Particles

18 pages, 3873 KiB

Open AccessArticle

Curvature Invariants for the Accelerating Natário Warp Drive

by Brandon Mattingly, Abinash Kar, Matthew Gorban, William Julius, Cooper K. Watson, M.D. Ali, Andrew Baas, Caleb Elmore, Jeffrey S. Lee, Bahram Shakerin, Eric W. Davis and Gerald B. Cleaver

Particles 2020, 3(3), 642-659; https://0-doi-org.brum.beds.ac.uk/10.3390/particles3030042 - 16 Sep 2020

Cited by 8 | Viewed by 4664

Abstract

A process for using curvature invariants is applied to evaluate the accelerating Natário warp drive. Curvature invariants are independent of coordinate bases and plotting the invariants is free of coordinate mapping distortions. While previous works focus mainly on the mathematical description of the [...] Read more.

A process for using curvature invariants is applied to evaluate the accelerating Natário warp drive. Curvature invariants are independent of coordinate bases and plotting the invariants is free of coordinate mapping distortions. While previous works focus mainly on the mathematical description of the warp bubble, plotting curvature invariants provides a novel pathway to investigate the Natário spacetime and its characteristics. For warp drive spacetimes, there are four independent curvature invariants the Ricci scalar,

r_{1}

,

r_{2}

, and

w_{2}

. The invariant plots demonstrate how each curvature invariant evolves over the parameters of time, acceleration, skin depth and radius of the warp bubble. They show that the Ricci scalar has the greatest impact of the invariants on the surrounding spacetime. They also reveal key features of the Natário warp bubble such as a flat harbor in the center of it, a dynamic wake, and the internal structures of the warp bubble. Full article

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12 pages, 306 KiB

Open AccessArticle

Squeezing the Parameter Space for Lorentz Violation in the Neutrino Sector with Additional Decay Channels

by Ulrich D. Jentschura

Particles 2020, 3(3), 630-641; https://0-doi-org.brum.beds.ac.uk/10.3390/particles3030041 - 26 Aug 2020

Cited by 4 | Viewed by 2161

Abstract

The hypothesis of Lorentz violation in the neutrino sector has intrigued scientists for the last two to three decades. A number of theoretical arguments support the emergence of such violations, first and foremost for neutrinos, which constitute the “most elusive” and “least interacting” [...] Read more.

The hypothesis of Lorentz violation in the neutrino sector has intrigued scientists for the last two to three decades. A number of theoretical arguments support the emergence of such violations, first and foremost for neutrinos, which constitute the “most elusive” and “least interacting” particles known to mankind. It is of obvious interest to place stringent bounds on the Lorentz-violating parameters in the neutrino sector. In the past, the most stringent bounds have been placed by calculating the probability of neutrino decay into a lepton pair, a process made kinematically feasible by Lorentz violation in the neutrino sector, above a certain threshold. However, even more stringent bounds can be placed on the Lorentz-violating parameters if one takes into account, additionally, the possibility of neutrino splitting, i.e., of neutrino decay into a neutrino of lower energy, accompanied by “neutrino-pair Čerenkov radiation.” This process has a negligible threshold and can be used to improve the bounds on Lorentz-violating parameters in the neutrino sector. Finally, we take the opportunity to discuss the relation of Lorentz and gauge symmetry breaking, with a special emphasis on the theoretical models employed in our calculations. Full article

(This article belongs to the Special Issue Beyond the Standard Models in Particle Physics and Cosmology)

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9 pages, 624 KiB

Open AccessEditor’s ChoiceArticle

A Bayesian Analysis on Neutron Stars within Relativistic Mean Field Models

by Prasanta Char, Silvia Traversi and Giuseppe Pagliara

Particles 2020, 3(3), 621-629; https://0-doi-org.brum.beds.ac.uk/10.3390/particles3030040 - 07 Aug 2020

Cited by 4 | Viewed by 2453

Abstract

We present a Bayesian analysis on the equation of state of neutron stars based on a class of relativistic mean field models. The priors on the equation of state are related to the properties of nuclear matter at saturation and the posteriors are [...] Read more.

We present a Bayesian analysis on the equation of state of neutron stars based on a class of relativistic mean field models. The priors on the equation of state are related to the properties of nuclear matter at saturation and the posteriors are obtained through the Bayesian procedure by exploiting recent astrophysical constraints on the mass–radius relations of neutron stars. We find indications of a tension (within the adopted model) between the prior on the nuclear incompressibility and its posterior which in turn seems to suggest a possible phase transition at about twice saturation density to a phase where the nucleon effective mass is strongly reduced. A possible relation with the chiral phase transition in dense matter is also discussed. Full article

(This article belongs to the Special Issue Selected Papers from “The Modern Physics of Compact Stars and Relativistic Gravity 2019”)

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45 pages, 1434 KiB

Open AccessArticle

New Concept for Studying the Classical and Quantum Three-Body Problem: Fundamental Irreversibility and Time’s Arrow of Dynamical Systems

by A. S. Gevorkyan

Particles 2020, 3(3), 576-620; https://0-doi-org.brum.beds.ac.uk/10.3390/particles3030039 - 04 Aug 2020

Viewed by 2174

Abstract

The article formulates the classical three-body problem in conformal-Euclidean space (Riemannian manifold), and its equivalence to the Newton three-body problem is mathematically rigorously proved. It is shown that a curved space with a local coordinate system allows us to detect new hidden symmetries [...] Read more.

The article formulates the classical three-body problem in conformal-Euclidean space (Riemannian manifold), and its equivalence to the Newton three-body problem is mathematically rigorously proved. It is shown that a curved space with a local coordinate system allows us to detect new hidden symmetries of the internal motion of a dynamical system, which allows us to reduce the three-body problem to the 6th order system. A new approach makes the system of geodesic equations with respect to the evolution parameter of a dynamical system (internal time) fundamentally irreversible. To describe the motion of three-body system in different random environments, the corresponding stochastic differential equations (SDEs) are obtained. Using these SDEs, Fokker-Planck-type equations are obtained that describe the joint probability distributions of geodesic flows in phase and configuration spaces. The paper also formulates the quantum three-body problem in conformal-Euclidean space. In particular, the corresponding wave equations have been obtained for studying the three-body bound states, as well as for investigating multichannel quantum scattering in the framework of the concept of internal time. This allows us to solve the extremely important quantum-classical correspondence problem for dynamical Poincaré systems. Full article

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14 pages, 1881 KiB

Open AccessArticle

Quantum Effects on the Mesoscale

by Tatiana A. Khantuleva and Victor M. Kats

Particles 2020, 3(3), 562-575; https://0-doi-org.brum.beds.ac.uk/10.3390/particles3030038 - 30 Jul 2020

Cited by 2 | Viewed by 1897

Abstract

In different areas of mechanics, highly non-equilibrium processes are accompanied by self-organization of various type turbulent structures and localized inhomogeneities at intermediate scale between macro and micro levels. In order to describe the self-organization of the new dynamic structures on the mesoscale, a [...] Read more.

In different areas of mechanics, highly non-equilibrium processes are accompanied by self-organization of various type turbulent structures and localized inhomogeneities at intermediate scale between macro and micro levels. In order to describe the self-organization of the new dynamic structures on the mesoscale, a new problem formulation based on the results of non-equilibrium statistical mechanics, control theory of adaptive systems, and theory of a special type nonlinear operator sets is proposed. Determination of the turbulent structure parameters through constraints imposed on the system in the form of nonlinear functionals is an inverse problem similar to problems on spectra in quantum mechanics. Like in quantum mechanics, the bounded system in response to impact forms a discrete spectrum of the turbulent structure sizes and lifetimes which goes into continuous spectrum close-to-equilibrium. The proposed description of the structure evolution on the intermediate scale level which is valid far from thermodynamic equilibrium bridges the gap between macroscopic theories and quantum mechanics and affirms the unity of the physical laws of nature. Full article

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19 pages, 326 KiB

Open AccessEditor’s ChoiceTutorial

Gauge Dependence of the Gauge Boson Projector

by Priidik Gallagher, Stefan Groote and Maria Naeem

Particles 2020, 3(3), 543-561; https://0-doi-org.brum.beds.ac.uk/10.3390/particles3030037 - 28 Jul 2020

Cited by 3 | Viewed by 2376

Abstract

The propagator of a gauge boson, like the massless photon or the massive vector bosons

W^{\pm}

and Z of the electroweak theory, can be derived in two different ways, namely via Green’s functions (semi-classical approach) or via the vacuum expectation value of [...] Read more.

The propagator of a gauge boson, like the massless photon or the massive vector bosons

W^{\pm}

and Z of the electroweak theory, can be derived in two different ways, namely via Green’s functions (semi-classical approach) or via the vacuum expectation value of the time-ordered product of the field operators (field theoretical approach). Comparing the semi-classical with the field theoretical approach, the central tensorial object can be defined as the gauge boson projector, directly related to the completeness relation for the complete set of polarisation four-vectors. In this paper we explain the relation for this projector to different cases of the

R_{ξ}

gauge and explain why the unitary gauge is the default gauge for massive gauge bosons. Full article

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11 pages, 750 KiB

Open AccessEditor’s ChoiceArticle

Neutron Stars in f(R)-Gravity and Its Extension with a Scalar Axion Field

by Artyom Astashenok and Sergey Odintsov

Particles 2020, 3(3), 532-542; https://0-doi-org.brum.beds.ac.uk/10.3390/particles3030036 - 01 Jul 2020

Cited by 5 | Viewed by 2448

Abstract

We present a brief review of general results about non-rotating neutron stars in simple

R^{2}

gravity and its extension with a scalar axion field. Modified Einstein equations are presented for metrics in isotropical coordinates. The mass–radius relation, mass profile and dependence of [...] Read more.

We present a brief review of general results about non-rotating neutron stars in simple

R^{2}

gravity and its extension with a scalar axion field. Modified Einstein equations are presented for metrics in isotropical coordinates. The mass–radius relation, mass profile and dependence of mass from central density on various equations of state are given in comparison to general relativity. Full article

(This article belongs to the Special Issue Selected Papers from “The Modern Physics of Compact Stars and Relativistic Gravity 2019”)

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14 pages, 326 KiB

Open AccessArticle

Relations between Clifford Algebra and Dirac Matrices in the Presence of Families

by Dragan Lukman, Mickael Komendyak and Norma Susana Mankoč Borštnik

Particles 2020, 3(3), 518-531; https://0-doi-org.brum.beds.ac.uk/10.3390/particles3030035 - 29 Jun 2020

Cited by 3 | Viewed by 2063

Abstract

The internal degrees of freedom of fermions are in the spin-charge-family theory described by the Clifford algebra objects, which are superposition of an odd number of

γ^{a}

’s. Arranged into irreducible representations of “eigenvectors” of the Cartan subalgebra of the Lorentz algebra [...] Read more.

The internal degrees of freedom of fermions are in the spin-charge-family theory described by the Clifford algebra objects, which are superposition of an odd number of

γ^{a}

’s. Arranged into irreducible representations of “eigenvectors” of the Cartan subalgebra of the Lorentz algebra

S^{a b}

(= \frac{i}{2} γ^{a} γ^{b} |_{a \neq b})

these objects form

2^{\frac{d}{2} - 1}

families with

2^{\frac{d}{2} - 1}

family members each. Family members of each family offer the description of all the observed quarks and leptons and antiquarks and antileptons, appearing in families. Families are reachable by

{\tilde{S}}^{a b}

= \frac{1}{2} {\tilde{γ}}^{a} {\tilde{γ}}^{b} |_{a \neq b}

. Creation operators, carrying the family member and family quantum numbers form the basis vectors. The action of the operators

γ^{a}

’s,

S^{a b}

,

{\tilde{γ}}^{a}

’s and

{\tilde{S}}^{a b}

, applying on the basis vectors, manifests as matrices. In this paper the basis vectors in

d = (3 + 1)

Clifford space are discussed, chosen in a way that the matrix representations of

γ^{a}

and of

S^{a b}

coincide for each family quantum number, determined by

{\tilde{S}}^{a b}

, with the Dirac matrices. The appearance of charges in Clifford space is discussed by embedding

d = (3 + 1)

space into

d = (5 + 1)

-dimensional space. The achievements and predictions of the spin-charge-family theory is also shortly presented. Full article

(This article belongs to the Special Issue Beyond the Standard Models in Particle Physics and Cosmology)

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Particles, Volume 3, Issue 3 (September 2020) – 8 articles

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