Physical Symmetry Research Articles

A De Sitter-Hubble Equation, the Force in Special Relativity and Some Concepts on Symmetry

Previous works [1] [2] proposed several relevant characteristics of the Hubble field such as the intensity ΓH, potential VH, force FH, Poisson equation, energy EH and a tensor (Tμν)H as well as Ricci and Hubble scalars. In this paper, it is made a proposal for two new ones: the kind of the Hubble field as well as a De Sitter-Hubble equation. Moreover, it is proposed a necessary change in the equation of force in Special Relativity. It is included a paragraph on the search for Symmetry in Physics, Chemistry and Time. Conclusions mention an eventual mirror image both the intensity of the Hubble and gravitational fields as well as the relative impossibility for a Big Crunch.

Зрительное восприятие симметрии как фактор эстетического переживания

The article deals with the formation of aesthetic experience in connection with the perception of physical symmetry of objects and their images. An overview of modern works on the psychology of aesthetic perception in the context of the problem of the perception of symmetry is presented. The phenomenon of symmetry preference in visual perception is illustrated by arguments in its favor and data on its situationality. The ecological context of symmetry in animals and plants is touched in connection with the phenomenon of fluctuating asymmetry as an undirected deviation in the symmetry of a two-sided structure normally distributed in the population. Mathematical models of symmetry of forms and their multiscale representation are discussed. The analysis of the study of the Zen stone garden perceptual peculiarities from the position of the medial axes’ model is carried out.On the basis of the provisions of the transcendental psychology of perception, a hypothesis is advanced about the meta-sensory origin of the aesthetic sense, based on the process of interrelation of the internal symmetrical mechanisms of visual perception and the cognitive processes of creating figurative representations. The relation to the principle of symmetry in the context of the transcendental psychology of perception is shown.

Symmetry, beauty and belief in high-energy physics

This paper engages with the aesthetics of knowl-edge, both in its sense as the connection between knowledge and ‘aesthetic’ judgements of beauty, or ugliness, and of the many ‘aesthetic’ – that is to say sensually perceivable – dimensions of knowledge, which are always to be seen to be constituting an epistemic factor in its production and consumption. On the one hand I analyse how in recent decades the connection between beauty and truth has been systematically employed to both inspire and guide research in high-energy physics; at the same time I also show how this use of aesthetic judgement only reveals its constitutive role in physics research when paying attention to the broad range of aesthetic strategies employed for expressing scientific knowledge.

Maximal Entanglement in High Energy Physics

We analyze how maximal entanglement is generated at the fundamental level in QED by studying correlations between helicity states in tree-level scattering processes at high energy. We demonstrate that two mechanisms for the generation of maximal entanglement are at work: i)ss-channel processes where the virtual photon carries equal overlaps of the helicities of the final state particles, and ii) the indistinguishable superposition between tt- and uu-channels. We then study whether requiring maximal entanglement constrains the coupling structure of QED and the weak interactions. In the case of photon-electron interactions unconstrained by gauge symmetry, we show how this requirement allows to reproduce QED. For ZZ-mediated weak scattering, the maximal entanglement principle leads to non-trivial predictions for the value of the weak mixing angle \theta_WθW. Our results are a first step towards understanding the connections between maximal entanglement and the fundamental symmetries of high-energy physics.

DIII topological superconductivity with emergent time-reversal symmetry

We find a new class of topological superconductors which possess an emergent time-reversal symmetry that is present only after projecting to an effective low-dimensional model. We show that a topological phase in symmetry class DIII can be realized in a noninteracting system coupled to an $s$-wave superconductor only if the physical time-reversal symmetry of the system is broken, and we provide three general criteria that must be satisfied in order to have such a phase. We also provide an explicit model which realizes the class DIII topological superconductor in 1D. We show that, just as in time-reversal invariant topological superconductors, the topological phase is characterized by a Kramers pair of Majorana fermions that are protected by the emergent time-reversal symmetry.

Analysis of Waveguide Devices Involving Lateral and Transverse Perfect Magnetic Wall Boundary Conditions by the Mode‐Matching Method

AbstractThis contribution presents the analysis of waveguide problems involving general boundary conditions of perfect magnetic wall. This type of boundary condition is used in electromagnetic solvers very commonly when the device under analysis has physical symmetry, in order to speed up the computation time. This paper is focused on extending its use in problems having this type of boundary condition in the lateral and transverse walls of the waveguides involved in the problem. The presented formulation, based on the mode‐matching method, will be applied to classical waveguide devices, but also to address radiating problems with a novel formulation. Different applications will be targeted, and the simulation results will be compared with those obtained by other numerical techniques (based on different solvers), validating the presented approach as another suitable tool for computer‐aided design.

Emerging internal symmetries from effective spacetimes

Can global internal and spacetime symmetries be connected without supersymmetry? To answer this question, we investigate Minkowski spacetimes with d space-like extra dimensions and point out under which general conditions external symmetries induce internal symmetries in the effective 4-dimensional theories. We further discuss in this context how internal degrees of freedom and spacetime symmetries can mix without supersymmetry in agreement with the Coleman–Mandula theorem. We present some specific examples which rely on a direct product structure of spacetime such that orthogonal extra dimensions can have symmetries which mix with global internal symmetries. This mechanism opens up new opportunities to understand global symmetries in particle physics.

Optimization of Fusion Kernels on Accelerators with Indirect or Strided Memory Access Patterns

This paper describes optimization for high-dimensional stencil computations on accelerators involving complex memory access patterns, which appear in five dimensional fusion plasma turbulence codes, GYSELA and GT5D. They include different types of memory access patterns, the indirect memory access in GYSELA with a Semi-Lagrangian scheme and the strided memory access in GT5D with a Finite-Difference scheme. We focus on the affinity of the memory access patterns to accelerators such as GPGPUs and Xeon Phi coprocessors. On both devices, the Array of Structure of Array (AoSoA) data layout is preferable for contiguous memory accesses. It is shown that the effective local cache usage by improving spatial and temporal data locality is critical on Xeon Phi. On GPGPU, the texture memory usage improves the performance of the indirect memory accesses in the Semi-Lagrangian scheme. The reuse of registers by taking account of the physical symmetry of the Finite-Difference scheme reduces the amount of memory accesses. Through these optimizations, we achieve acceleration of 3.9 (8.1) on Xeon Phi (GPGPU) for the Semi-Lagrangian scheme and of 1.4 (3.9) on Xeon Phi (GPGPU) for the Finite-Different scheme with respect to the fully optimized codes on Sandy Bridge.

AN ANTHOLOGY OF THE DISTINGUISHED ACHIEVEMENTS IN SCIENCE AND TECHNIQUE. PART 38: NOBEL PRIZE LAUREATES IN PHYSICS FOR 2005-2010

Purpose. Implementation of brief analytical review of the distinguished scientific achievements of the world scientists-physicists, awarded the Nobel Prize in physics for period 2005-2010 yy. Methodology. Scientific methods of collection, analysis and analytical treatment of scientific and technical information of world level in area of modern theoretical and experimental physics. Results. The brief analytical review of the scientific openings and distinguished achievements of scientists-physicists is resulted in area of modern physical and technical problems which were marked by the Nobel Prizes in physics for the period 2005-2010. Originality. Systematization is executed with exposition in the short concentrated form of the known scientific and technical materials, devoted creation of quantum theory of optical coherentness by scientists-physicists, development of laser exact spectroscopy, opening form of spectrum for a black body and anisotropy of space microwave base-line radiation, opening of effect of giant magnetoresistance, opening of mechanism of spontaneous violation of symmetry in subatomic physics, development of new technology of transmission of light in optical fibres, invention of a semiconductor circuit for registration of images and results of innovative experiments on research of 2D material of graphen. Practical value. Popularization and deepening of scientific and technical knowledges for students, engineers and technical specialists and research workers in area of modern theoretical and experimental physics, extending their scientific range of interests and collaboration in further development of scientific and technical progress in human society.

Klein-Weyl's program and the ontology of gauge and quantum systems

We distinguish two orientations in Weyl's analysis of the fundamental role played by the notion of symmetry in physics, namely an orientation inspired by Klein's Erlangen program and a phenomenological-transcendental orientation. By privileging the former to the detriment of the latter, we sketch a group(oid)-theoretical program—that we call the Klein-Weyl program—for the interpretation of both gauge theories and quantum mechanics in a single conceptual framework. This program is based on Weyl's notion of a “structure-endowed entity” equipped with a “group of automorphisms”. First, we analyze what Weyl calls the “problem of relativity” in the frameworks provided by special relativity, general relativity, and Yang-Mills theories. We argue that both general relativity and Yang-Mills theories can be understood in terms of a localization of Klein's Erlangen program: while the latter describes the group-theoretical automorphisms of a single structure (such as homogenous geometries), local gauge symmetries and the corresponding gauge fields (Ehresmann connections) can be naturally understood in terms of the groupoid-theoretical isomorphisms in a family of identical structures. Second, we argue that quantum mechanics can be understood in terms of a linearization of Klein's Erlangen program. This stance leads us to an interpretation of the fact that quantum numbers are “indices characterizing representations of groups” ((Weyl, 1931a), p.xxi) in terms of a correspondence between the ontological categories of identity and determinateness.

Combining symmetry collective states with coupled-cluster theory: Lessons from the Agassi model Hamiltonian

The failures of single-reference coupled cluster for strongly correlated many-body systems is flagged at the mean-field level by the spontaneous breaking of one or more physical symmetries of the Hamiltonian. Restoring the symmetry of the mean-field determinant by projection reveals that coupled cluster fails because it factorizes high-order excitation amplitudes incorrectly. However, symmetry-projected mean-field wave functions do not account sufficiently for dynamic (or weak) correlation. Here we pursue a merger of symmetry projection and coupled cluster theory, following previous work along these lines that utilized the simple Lipkin model system as a testbed [J. Chem. Phys. 146, 054110 (2017)]. We generalize the concept of a symmetry-projected mean-field wave function to the concept of a symmetry projected state, in which the factorization of high-order excitation amplitudes in terms of low-order ones is guided by symmetry projection and is not exponential, and combine them with coupled cluster theory in order to model the ground state of the Agassi Hamiltonian. This model has two separate channels of correlation and two separate physical symmetries which are broken under strong correlation. We show how the combination of symmetry collective states and coupled cluster is effective in obtaining correlation energies and order parameters of the Agassi model throughout its phase diagram.

Low-Profile Dual-Band Pattern Diversity Patch Antenna Based on Composite Right/Left-Handed Transmission Line

A low-profile patch antenna with pattern diversity is proposed. The topology combines an annular ring together with a center-fed circular patch. The composite right/left-handed transmission line is loaded on both the annular ring and the circular patch, to realize the 2.4/3.5-GHz dual-band operation. The outer annular ring works at its first pair of symmetric modes, which results in broadside radiation patterns, while the inner circular patch provides omnidirectional patterns in the horizontal plane, as a consequence of its physical circular symmetry. The field distribution is analyzed to verify the operational principle. By optimizing the feeding network, the antenna reaches a good impedance matching in both bands. A prototype is fabricated, and the measured results agree well with the simulated ones. The measured correlation coefficient is lower than 0.04 and 0.05 in the lower and upper band, respectively.

Stochastic modeling and generation of random fields of elasticity tensors: A unified information-theoretic approach

In this Note, we present a unified approach to the information-theoretic modeling and simulation of a class of elasticity random fields, for all physical symmetry classes. The new stochastic representation builds upon a Walpole tensor decomposition, which allows the maximum entropy constraints to be decoupled in accordance with the tensor (sub)algebras associated with the class under consideration. In contrast to previous works where the construction was carried out on the scalar-valued Walpole coordinates, the proposed strategy involves both matrix-valued and scalar-valued random fields. This enables, in particular, the construction of a generation algorithm based on a memoryless transformation, hence improving the computational efficiency of the framework. Two applications involving weak symmetries and sampling over spherical and cylindrical geometries are subsequently provided. These numerical experiments are relevant to the modeling of elastic interphases in nanocomposites, as well as to the simulation of spatially dependent wood properties for instance.

Li(e)nearity

This article brings to light the fact that linearity is by itself a meaningful symmetry in the senses of Lie and Noether. First, the role played by that ‘linearity symmetry’ in the quadrature of linear second-order differential equations is revisited through the use of adapted variables and the identification of a conserved quantity as Lie invariant. Second, the celebrated Caldirola–Kanai Lagrangian—from which the differential equation is deducible—is shown to be naturally generated by a Jacobi last multiplier inherited from the linearity symmetry. Then, the latter is recognised to be also a Noether one. Finally, the study is extended to higher-order linear differential equations, derivable or not from an action principle. Incidentally, this work can serve as an introduction to the central question of continuous symmetries in physics and mathematics. It has the advantage of being approachable to undergraduate students since the linearity symmetry is by its very nature sufficiently simple to be treatable without any use of Lie generators.

A crystal plasticity model for slip in hexagonal close packed metals based on discrete dislocation simulations

This work develops a method for calibrating a crystal plasticity model to the results of discrete dislocation (DD) simulations. The crystal model explicitly represents junction formation and annihilation mechanisms and applies these mechanisms to describe hardening in hexagonal close packed metals. The model treats these dislocation mechanisms separately from elastic interactions among populations of dislocations, which the model represents through a conventional strength-interaction matrix. This split between elastic interactions and junction formation mechanisms more accurately reproduces the DD data and results in a multi-scale model that better represents the lower scale physics. The fitting procedure employs concepts of machine learning—feature selection by regularized regression and cross-validation—to develop a robust, physically accurate crystal model. The work also presents a method for ensuring the final, calibrated crystal model respects the physical symmetries of the crystal system. Calibrating the crystal model requires fitting two linear operators: one describing elastic dislocation interactions and another describing junction formation and annihilation dislocation reactions. The structure of these operators in the final, calibrated model reflect the crystal symmetry and slip system geometry of the DD simulations.

Wigner-Araki-Yanase theorem beyond conservation laws

The ability to measure every quantum observable is ensured by a fundamental result in quantum measurement theory. Nevertheless, additive conservation laws associated with physical symmetries, such as the angular momentum conservation, may lead to restrictions on the measurability of the observables. Such limitations are imposed by the theorem of Wigner, Araki, and Yanase (WAY). In this paper a formulation of the WAY theorem is presented rephrasing the measurability limitations in terms of quantum incompatibility. This broader mathematical basis enables us to both capture and generalize the WAY theorem by allowing us to drop the assumptions of additivity and even conservation of the involved quantities. Moreover, we extend the WAY theorem to the general level of positive operator-valued measures.

A few questions related to information and symmetries in physics

Information exchange between inanimate objects (like individual physical particles, or systems) involves special approaches, due to the peculiarity that conscious information emitters/recipients are excluded from the process. This paper aims at answering a part of some questions arising by such approaches. One can ask the question, whether is it possible to speak about physical information when there is no live recipient to accept, evaluate, and use it? Can one speak about “physical information” (e.g., signal exchange) between inanimate physical objects at all? (cf., Feynman diagrams.) If yes, what is the nature of that information? Is (physical) information a passive phenomenon, or its existence presumes activity? What does a signal represent if it is not observed and used at the other end, and where is that other end when one can say that the signal in question was lost without observation or use? I try to illustrate my personal answers with a few examples quoted from the history of 20th c. physics. My answers to the questions are not intended to be revelations and to provide final solutions, rather they serve as arguments and indicate that nothing is closed, the discussion is open.

Application of the hidden local symmetry in hadron physics

About two decades ago, Gerry Brown pushed me to study hadron physics using hadronic models based on the hidden local symmetry (HLS). Since then, I have been involving many works related to the HLS. In this contribution to Gerry’s memorial, I will summarize my recent analyses associated with the HLS. After a very brief summary of the HLS, I will show a way to determine parameters of the HLS model from holographic QCD models. This model provides a soliton solution which is identified with the nucleon. I will briefly introduce a model in which the solitons are put onto a crystal lattice for simulating nuclear matter. The results suggest existence of the chiral invariant mass of nucleon. I also briefly review my recent analyses on the nuclear matter by using a hadronic model including nucleon field together with the [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] mesons based on the parity doublet structure of nucleon combined with the HLS, in which the chiral invariant mass of the nucleon is naturally embedded. The result implies that studying effective masses of nucleons will give a clue for the chiral invariant mass. Finally, I will show our recent analysis on the medium modification of charmed meson masses using a chiral model based on the chiral doubling structure of charmed mesons. The result shows that the masses of the chiral partners of charmed mesons become closer in high density reflecting the particle chiral symmetry restoration in medium.

In search of a pristine signal for (scale-)chiral symmetry in nuclei

I describe the long-standing search for a “smoking-gun” signal for the manifestation of (scale-)chiral symmetry in nuclear interactions. It is prompted by Gerry Brown’s last unpublished note, reproduced verbatim below, on the preeminent role of pions and vector ([Formula: see text]) mesons in providing a simple and elegant description of strongly correlated nuclear interactions. In this note written in tribute to Gerry Brown, I first describe a case of an unambiguous signal in axial-charge transitions in nuclei and then combine his ideas with the more recent development on the role of hidden symmetries in nuclear physics. What transpires is the surprising conclusion that the Landau–Migdal fixed point interaction [Formula: see text], the nuclear tensor forces and Brown–Rho scaling, all encoded in scale-invariant hidden local symmetry, as Gerry put, “run the show and make all forces equal.”

Joint System and Algorithm Design for Computationally Efficient Fan Beam Coded Aperture X-Ray Coherent Scatter Imaging

In x-ray coherent scatter tomography, tomographic measurements of the forward scatter distribution are used to infer scatter densities within a volume. A radiopaque 2D pattern placed between the object and the detector array enables the disambiguation between different scatter events. The use of a fan beam source illumination to speed up data acquisition relative to a pencil beam presents computational challenges. To facilitate the use of iterative algorithms based on a penalized Poisson log-likelihood function, efficient computational implementation of the forward and backward models are needed. Our proposed implementation exploits physical symmetries and structural properties of the system and suggests a joint system-algorithm design, where the system design choices are influenced by computational considerations, and in turn lead to reduced reconstruction time. Computational-time speedups of approximately 146 and 32 are achieved in the computation of the forward and backward models, respectively. Results validating the forward model and reconstruction algorithm are presented on simulated analytic and Monte Carlo data.