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A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Physics".

Deadline for manuscript submissions: closed (31 October 2023) | Viewed by 63873

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Dr. Giovanni Modanese

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Faculty of Science and Technology, Free University of Bozen-Bolzano, 39100 Bolzano, Italy
Interests: quantum and classical field theory; gravitation; complex systems in connection to social science and economics; mathematical methods
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Special Issue Information

Dear Colleagues,

Maxwell's equations are so successful and useful that examples of their elementary and advanced applications are on display everywhere in real life. Furthermore QED, the quantum field theory obtained from the quantization of the Maxwell Lagrangian is today our most precise physical theory. Yet there is still room for extensions of Maxwell's theory, and work by several authors in the last several years has led to progress in multiple directions. One possible extension relies on the introduction of additional degrees of freedom, like the field "dA" in the extended Lagrangian of Ohmura and Aharonov–Bohm, with ensuing reduction of the gauge symmetry. These extra degrees of freedom can have major consequences in curved space (with applications to cosmology). They can also be relevant in flat space, at least at the level of effective theories, if local conservation of charge is violated for some reason, for instance because (1) the effective quantum theory describing the field source obeys non-local wave equations, or (2) this effective theory has fractional dimension, or (3) renormalization leads to anomalies in the Ward identities. All these special circumstances are also, of course, of fundamental interest in their own right. Further of interest for this Special Issue are extended theories of the electromagnetic field in which the field equations themselves become non-local and acquire new properties due to the coupling with special systems in condensed matter, like systems with memory, superconductors, or superfluids with macroscopic coherence. Such equations require new solution methods and a careful analysis of their relativistic invariance, possibly disclosing violations of Lorentz symmetry compatible with observational constraints. Both original research articles and review articles are welcome for this Special Issue.

Dr. Giovanni Modanese
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Symmetry is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Published Papers (7 papers)

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Research

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15 pages, 295 KiB

Open AccessArticle

Aharonov–Bohm Electrodynamics in Material Media: A Scalar e.m. Field Cannot Cause Dissipation in a Medium

by Fernando Minotti and Giovanni Modanese

Symmetry 2023, 15(5), 1119; https://doi.org/10.3390/sym15051119 - 19 May 2023

Cited by 1 | Viewed by 879

Abstract

In the extension of Maxwell equations based on the Aharonov–Bohm Lagrangian, the e.m. field has an additional degree of freedom, namely, a scalar field generated by charge and currents that are not locally conserved. We analyze the propagation of this scalar field through two different media (a pure dielectric and an ohmic conductor) and study its property over a frequency range where the properties of the media are frequency-independent. We find that an electromagnetic (e.m.) scalar wave cannot propagate in a material medium. If a scalar wave in vacuum impinges on a material medium it is reflected, at most exciting in the medium a pure “potential” wave (which we also call a “gauge” wave) propagating at c, the speed of light in vacuum, with a vector potential whose Fourier amplitude is related to that of the scalar potential by

ω A_{0} = k ϕ_{0}

, where

ω^{2} = c^{2} {|k|}^{2}

. Full article

(This article belongs to the Special Issue Symmetry, Extended Maxwell Equations and Non-local Wavefunctions)

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20 pages, 407 KiB

Open AccessFeature PaperArticle

Coherent Plasma in a Lattice

by Luca Gamberale and Giovanni Modanese

Symmetry 2023, 15(2), 454; https://doi.org/10.3390/sym15020454 - 08 Feb 2023

Cited by 3 | Viewed by 989

Abstract

We present a fully second-quantized calculation showing the emergence of spontaneous coherent configurations of the electromagnetic field interacting with charged bosons in a regular lattice. The bosons tend to oscillate at their plasma frequency, and in addition are subjected to electrostatic forces which keep them confined close to the lattice sites while causing a frequency shift in the oscillation. Under certain conditions upon these frequencies, we find that a suitably defined set of coherent states (coherent both in the field and matter degrees of freedom) exhibit a negative energy gap with respect to the perturbative ground state. This is true in the RWA approximation and for position-independent fields to both the first and second order in the interaction Hamiltonian. We compare this result with other recent findings from cavity QED, and note that (1) consideration of full 3D wavefunctions and a careful definition of the coherent states are essential for obtaining the energy gap, and (2) although our calculation is made in reference to bosons, it may apply to protons bound in a crystal matrix as well if their density is very low compared to the density of available states. Full article

(This article belongs to the Special Issue Symmetry, Extended Maxwell Equations and Non-local Wavefunctions)

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17 pages, 486 KiB

Open AccessArticle

Are Current Discontinuities in Molecular Devices Experimentally Observable?

by F. Minotti and G. Modanese

Symmetry 2021, 13(4), 691; https://doi.org/10.3390/sym13040691 - 15 Apr 2021

Cited by 4 | Viewed by 1479

Abstract

An ongoing debate in the first-principles description of conduction in molecular devices concerns the correct definition of current in the presence of non-local potentials. If the physical current density [...] Read more.

j = (- i e ℏ / 2 m) (Ψ^{*} \nabla Ψ - Ψ \nabla Ψ^{*})

is not locally conserved but can be re-adjusted by a non-local term, which current should be regarded as real? Situations of this kind have been studied for example, for currents in saturated chains of alkanes, silanes and germanes, and in linear carbon wires. We prove that in any case the extended Maxwell equations by Aharonov-Bohm give the e.m. field generated by such currents without any ambiguity. In fact, the wave equations have the same source terms as in Maxwell theory, but the local non-conservation of charge leads to longitudinal radiative contributions of

E

, as well as to additional transverse radiative terms in both

E

and

B

. For an oscillating dipole we show that the radiated electrical field has a longitudinal component proportional to

ω \hat{P}

, where

\hat{P}

is the anomalous moment

\int \hat{I} (x) x d^{3} x

and

\hat{I}

is the space-dependent part of the anomaly

I = \partial_{t} ρ + \nabla \cdot j

. For example, if a fraction

η

of a charge q oscillating over a distance

2 a

lacks a corresponding current, the predicted maximum longitudinal field (along the oscillation axis) is

E_{L, m a x} = 2 η ω^{2} q a / (c^{2} r)

. In the case of a stationary current in a molecular device, a failure of local current conservation causes a “missing field” effect that can be experimentally observable, especially if its entity depends on the total current; in this case one should observe at a fixed position changes in the ratio

B / i

in dependence on i, in contrast with the standard Maxwell equations. The missing field effect is confirmed by numerical solutions of the extended equations, which also show the spatial distribution of the non-local term in the current. Full article

(This article belongs to the Special Issue Symmetry, Extended Maxwell Equations and Non-local Wavefunctions)

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96 pages, 23815 KiB

Open AccessArticle

Polarity Free Magnetic Repulsion and Magnetic Bound State

by Hamdi Ucar

Symmetry 2021, 13(3), 442; https://doi.org/10.3390/sym13030442 - 09 Mar 2021

Cited by 3 | Viewed by 51813

Abstract

This is a report on a dynamic autonomous magnetic interaction which does not depend on polarities resulting in short ranged repulsion involving one or more inertial bodies and a new class of bound state based on this interaction. Both effects are new to the literature, found so far. Experimental results are generalized and reported qualitatively. Working principles of these effects are provided within classical mechanics and found consistent with observations and simulations. The effects are based on the interaction of a rigid and finite inertial body (an object having mass and moment of inertia) endowed with a magnetic moment with a cyclic inhomogeneous magnetic field which does not require to have a local minimum. Such a body having some degrees of freedom involved in driven harmonic motion by this interaction can experience a net force in the direction of the weak field regardless of its position and orientation or can find stable equilibrium with the field itself autonomously. The former is called polarity free magnetic repulsion and the latter is classified as a magnetic bound state. Experiments show that a bound state can be obtained between two free bodies having magnetic dipole moment as a solution of two-body problem. Various schemes of trapping bodies having magnetic moments by rotating fields are realized as well as rotating bodies trapped by a static dipole field in presence of gravity. Additionally, a special case of bound state called bipolar bound state between free dipole bodies is investigated. Full article

(This article belongs to the Special Issue Symmetry, Extended Maxwell Equations and Non-local Wavefunctions)

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Graphical abstract

22 pages, 3495 KiB

Open AccessArticle

Inverse Maxwell Distribution and Statistical Process Control: An Efficient Approach for Monitoring Positively Skewed Process

by M. Hafidz Omar, Sheikh Y. Arafat, M. Pear Hossain and Muhammad Riaz

Symmetry 2021, 13(2), 189; https://doi.org/10.3390/sym13020189 - 25 Jan 2021

Cited by 11 | Viewed by 2527

Abstract

(1) Background: The literature discusses the inverse Maxwell distribution theoretically without application. Control charting is promising, but needs development for inverse Maxwell processes. (2) Methods: Thus, we develop the

V_{I M}

control chart for monitoring the inverse Maxwell scale parameter and studied [...] Read more.

V_{I M}

control chart for monitoring the inverse Maxwell scale parameter and studied its statistical properties. The chart’s performance is evaluated using power curves and run length properties. (3) Results: Further, we use simulated data to compare the shift detection capability of our chart with Weibull, gamma, and lognormal charts. (4) Conclusion: The analysis demonstrates our chart’s efficiency for monitoring skewed processes. Finally, we apply our chart for monitoring real world lifetimes of car brake pads. Full article

(This article belongs to the Special Issue Symmetry, Extended Maxwell Equations and Non-local Wavefunctions)

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Review

Jump to: Research

28 pages, 427 KiB

Open AccessFeature PaperReview

Lorentz Violation in Finsler Geometry

by Jie Zhu and Bo-Qiang Ma

Symmetry 2023, 15(5), 978; https://doi.org/10.3390/sym15050978 - 25 Apr 2023

Cited by 2 | Viewed by 1477

Abstract

Lorentz invariance is one of the foundations of modern physics; however, Lorentz violation may happen from the perspective of quantum gravity, and plenty of studies on Lorentz violation have arisen in recent years. As a good tool to explore Lorentz violation, Finsler geometry is a natural and fundamental generalization of Riemann geometry. The Finsler structure depends on both coordinates and velocities. Here, we simply introduce the mathematics of Finsler geometry. We review the connection between modified dispersion relations and Finsler geometries and discuss the physical influence from Finsler geometry. We review the connection between Finsler geometries and theories of Lorentz violation, such as the doubly special relativity, the standard-model extension, and the very special relativity. Full article

(This article belongs to the Special Issue Symmetry, Extended Maxwell Equations and Non-local Wavefunctions)

22 pages, 2863 KiB

Open AccessReview

Implications of Gauge-Free Extended Electrodynamics

by Donald Reed and Lee M. Hively

Symmetry 2020, 12(12), 2110; https://doi.org/10.3390/sym12122110 - 18 Dec 2020

Cited by 5 | Viewed by 3339

Abstract

Recent tests measured an irrotational (curl-free) magnetic vector potential (A) that is contrary to classical electrodynamics (CED). A (irrotational) arises in extended electrodynamics (EED) that is derivable from the Stueckelberg Lagrangian. A (irrotational) implies an irrotational (gradient-driven) electrical current density, J. Consequently, EED is gauge-free and provably unique. EED predicts a scalar field that equals the quantity usually set to zero as the Lorenz gauge, making A and the scalar potential () independent and physically-measureable fields. EED predicts a scalar-longitudinal wave (SLW) that has an electric field along the direction of propagation together with the scalar field, carrying both energy and momentum. EED also predicts the scalar wave (SW) that carries energy without momentum. EED predicts that the SLW and SW are unconstrained by the skin effect, because neither wave has a magnetic field that generates dissipative eddy currents in electrical conductors. The novel concept of a “gradient-driven” current is a key feature of US Patent 9,306,527 that disclosed antennas for SLW generation and reception. Preliminary experiments have validated the SLW’s no-skin-effect constraint as a potential harbinger of new technologies, a possible explanation for poorly understood laboratory and astrophysical phenomena, and a forerunner of paradigm revolutions. Full article

(This article belongs to the Special Issue Symmetry, Extended Maxwell Equations and Non-local Wavefunctions)

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