explore the quantum theory of a p-form gauge field propagating in D-dimensional de Sitter spacetimes. Thus, we present a generalization, through [...] Read more.

In this work, we utilize the dynamic invariant method to obtain a solution for the time-dependent Schrödinger equation, aiming to explore the quantum theory of a p-form gauge field propagating in D-dimensional de Sitter spacetimes. Thus, we present a generalization, through the use of p-form gauge fields, of the quantization procedure for the scalar, electromagnetic, and Kalb–Ramond fields, all of which have been previously studied in the literature. We present an exact solution for the p-form gauge field when

D = 2 (p + 1)

, and we highlight the connection of the

p = 4

case with the chiral

N = 2

,

D = 10

superstring model. We could observe particle production for

D \neq 2 (p + 1)

because the solutions are time-dependent. Additionally, observers in an accelerated co-moving reference frame will also experience a thermal bath. This could have significance in the realm of extra-dimensional physics, and presents the intriguing prospect that precise observations of the Cosmic Microwave Background might confirm the presence of additional dimensions. Full article

(This article belongs to the Special Issue Quantum Physics including Gravity: Highlights and Novelties)

16 pages, 381 KiB

Open AccessArticle

Quantum-Spacetime Symmetries: A Principle of Minimum Group Representation

by Diego J. Cirilo-Lombardo and Norma G. Sanchez

Universe 2024, 10(1), 22; https://doi.org/10.3390/universe10010022 - 4 Jan 2024

Cited by 3 | Viewed by 1522

Abstract

We show that, as in the case of the principle of minimum action in classical and quantum mechanics, there exists an even more general principle in the very fundamental structure of quantum spacetime: this is the principle of minimal group representation, [...] Read more.

We show that, as in the case of the principle of minimum action in classical and quantum mechanics, there exists an even more general principle in the very fundamental structure of quantum spacetime: this is the principle of minimal group representation, which allows us to consistently and simultaneously obtain a natural description of spacetime’s dynamics and the physical states admissible in it. The theoretical construction is based on the physical states that are average values of the generators of the metaplectic group

M p (n)

, the double covering of

S L (2 C)

in a vector representation, with respect to the coherent states carrying the spin weight. Our main results here are: (i) There exists a connection between the dynamics given by the metaplectic-group symmetry generators and the physical states (the mappings of the generators through bilinear combinations of the basic states). (ii) The ground states are coherent states of the Perelomov–Klauder type defined by the action of the metaplectic group that divides the Hilbert space into even and odd states that are mutually orthogonal. They carry spin weight of 1/4 and 3/4, respectively, from which two other basic states can be formed. (iii) The physical states, mapped bilinearly with the basic 1/4- and 3/4-spin-weight states, plus their symmetric and antisymmetric combinations, have spin contents

s = 0, 1 / 2, 1, 3 / 2

and 2. (iv) The generators realized with the bosonic variables of the harmonic oscillator introduce a natural supersymmetry and a superspace whose line element is the geometrical Lagrangian of our model. (v) From the line element as operator level, a coherent physical state of spin 2 can be obtained and naturally related to the metric tensor. (vi) The metric tensor is naturally discretized by taking the discrete series given by the basic states (coherent states) in the n number representation, reaching the classical (continuous) spacetime for n

\to \infty

. (vii) There emerges a relation between the eigenvalue

α

of our coherent-state metric solution and the black-hole area (entropy) as

A_{b h} / 4 l_{p}^{2} = |α|

, relating the phase space of the metric found,

g_{a b}

, and the black hole area,

A_{b h}

, through the Planck length

l_{p}^{2}

and the eigenvalue

|α|

of the coherent states. As a consequence of the lowest level of the quantum-discrete-spacetime spectrum—e.g., the ground state associated to

n = 0

and its characteristic length—there exists a minimum entropy related to the black-hole history. Full article

(This article belongs to the Special Issue Quantum Physics including Gravity: Highlights and Novelties)

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16 pages, 668 KiB

Open AccessFeature PaperArticle

Classical Mechanics with Inequality Constraints and Gravity Models with Limiting Curvature

by Andrei V. Frolov and Valeri P. Frolov

Universe 2023, 9(6), 284; https://doi.org/10.3390/universe9060284 - 10 Jun 2023

Cited by 1 | Viewed by 1608

Abstract

In this paper, we discuss mechanical systems with inequality constraints

Φ (q, \dot{q}, . . .) \leq 0

. We demonstrate how such constraints can be taken into account by proper modification of the action which describes the [...] Read more.

In this paper, we discuss mechanical systems with inequality constraints

Φ (q, \dot{q}, . . .) \leq 0

. We demonstrate how such constraints can be taken into account by proper modification of the action which describes the original unconstrained dynamics. To illustrate this approach, we consider a harmonic oscillator in the model with limiting velocity. We compare the behavior of such an oscillator with the behavior of a relativistic oscillator and demonstrate that when the amplitude of the oscillator is large, the properties of both types of oscillators are quite similar. We also discuss inequality constraints, which contain higher derivatives. At the end of the paper, we briefly discuss possible applications of the developed approach to gravity models with limiting curvature. Full article

(This article belongs to the Special Issue Quantum Physics including Gravity: Highlights and Novelties)

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30 pages, 493 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Dark Energy Is the Cosmological Quantum Vacuum Energy of Light Particles—The Axion and the Lightest Neutrino

by Héctor J. de Vega and Norma G. Sanchez

Universe 2023, 9(4), 167; https://doi.org/10.3390/universe9040167 - 30 Mar 2023

Cited by 2 | Viewed by 2137

Abstract

We uncover the general mechanism and the nature of today’s dark energy (DE). This is only based on well-known quantum physics and cosmology. We show that the observed DE today originates from the cosmological quantum vacuum of light particles, which provides a continuous [...] Read more.

We uncover the general mechanism and the nature of today’s dark energy (DE). This is only based on well-known quantum physics and cosmology. We show that the observed DE today originates from the cosmological quantum vacuum of light particles, which provides a continuous energy distribution able to reproduce the data. Bosons give positive contributions to the DE, while fermions yield negative contributions. As usual in field theory, ultraviolet divergences are subtracted from the physical quantities. The subtractions respect the symmetries of the theory, and we normalize the physical quantities to be zero for the Minkowski vacuum. The resulting finite contributions to the energy density and the pressure from the quantum vacuum grow as

log a (t)

, where

a (t)

is the scale factor, while the particle contributions dilute as

1 / a^{3} (t)

, as it must be for massive particles. We find the explicit dark energy equation of state of today to be

P = w (z) H

: it turns to be slightly

w (z) < - 1

with

w (z)

asymptotically reaching the value

- 1

from below. A scalar particle can produce the observed dark energy through its quantum cosmological vacuum provided that (i) its mass is of the order of

10^{- 3}

eV = 1 meV, (ii) it is very weakly coupled, and (iii) it is stable on the time scale of the age of the universe. The axion vacuum thus appears as a natural candidate. The neutrino vacuum (especially the lightest mass eigenstate) can give negative contributions to the dark energy. We find that

w (z = 0)

is slightly below

- 1

by an amount ranging from

(- 1.5 \times 10^{- 3})

to

(- 8 \times 10^{- 3})

and we predict the axion mass to be in the range between 4 and 5

meV

. We find that the universe will expand in the future faster than the de Sitter universe as an exponential in the square of the cosmic time. Dark energy today arises from the quantum vacuum of light particles in FRW cosmological space-time in an analogous way to the Casimir vacuum effect of quantum fields in Minkowski space-time with non-trivial boundary conditions. Full article

(This article belongs to the Special Issue Quantum Physics including Gravity: Highlights and Novelties)

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11 pages, 277 KiB

Open AccessArticle

Quantum Scalar-Field Propagator in a Stochastic Gravitational-Plane Wave

by Zbigniew Haba

Universe 2022, 8(12), 648; https://doi.org/10.3390/universe8120648 - 5 Dec 2022

Cited by 2 | Viewed by 2111

Abstract

A stochastic metric can appear in classical as well as in quantum gravity. We show that if the linearized stochastic Gaussian gravitational-plane wave has the frequency spectrum

ω^{4 γ - 1}

(

0 \leq γ < 1

), then the equal-time propagator [...] Read more.

A stochastic metric can appear in classical as well as in quantum gravity. We show that if the linearized stochastic Gaussian gravitational-plane wave has the frequency spectrum

ω^{4 γ - 1}

(

0 \leq γ < 1

), then the equal-time propagator of the scalar field behaves as

p^{- \frac{1}{1 - γ}}

for large momenta. We discuss models of quantum-field theory where such anomalous behavior can appear. Full article

(This article belongs to the Special Issue Quantum Physics including Gravity: Highlights and Novelties)

Review

Jump to: Research, Other

15 pages, 324 KiB

Open AccessReview

Phenomenologies in Hypersphere Soliton and Stringy Photon Models

by Soon-Tae Hong

Universe 2023, 9(9), 378; https://doi.org/10.3390/universe9090378 - 23 Aug 2023

Cited by 1 | Viewed by 935

Abstract

We consider the Dirac quantization in the first-class formalism to investigate the hypersphere soliton model (HSM) defined on the

S^{3}

hypersphere. To do this, we construct the first-class Hamiltonian possessing the Weyl ordering correction. In the HSM, we evaluate the baryon physical [...] Read more.

We consider the Dirac quantization in the first-class formalism to investigate the hypersphere soliton model (HSM) defined on the

S^{3}

hypersphere. To do this, we construct the first-class Hamiltonian possessing the Weyl ordering correction. In the HSM, we evaluate the baryon physical quantities such as the baryon masses, magnetic moments, axial coupling constant and charge radii, most predicted values of which are in good agreement with the corresponding experimental data. Moreover, shuffling the baryon and transition magnetic moments, we find the model independent sum rules. In the HSM we also evaluate the baryon intrinsic frequencies such as

ω_{N} = 0.87 \times 10^{23} s^{- 1}

and

ω_{Δ} = 1.74 \times 10^{23} s^{- 1}

of the nucleon and delta baryon, respectively, to yield the identity

ω_{Δ} = 2 ω_{N}

. Next, making use of the Nambu-Goto string action and its extended rotating bosonic string theory, we formulate the stringy photon model to obtain the energy of the string configuration, which consists of the rotational and vibrational energies of the open string. Exploiting this total string energy, we evaluate the photon intrinsic frequency

ω_{γ} = 9.00 \times 10^{23} s^{- 1}

, which is comparable to the corresponding baryon intrinsic frequencies. We also predict the photon size

{⟨ r^{2} ⟩}^{1 / 2} (photon) = 0.17 fm

, which is approximately 21% of the proton magnetic charge radius. Full article

(This article belongs to the Special Issue Quantum Physics including Gravity: Highlights and Novelties)

Other

Jump to: Research, Review

26 pages, 416 KiB

Open AccessPerspective

Foundational Issues in Dynamical Casimir Effect and Analogue Features in Cosmological Particle Creation

by Jen-Tsung Hsiang and Bei-Lok Hu

Universe 2024, 10(11), 418; https://doi.org/10.3390/universe10110418 - 7 Nov 2024

Viewed by 456

Abstract

Moving mirrors as analogue sources of Hawking radiation from black holes have been explored extensively but less so with cosmological particle creation (CPC), even though the analogy between the dynamical Casimir effect (DCE) and CPC based on the mechanism of the parametric amplification [...] Read more.

Moving mirrors as analogue sources of Hawking radiation from black holes have been explored extensively but less so with cosmological particle creation (CPC), even though the analogy between the dynamical Casimir effect (DCE) and CPC based on the mechanism of the parametric amplification of quantum field fluctuations has also been known for a long time. This ‘perspective’ essay intends to convey some of the rigor and thoroughness of quantum field theory in curved spacetime, which serves as the theoretical foundation of CPC, to DCE, which enjoys a variety of active experimental explorations. We have selected seven issues of relevance to address, starting from the naively simple ones, e.g., why one should be bothered with ‘curved’ spacetime when performing a laboratory experiment in ostensibly flat space, to foundational theoretical ones, such as the frequent appearance of nonlocal dissipation in the system dynamics induced by colored noises in its field environment, the existence of quantum Lenz law and fluctuation–dissipation relations in the backreaction effects of DCE emission on the moving atom/mirror or the source, and the construction of a microphysics model to account for the dynamical responses of a mirror or medium. The strengthening of the theoretical ground for DCE is not only useful for improving conceptual clarity but needed for the development of the proof-of-concept type of future experimental designs for DCE. The results from the DCE experiments in turn will enrich our understanding of quantum field effects in the early universe because they are, in the spirit of analogue gravity, our best hopes for the verification of these fundamental processes. Full article

(This article belongs to the Special Issue Quantum Physics including Gravity: Highlights and Novelties)

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