Searching for integrable Hamiltonian systems with Platonic symmetries
Rastelli, Giovanni
2010-01-01
In this paper we try to find examples of integrable natural Hamiltonian systems on the sphere $S^2$ with the symmetries of each Platonic polyhedra. Although some of these systems are known, their expression is extremely complicated; we try here to find the simplest possible expressions for this kind of dynamical systems. Even in the simplest cases it is not easy to prove their integrability by direct computation of the first integrals, therefore, we make use of numerical methods to provide evidences of integrability; namely, by analyzing their Poincar\\'e sections (surface sections). In this way we find three systems with platonic symmetries, one for each class of equivalent Platonic polyhedra: tetrahedral, exahedral-octahedral, dodecahedral-icosahedral, showing evidences of integrability. The proof of integrability and the construction of the first integrals are left for further works. As an outline of the possible developments if the integrability of these systems will be proved, we show how to build from th...
Symmetry and resonant modes in platonic grating stacks
Haslinger, Stewart G; Movchan, Natasha V; McPhedran, Ross C
2013-01-01
We study the flexural wave modes existing in finite stacks of gratings containing rigid, zero-radius pins. We group the modes into even and odd classes, and derive dispersion equations for each. We study the recently discovered EDIT (elasto-dynamically inhibited transmission) phenomenon, and relate it to the occurrence of trapped waves of even and odd symmetries being simultaneously resonant. We show how the EDIT interaction may be steered over a wide range of frequencies and angles, using a strategy in which the single-grating reflectance is kept high, so enabling the quality factors of the even and odd resonances to be kept large.
Farmer, David W
1995-01-01
In most mathematics textbooks, the most exciting part of mathematics-the process of invention and discovery-is completely hidden from the reader. The aim of Groups and Symmetry is to change all that. By means of a series of carefully selected tasks, this book leads readers to discover some real mathematics. There are no formulas to memorize; no procedures to follow. The book is a guide: Its job is to start you in the right direction and to bring you back if you stray too far. Discovery is left to you. Suitable for a one-semester course at the beginning undergraduate level, there are no prerequ
Symmetry and group theory in chemistry
Ladd, M
1998-01-01
A comprehensive discussion of group theory in the context of molecular and crystal symmetry, this book covers both point-group and space-group symmetries.Provides a comprehensive discussion of group theory in the context of molecular and crystal symmetryCovers both point-group and space-group symmetriesIncludes tutorial solutions
Platonic solids generate their four-dimensional analogues
Dechant, Pierre-Philippe
2013-01-01
In this paper, we show how regular convex 4-polytopes - the analogues of the Platonic solids in four dimensions - can be constructed from three-dimensional considerations concerning the Platonic solids alone. Via the Cartan-Dieudonne theorem, the reflective symmetries of the Platonic solids generate rotations. In a Clifford algebra framework, the space of spinors generating such three-dimensional rotations has a natural four-dimensional Euclidean structure. The spinors arising from the Platonic Solids can thus in turn be interpreted as vertices in four-dimensional space, giving a simple construction of the 4D polytopes 16-cell, 24-cell, the F_4 root system and the 600-cell. In particular, these polytopes have `mysterious' symmetries, that are almost trivial when seen from the three-dimensional spinorial point of view. In fact, all these induced polytopes are also known to be root systems and thus generate rank-4 Coxeter groups, which can be shown to be a general property of the spinor construction. These cons...
Manton, Nicholas
2014-01-01
We construct a number of explicit examples of hyperbolic monopoles, with various charges and often with some platonic symmetry. The fields are obtained from instanton data in four-dimensional Euclidean space that are invariant under a circle action, and the monopole charge is equal to the instanton charge. A key ingredient is the identification of a new set of constraints on ADHM instanton data that are sufficient to ensure the circle invariance. Algebraic formulae for the Higgs field magnitude are given and from these we compute and illustrate the energy density of the monopoles. For particular monopoles, the explicit formulae provide a proof that the number of zeros of the Higgs field is greater than the monopole charge. We also present some one-parameter families of monopoles analogous to known scattering events for Euclidean monopoles within the geodesic approximation.
Parity-time symmetry broken by point-group symmetry
Energy Technology Data Exchange (ETDEWEB)
Fernández, Francisco M., E-mail: fernande@quimica.unlp.edu.ar; Garcia, Javier [INIFTA (UNLP, CCT La Plata-CONICET), División Química Teórica, Blvd. 113 S/N, Sucursal 4, Casilla de Correo 16, 1900 La Plata (Argentina)
2014-04-15
We discuss a parity-time (PT) symmetric Hamiltonian with complex eigenvalues. It is based on the dimensionless Schrödinger equation for a particle in a square box with the PT-symmetric potential V(x, y) = iaxy. Perturbation theory clearly shows that some of the eigenvalues are complex for sufficiently small values of |a|. Point-group symmetry proves useful to guess if some of the eigenvalues may already be complex for all values of the coupling constant. We confirm those conclusions by means of an accurate numerical calculation based on the diagonalization method. On the other hand, the Schrödinger equation with the potential V(x, y) = iaxy{sup 2} exhibits real eigenvalues for sufficiently small values of |a|. Point group symmetry suggests that PT-symmetry may be broken in the former case and unbroken in the latter one.
Topology of Platonic Spherical Manifolds: From Homotopy to Harmonic Analysis
Kramer, Peter
2015-01-01
We carry out the harmonic analysis on four Platonic spherical three-manifolds with different topologies. Starting out from the homotopies (Everitt 2004), we convert them into deck operations, acting on the simply connected three-sphere as the cover, and obtain the corresponding variety of deck groups. For each topology, the three-sphere is tiled into copies of a fundamental domain under the corresponding deck group. We employ the point symmetry of each Platonic manifold to construct its fundamental domain as a spherical orbifold. While the three-sphere supports an~orthonormal complete basis for harmonic analysis formed by Wigner polynomials, a given spherical orbifold leads to a selection of a specific subbasis. The resulting selection rules find applications in cosmic topology, probed by the cosmic microwave background.
Symmetry and group theory throughout physics
Directory of Open Access Journals (Sweden)
Villain J.
2012-03-01
Full Text Available As noticed in 1884 by Pierre Curie [1], physical properties of matter are tightly related to the kind of symmetry of the medium. Group theory is a systematic tool, though not always easy to handle, to exploit symmetry properties, for instance to find the eigenvectors and eigenvalues of an operator. Certain properties (optical activity, piezoelectricity are forbidden in molecules or crystals of high symmetry. A few theorems (Noether, Goldstone establish general relations between physical properties and symmetry. Applications of group theory to condensed matter physics, elementary particle physics, quantum mechanics, electromagnetism are reviewed. Group theory is not only a tool, but also a beautiful construction which casts insight into natural phenomena.
Continuous point symmetries in Group Field Theories
Kegeles, Alexander
2016-01-01
We discuss the notion of symmetries in non-local field theories characterized by integro-differential equation of motion, from a geometric perspective. We then focus on Group Field Theory (GFT) models of quantum gravity. We provide a general analysis of their continuous point symmetry transformations, including the generalized conservation laws following from them, and apply it to several GFT models of interest to current research.
Symmetries and Laplacians introduction to harmonic analysis, group representations and applications
Gurarie, D
1992-01-01
Designed as an introduction to harmonic analysis and group representations,this book covers a wide range of topics rather than delving deeply into anyparticular one. In the words of H. Weyl ...it is primarily meant forthe humble, who want to learn as new the things set forth therein, rather thanfor the proud and learned who are already familiar with the subject and merelylook for quick and exact information.... The main objective is tointroduce the reader to concepts, ideas, results and techniques that evolvearound symmetry-groups, representations and Laplacians. Morespecifically, the main interest concerns geometrical objects and structures{X}, discrete or continuous, that possess sufficiently large symmetrygroup G, such as regular graphs (Platonic solids), lattices, andsymmetric Riemannian manifolds. All such objects have a natural Laplacian&Dgr;, a linear operator on functions over X, invariant underthe group action. There are many problems associated with Laplacians onX, such as continuous or discrete...
Faces of platonic solids in all dimensions
Szajewska, Marzena
2012-01-01
This paper considers Platonic solids/polytopes in the real Euclidean space R^n of dimension 3 <= n < infinity. The Platonic solids/polytopes are described together with their faces of dimensions 0 <= d <= n-1. Dual pairs of Platonic polytopes are considered in parallel. The underlying fi?nite Coxeter groups are those of simple Lie algebras of types An, Bn, Cn, F4 and of non-crystallographic Coxeter groups H3, H4. Our method consists in recursively decorating the appropriate Coxeter-Dynkin diagram. Each recursion step provides the essential information about faces of a speci?c dimension. If, at each recursion step, all of the faces are in the same Coxeter group orbit, i.e. are identical, the solid is called Platonic.
Quregisters, Symmetry Groups and Clifford Algebras
Cervantes, D.; Morales-Luna, G.
2016-03-01
Natural one-to-one and two-to-one homomorphisms from SO(3) into SU(2) are built conventionally, and the collection of qubits, is identified with a subgroup of SU(2). This construction is suitable to be extended to corresponding tensor powers. The notions of qubits, quregisters and qugates are translated into the language of symmetry groups. The corresponding elements to entangled states in the tensor product of Hilbert spaces reflect entanglement properties as well, and in this way a notion of entanglement is realised in the tensor product of symmetry groups.
Socrates: Platonic Political Ideal
Directory of Open Access Journals (Sweden)
Christopher P. Long
2012-08-01
Full Text Available This essay articulates the differences and suggests the similarities between the practices of Socratic political speaking and those of Platonic political writing. The essay delineates Socratic speaking and Platonic writing as both erotically oriented toward ideals capable of transforming the lives of individuals and their relationships with one another. Besides it shows that in the Protagoras the practices of Socratic political speaking are concerned less with Protagoras than with the individual young man, Hippocrates. In the Phaedo, this ideal of a Socrates is amplified in such a way that Platonic writing itself emerges as capable of doing with readers what Socratic speaking did with those he encountered. Socrates is the Platonic political ideal. The result is a picture of the transformative political power of Socratic speaking and Platonic writing both.
Group Parametrized Tunneling and Local Symmetry Conditions
Harter, William; Mitchell, Justin
2010-06-01
Recently, Hougen showed an ad hoc symmetry-based parameterization scheme for analyzing tunneling dynamics and high resolution spectra of fluxional molecular structure similar to S-parameter analysis of superfine structure in SF_6 or NH_3 maser inversion dynamics by Feynman et.al. The problem is that ad hoc parametrization, like path integration in general, can lead to logjams of parameters or ``paths'' with no way to pick out the relevant ones. We show a way to identify and use relevant parameters for a tunneling Hamiltonian H having global G-symmetry-defined bases by first expressing H as a linear combination bar γ ^i {bar g}_i of operators in dual symmetry group bar G. The coefficients bar γ ^i are parameters that define a complete set of allowed paths for any H with G-symmetry and are related thru spectral decomposition of G to eigensolutions of H. Quantum G vs.bar G duality generalizes lab -vs. -body and state -vs. -particle. The number of relevant bar γ ^i-parameters is reduced if a system tends to stick in states of a local symmetry subgroup LsubsetG so the H spectrum forms level clusters labeled by induced representations d(ℓ)(L)\\uparrowG. A cluster-(ℓ) has one E(epsilon)-level labeled by G species (epsilon) for each L species (ℓ) in Depsilon(G)downarrowL by Frobenius reciprocity. Then we apply local symmetry conditions to each irrep Depsilon(bar γ ^i {bar g}_i) that has already been reduced with respect to local symmetry L. This amounts to setting each off-diagonal component Dj,kepsilon(H) to zero. Local symmetry conditions may tell which bar γ ^i-parameters are redundant or zero and directly determine d(ℓ)\\uparrowG tunneling matrix eigenvalues that give E(epsilon)-levels as well as eigenvectors. Otherwise one may need to choose a particular localizing subgroup chain LsubsetL_1subsetL_2...G and further reduce the number of path parameters to facilitate spectral fitting. J.T. Hougen, 2009 MSS RJ01, {J Mol Spect 123, 197 (1987) W.G. Harter and
Holonomy groups and W-symmetries
Howe, Paul S
1993-01-01
Irreducible sigma models, i.e. those for which the partition function does not factorise, are defined on Riemannian spaces with irreducible holonomy groups. These special geometries are characterised by the existence of covariantly constant forms which in turn give rise to symmetries of the supersymmetric sigma model actions. The Poisson bracket algebra of the corresponding currents is a W-algebra. Extended supersymmetries arise as special cases.
Discrete flavour symmetries from the Heisenberg group
Floratos, E. G.; Leontaris, G. K.
2016-04-01
Non-abelian discrete symmetries are of particular importance in model building. They are mainly invoked to explain the various fermion mass hierarchies and forbid dangerous superpotential terms. In string models they are usually associated to the geometry of the compactification manifold and more particularly to the magnetised branes in toroidal compactifications. Motivated by these facts, in this note we propose a unified framework to construct representations of finite discrete family groups based on the automorphisms of the discrete and finite Heisenberg group. We focus in particular, on the PSL2 (p) groups which contain the phenomenologically interesting cases.
Discrete Flavour Symmetries from the Heisenberg Group
Floratos, E G
2015-01-01
Non-abelian discrete symmetries are of particular importance in model building. They are mainly invoked to explain the various fermion mass hierarchies and forbid dangerous superpotential terms. In string models they are usually associated to the geometry of the compactification manifold and more particularly to the magnetised branes in toroidal compactifications. Motivated by these facts, in this note we propose a unified framework to construct representations of finite discrete family groups based on the automorphisms of the discrete and finite Heisenberg group. We focus in particular in the $PSL_2(p)$ groups which contain the phenomenologically interesting cases.
DEFF Research Database (Denmark)
Ostenfeld, Erik Nis
2011-01-01
Artiklen falder i to dele, en metodisk del og en gennemgang af hovedpunkter i Platons filosofi. Det er almindelig viden blandt oplyste, uddannede mennesker, at Platon er en af de vigtigste filosoffer overhovedet i den vesterlandske kultur. Dette illustreres af den indflydelse på filosofi......, litteratur og kultur, han har haft i de 2500 år, der er gået, siden han levede. Man mener også at vide, at Platons filosofi bl.a. indeholder forestillinger om en ideverden og en udødelig sjæl, der midlertidigt er havnet i en distraherende uvirkelig skyggeverden. Ved filosofiens hjælp kan den vende tilbage...... til skuet af ideerne. Hertil hører også billedet af den tredelte sjæl som en kusk med vognspand af to mere eller mindre uregerlige heste. Endelig er Platon forbundet med ideen om en idealstat regeret af filosoffer. Skønt alle disse forestillinger findes i Platons værk, er det ikke korrekt at antage...
DEFF Research Database (Denmark)
Ostenfeld, Erik Nis
2011-01-01
Artiklen falder i to dele, en metodisk del og en gennemgang af hovedpunkter i Platons filosofi. Det er almindelig viden blandt oplyste, uddannede mennesker, at Platon er en af de vigtigste filosoffer overhovedet i den vesterlandske kultur. Dette illustreres af den indflydelse på filosofi......, litteratur og kultur, han har haft i de 2500 år, der er gået, siden han levede. Man mener også at vide, at Platons filosofi bl.a. indeholder forestillinger om en ideverden og en udødelig sjæl, der midlertidigt er havnet i en distraherende uvirkelig skyggeverden. Ved filosofiens hjælp kan den vende tilbage...... til skuet af ideerne. Hertil hører også billedet af den tredelte sjæl som en kusk med vognspand af to mere eller mindre uregerlige heste. Endelig er Platon forbundet med ideen om en idealstat regeret af filosoffer. Skønt alle disse forestillinger findes i Platons værk, er det ikke korrekt at antage...
Directory of Open Access Journals (Sweden)
Maria Chiara Pievatolo
2014-03-01
Full Text Available L’ipertesto dedicata al Carmide di Platone, composto per l’uso degli studenti dell’ateneo pisano, è a disposizione di tutti qui. Il Carmide è – canonicamente – un dialogo aporetico. Ma almeno dei suoi paradossi – quello di una superscienza che pretende...
Directory of Open Access Journals (Sweden)
Maria Chiara Pievatolo
2013-01-01
Full Text Available Pensate che i testi antichi siano semplicemente vecchi? Che l’amore platonico non vada mai al sodo? Leggere il Simposio di Platone confrontandosi direttamente col testo, com’è possibile fare grazie al Perseus Project, vi farà cambiare idea.
Directory of Open Access Journals (Sweden)
Maria Chiara Pievatolo
2015-06-01
Full Text Available La guida ipertestuale alla lettura del Cratilo di Platone composta per gli studenti della facoltà di Scienze politiche dell’università di Pisa è ora visibile a tutti qui. L’ipertesto ha tratto vantaggio dall’Introduzione alla linguistica generale del professor Manuel Barbera dell’università...
Inverse Symmetry Breaking and the Exact Renormalization Group
Pietroni, M; Tetradis, N
1997-01-01
We discuss the question of inverse symmetry breaking at non-zero temperature using the exact renormalization group. We study a two-scalar theory and concentrate on the nature of the phase transition during which the symmetry is broken. We also examine the persistence of symmetry breaking at temperatures higher than the critical one.
Fuchigami, Kei; Schrandt, Matthew; Miessler, Gary L.
2016-01-01
A hands-on symmetry project is proposed as an innovative way of teaching point groups to undergraduate chemistry students. Traditionally, courses teaching symmetry require students to identify the point group of a given object. This project asks the reverse: students are instructed to identify an object that matches each point group. Doing so…
The symmetry groups of bifurcations of integrable Hamiltonian systems
Energy Technology Data Exchange (ETDEWEB)
Orlova, E I [M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Moscow (Russian Federation)
2014-11-30
Two-dimensional atoms are investigated; these are used to code bifurcations of the Liouville foliations of nondegenerate integrable Hamiltonian systems. To be precise, the symmetry groups of atoms with complexity at most 3 are under study. Atoms with symmetry group Z{sub p}⊕Z{sub q} are considered. It is proved that Z{sub p}⊕Z{sub q} is the symmetry group of a toric atom. The symmetry groups of all nonorientable atoms with complexity at most 3 are calculated. The concept of a geodesic atom is introduced. Bibliography: 9 titles.
Platons ‘respekt’ for Protagoras
DEFF Research Database (Denmark)
Bloch, David
2011-01-01
Platons forhold til sofisten Protagoras behandles. Hvor forskningen oftest har hævdet, at Platon har stor respekt for denne, argumenteres der her for, at Platons dialog "Protagoras" viser alt andet end respekt.......Platons forhold til sofisten Protagoras behandles. Hvor forskningen oftest har hævdet, at Platon har stor respekt for denne, argumenteres der her for, at Platons dialog "Protagoras" viser alt andet end respekt....
Architecture of Platonic and Archimedean polyhedral links
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
A new methodology for understanding the construction of polyhedral links has been developed on the basis of the Platonic and Archimedean solids by using our method of the 'three-cross-curve and doubletwist-line covering'. There are five classes of polyhedral links that can be explored: the tetrahedral and truncated tetrahedral links; the hexahedral and truncated hexahedral links; the dodecahedral and truncated dodecahedral links; the truncated octahedral and icosahedral links. Our results show that the tetrahedral and truncated tetrahedral links have T symmetry; the hexahedral and truncated hexahedral links, as well as the truncated octahedral links, O symmetry; the dodecahedral and truncated dodecahedral links, as well as the truncated icosahedral links, I symmetry, respectively. This study provides further insight into the molecular design, as well as theoretical characterization, of the DNA and protein catenanes.
Architecture of Platonic and Archimedean polyhedral links
Institute of Scientific and Technical Information of China (English)
2008-01-01
A new methodology for understanding the construction of polyhedral links has been developed on the basis of the Platonic and Archimedean solids by using our method of the ‘three-cross-curve and dou- ble-twist-line covering’. There are five classes of polyhedral links that can be explored: the tetrahedral and truncated tetrahedral links; the hexahedral and truncated hexahedral links; the dodecahedral and truncated dodecahedral links; the truncated octahedral and icosahedral links. Our results show that the tetrahedral and truncated tetrahedral links have T symmetry; the hexahedral and truncated hexahedral links, as well as the truncated octahedral links, O symmetry; the dodecahedral and truncated dodeca- hedral links, as well as the truncated icosahedral links, I symmetry, respectively. This study provides further insight into the molecular design, as well as theoretical characterization, of the DNA and protein catenanes.
Lie symmetries and differential galois groups of linear equations
Oudshoorn, W.R.; Put, M. van der
2002-01-01
For a linear ordinary differential equation the Lie algebra of its infinitesimal Lie symmetries is compared with its differential Galois group. For this purpose an algebraic formulation of Lie symmetries is developed. It turns out that there is no direct relation between the two above objects. In co
Symmetry, Group Theory, and the Physical Properties of Crystals
Powell, Richard C.
The intent of this book is to demonstrate the importance of symmetry in determining the properties of solids and the power of using group theory and tensor algebra to elucidate these properties. It is not meant to be a comprehensive text on solid state physics, so many important aspects of condensed matter physics not related to symmetry are not covered here. The book begins by discussing the concepts of symmetry relevant to crystal structures. This is followed by a summary of the basics of group theory and how it is applied to quantum mechanics. Next is a discussion of the description of the macroscopic properties of crystals by tensors and how symmetry determines the form of these tensors. The basic concepts covered in these early chapters are then applied to a series of different examples. There is a discussion of the use of point symmetry in the crystal field theory treatment of point defects in solids. Next is a discussion of crystal symmetry in determining the optical properties of solids, followed by a chapter on the nonlinear optical properties of solids. Then the role of symmetry in treating lattice vibrations is described. The last chapter discusses the effects of translational symmetry on electronic energy bands in solids.
Platonism, Naturalism, and Mathematical Knowledge
Brown, James Robert
2011-01-01
This study addresses a central theme in current philosophy: Platonism vs Naturalism and provides accounts of both approaches to mathematics, crucially discussing Quine, Maddy, Kitcher, Lakoff, Colyvan, and many others. Beginning with accounts of both approaches, Brown defends Platonism by arguing that only a Platonistic approach can account for concept acquisition in a number of special cases in the sciences. He also argues for a particular view of applied mathematics, a view that supports Platonism against Naturalist alternatives. Not only does this engaging book present the Platonist-Natural
Full Non-Rigid Group and Symmetry of Dimethyltrichlorophosphorus
Institute of Scientific and Technical Information of China (English)
ASHRAFI; AliReza
2005-01-01
In this work, a simple method is described, by means of which it is possible to calculate character tables for the symmetry group of molecules consisting of a number of NH3 groups attached to a rigid framework. The full non-rigid group (f-NRG) of dimethyltrichlorophosphorus with the symmetry group D3h was studied. It has been proven that it is a group of order 216 with 27 conjugacy classes and its character table computed. Finally, the Permutation-lnversion group of this molecule was calculated.
Yong, Ee Hou; Nelson, David R; Mahadevan, L
2013-10-25
On microscopic scales, the crystallinity of flexible tethered or cross-linked membranes determines their mechanical response. We show that by controlling the type, number, and distribution of defects on a spherical elastic shell, it is possible to direct the morphology of these structures. Our numerical simulations show that by deflating a crystalline shell with defects, we can create elastic shell analogs of the classical platonic solids. These morphologies arise via a sharp buckling transition from the sphere which is strongly hysteretic in loading or unloading. We construct a minimal Landau theory for the transition using quadratic and cubic invariants of the spherical harmonic modes. Our approach suggests methods to engineer shape into soft spherical shells using a frozen defect topology.
Xi-Zhong, Liu
2012-01-01
In this paper, We derive the symmetry group theorem to the Lin-Tsien equation by using the modified CK's direct method, from which we obtain the corresponding symmetry group. More importantly, conservation laws corresponding to the Kac-Moody-Virasoro symmetry algebra of Lin-Tsien equation is obtained up to second order group invariants.
Partial symmetry, reflection monoids and Coxeter groups
Everitt, Brent; Fountain, John
2008-01-01
This is the first of a series of papers in which we initiate and develop the theory of reflection monoids, motivated by the theory of reflection groups. The main results identify a number of important inverse semigroups as reflection monoids, introduce new examples, and determine their orders.
Determining Symmetry Properties of Gravitational Fields of Terrestrial Group Planets
Directory of Open Access Journals (Sweden)
R.A. Kascheev
2016-09-01
Full Text Available Numerous models of gravity fields of the Solar system bodies have been constructed recently owing to successful space missions. These models are sets of harmonic coefficients of gravity potential expansion in series of spherical functions, which is Laplace series. The sets of coefficients are different in quantity of numerical parameters, sources and composition of the initial observational data, methods to obtain and process them, and, consequently, in a variety of properties and accuracy characteristics. For this reason, the task of comparison of different models of celestial bodies considered in the paper is of interest and relevant. The main purpose of this study is comparison of the models of gravitational potential of the Earth, Moon, Mars, and Venus with the quantitative criteria of different types of symmetries developed by us. It is assumed that some particular symmetry of the density distribution function of the planetary body causes similar symmetry of its gravitational potential. The symmetry of gravitational potential, in its turn, imposes additional conditions (restrictions, which must be satisfied by the harmonic coefficients. The paper deals with seven main types of symmetries: central, axial, two symmetries specular relative to the equatorial planes and prime meridian, as well as three rotational symmetries (at π angle around the coordinate system axes. According to the results of calculations carried out for the Earth, Moon, Mars, and Venus, the values of the criteria vary considerably for different types of symmetries and for different planets. It means that the specific value of each criterion corresponding to a particular celestial body is indicative of the properties and internal structure characteristics of the latter and, therefore, it can be used as a tool for comparative planetology. On the basis of the performed calculations, it is possible to distinguish two groups of celestial bodies having similar properties of
Exotic Newton-Hooke group, noncommutative plane and superconformal symmetry
Alvarez, Pedro D
2009-01-01
In this thesis we have studied some systems with exotic symmetries, which are a peculiarity in 2+1 space-time dimensions. Coded in the exotic structure appears noncommutative coordinates and a phases structure. This kind of systems has attracted attention from different areas of physics independently. Among them we can mention: theory of ray representations of Lie groups, anyons physics, some condensed matter systems, for instance the quantum Hall effect, planar gauge and gravitation theories, noncommutative field theory, noncommutative geometry and noncommutative quantum mechanics. We will focus our study in some topics on exotic nonrelativistic symmetries, such as the exotic Newton-Hooke group, the relation between the systems of exotic Newton-Hooke and the noncommutative Landau problem and the symmetries of noncommutative Landau problem, its conformal and supersymmetric extensions. The exotic Newton-Hooke group correspond to the nonrelativistic limit of the de Sitter groups, and has as a particular case (f...
Renormalisation group improved leptogenesis in family symmetry models
Energy Technology Data Exchange (ETDEWEB)
Cooper, Iain K., E-mail: ikc1g08@soton.ac.uk [School of Physics and Astronomy, University of Southampton, Southampton, SO17 1BJ (United Kingdom); King, Stephen F., E-mail: king@soton.ac.uk [School of Physics and Astronomy, University of Southampton, Southampton, SO17 1BJ (United Kingdom); Luhn, Christoph, E-mail: christoph.luhn@durham.ac.uk [School of Physics and Astronomy, University of Southampton, Southampton, SO17 1BJ (United Kingdom); Institute for Particle Physics Phenomenology, University of Durham, Durham, DH1 3LE (United Kingdom)
2012-06-11
We study renormalisation group (RG) corrections relevant for leptogenesis in the case of family symmetry models such as the Altarelli-Feruglio A{sub 4} model of tri-bimaximal lepton mixing or its extension to tri-maximal mixing. Such corrections are particularly relevant since in large classes of family symmetry models, to leading order, the CP violating parameters of leptogenesis would be identically zero at the family symmetry breaking scale, due to the form dominance property. We find that RG corrections violate form dominance and enable such models to yield viable leptogenesis at the scale of right-handed neutrino masses. More generally, the results of this paper show that RG corrections to leptogenesis cannot be ignored for any family symmetry model involving sizeable neutrino and {tau} Yukawa couplings.
Resource Letter SP-2: Symmetry and Group Theory in Physics.
Rosen, Joe
1981-01-01
Presents listings of selected reference materials relevant to symmetry and group theory in college physics and chemistry. Entries are classified according to a scheme involving 34 subject areas divided into four major groups. Comments on these materials and suggestions for future topics will be welcomed. (Author/SK)
Hypersurfaces in Pn with 1-parameter symmetry groups II
DEFF Research Database (Denmark)
Plessis, Andrew du; Wall, C.T.C.
2010-01-01
We assume V a hypersurface of degree d in with isolated singularities and not a cone, admitting a group G of linear symmetries. In earlier work we treated the case when G is semi-simple; here we analyse the unipotent case. Our first main result lists the possible groups G. In each case we discuss...
Origen and the Platonic Tradition
Directory of Open Access Journals (Sweden)
Ilaria L.E. Ramelli
2017-02-01
Full Text Available This study situates Origen of Alexandria within the Platonic tradition, presenting Origenas a Christian philosopher who taught and studied philosophy, of which theology was part and parcel. More speciﬁcally, Origen can be described as a Christian Platonist. He criticized “false philosophies” as well as “heresies,” but not the philosophy of Plato. Against the background of recent scholarly debates, the thorny issue of the possible identity between Origen the Christian Platonist and Origen the Neoplatonist is partially addressed (although it requires a much more extensive discussion; it is also discussed in the light of Origen’s formation at Ammonius’s school and the reception of his works and ideas in “pagan” Platonism. As a consequence, and against scholarly perspectives that tend to see Christianity as anti-Platonism, the ﬁnal section of this paper asks the question of what is imperial and late antique Platonism and, on the basis of rich evidence ,suggests that this was not only “pagan” institutional Platonism.
Symmetry group analysis of an ideal plastic flow
Lamothe, Vincent
2011-01-01
In this paper, we study the Lie point symmetry group of a system describing an ideal plastic plane flow in two dimensions in order to find analytical solutions. The infinitesimal generators that span the Lie algebra for this system are obtained. We completely classify the subalgebras of up to codimension two in conjugacy classes under the action of the symmetry group. Based on invariant forms, we use Ansatzes to compute symmetry reductions in such a way that the obtained solutions cover simultaneously many invariant and partially invariant solutions. We calculate solutions of the algebraic, trigonometric, inverse trigonometric and elliptic type. Some solutions depending on one or two arbitrary functions of one variable have also been found. In some cases, the shape of a potentially feasible extrusion die corresponding to the solution is deduced. These tools could be used to thin, curve, undulate or shape a ring in an ideal plastic material.
On the construction of double group molecular symmetry functions
Visscher, L
1996-01-01
A new procedure for constructing double group symmetry functions is presented. Using this method integrals over Hermitian operators can become real quantities, even though the integrand and the functions themselves are complex. This is especially of interest to 4-component relativistic methods that
Flack, H D; Wondratschek, H; Hahn, T; Abrahams, S C
2000-01-01
The definition of 'symmetry element' given in the Report of the IUCr Ad-Hoc Committee on the Nomenclature of Symmetry by de Wolff et al. [Acta Cryst. (1989). A45, 494-499] is shown to contain an ambiguity in the case of space groups P6/m, P6/mmm, P6/mcc and point groups 6/m and 6/mmm. The ambiguity is removed by redefining the 'geometric element' as a labelled geometric item in which the label is related to the rotation angle of the rotation or rotoinversion symmetry operation. The complete set of different types of glide plane is shown to contain three more than the 15 that are illustrated in the 1992 Report by de Wolff et al. [Acta Cryst. (1992). A48, 727-732].
Symmetries of KdV and loop groups
Schiff, J; Schiff, Jeremy; Sci, Comp
1996-01-01
A simple version of the Segal-Wilson map from the SL(2,C) loop group to a class of solutions of the KdV hierarchy is given, clarifying certain aspects of this map. It is explained how the known symmetries, including Backlund transformations, of KdV arise from simple, field independent, actions on the loop group. A variety of issues in understanding the algebraic structure of Backlund transformations are thus resolved.
Space Group Symmetry Fractionalization in a Chiral Kagome Heisenberg Antiferromagnet.
Zaletel, Michael P; Zhu, Zhenyue; Lu, Yuan-Ming; Vishwanath, Ashvin; White, Steven R
2016-05-13
The anyonic excitations of a spin liquid can feature fractional quantum numbers under space group symmetries. Detecting these fractional quantum numbers, which are analogs of the fractional charge of Laughlin quasiparticles, may prove easier than the direct observation of anyonic braiding and statistics. Motivated by the recent numerical discovery of spin-liquid phases in the kagome Heisenberg antiferromagnet, we theoretically predict the pattern of space group symmetry fractionalization in the kagome lattice SO(3)-symmetric chiral spin liquid. We provide a method to detect these fractional quantum numbers in finite-size numerics which is simple to implement in the density matrix renormalization group. Applying these developments to the chiral spin liquid phase of a kagome Heisenberg model, we find perfect agreement between our theoretical prediction and numerical observations.
The analysis of crystallographic symmetry types in finite groups
Sani, Atikah Mohd; Sarmin, Nor Haniza; Adam, Nooraishikin; Zamri, Siti Norziahidayu Amzee
2014-06-01
Undeniably, it is human nature to prefer objects which are considered beautiful. Most consider beautiful as perfection, hence they try to create objects which are perfectly balance in shape and patterns. This creates a whole different kind of art, the kind that requires an object to be symmetrical. This leads to the study of symmetrical objects and pattern. Even mathematicians and ethnomathematicians are very interested with the essence of symmetry. One of these studies were conducted on the Malay traditional triaxial weaving culture. The patterns derived from this technique are symmetrical and this allows for further research. In this paper, the 17 symmetry types in a plane, known as the wallpaper groups, are studied and discussed. The wallpaper groups will then be applied to the triaxial patterns of food cover in Malaysia.
Symmetry an introduction to group theory and its applications
McWeeny, R
2013-01-01
Symmetry: An Introduction to Group Theory and its Application is an eight-chapter text that covers the fundamental bases, the development of the theoretical and experimental aspects of the group theory. Chapter 1 deals with the elementary concepts and definitions, while Chapter 2 provides the necessary theory of vector spaces. Chapters 3 and 4 are devoted to an opportunity of actually working with groups and representations until the ideas already introduced are fully assimilated. Chapter 5 looks into the more formal theory of irreducible representations, while Chapter 6 is concerned largely w
Quantum group symmetry and q-tensor algebras
Biedenharn, Lawrence Christian
1995-01-01
Quantum groups are a generalization of the classical Lie groups and Lie algebras and provide a natural extension of the concept of symmetry fundamental to physics. This monograph is a survey of the major developments in quantum groups, using an original approach based on the fundamental concept of a tensor operator. Using this concept, properties of both the algebra and co-algebra are developed from a single uniform point of view, which is especially helpful for understanding the noncommuting co-ordinates of the quantum plane, which we interpret as elementary tensor operators. Representations
Projective symmetry group classification of chiral spin liquids
Bieri, Samuel; Lhuillier, Claire; Messio, Laura
2016-03-01
We present a general review of the projective symmetry group classification of fermionic quantum spin liquids for lattice models of spin S =1 /2 . We then introduce a systematic generalization of the approach for symmetric Z2 quantum spin liquids to the one of chiral phases (i.e., singlet states that break time reversal and lattice reflection, but conserve their product). We apply this framework to classify and discuss possible chiral spin liquids on triangular and kagome lattices. We give a detailed prescription on how to construct quadratic spinon Hamiltonians and microscopic wave functions for each representation class on these lattices. Among the chiral Z2 states, we study the subset of U(1) phases variationally in the antiferromagnetic J1-J2-Jd Heisenberg model on the kagome lattice. We discuss static spin structure factors and symmetry constraints on the bulk spectra of these phases.
Flavor Symmetry and Galois Group of Elliptic Curves
Hattori, Chuichiro; Matsuoka, Takeo; Nakanishi, Kenichi
2009-01-01
A new approach to the generation structure of fermions is proposed. We consider a brane configuration in which the brane intersection yields a two-torus in the extra space. It is assumed that the two-torus is discretized and is given by the torsion points of the elliptic curve over Q . We direct our attention to the arithmetic structure of the elliptic curve with complex multiplication (CM). In our approach the flavor symmetry including the R-parity has its origin in the Galois group of elliptic curves with CM. We study the possible types of the Galois group. The Galois group is shown to be an extension of Z_2 by some abelian group. A phenomenologically viable example of the Galois group is presented, in which the characteristic texture of fermion masses and mixings is reproduced and the mixed-anomaly conditions are satisfied.
New Insights into Viral Architecture via Affine Extended Symmetry Groups
Directory of Open Access Journals (Sweden)
T. Keef
2008-01-01
Full Text Available Since the seminal work of Caspar and Klug on the structure of the protein containers that encapsulate and hence protect the viral genome, it has been recognized that icosahedral symmetry is crucial for the structural organization of viruses. In particular, icosahedral symmetry has been invoked in order to predict the surface structures of viral capsids in terms of tessellations or tilings that schematically encode the locations of the protein subunits in the capsids. Whilst this approach is capable of predicting the relative locations of the proteins in the capsids, a prediction on the relative sizes of different virus particles in a family cannot be made. Moreover, information on the full 3D structure of viral particles, including the tertiary structures of the capsid proteins and the organization of the viral genome within the capsid are inaccessible with their approach. We develop here a mathematical framework based on affine extensions of the icosahedral group that allows us to address these issues. In particular, we show that the relative radii of viruses in the family of Polyomaviridae and the material boundaries in simple RNA viruses can be determined with our approach. The results complement Caspar and Klug's theory of quasi-equivalence and provide details on virus structure that have not been accessible with previous methods, implying that icosahedral symmetry is more important for virus architecture than previously appreciated.
Godel's Incompleteness Theorems and Platonic Metaphysics
Mikovic, Aleksandar
2015-01-01
We argue by using Godel's incompletness theorems in logic that platonism is the best metaphysics for science. This is based on the fact that a natural law in a platonic metaphysics represents a timeless order in the motion of matter, while a natural law in a materialistic metaphysics can be only defined as a temporary order which appears at random in the chaotic motion of matter. Although a logical possibility, one can argue that this type of metaphysics is highly implausible. Given that mathematics fits naturally within platonism, we conclude that a platonic metaphysics is more preferable than a materialistic metaphysics.
Platonism in Preface to Lyrical Ballads
Institute of Scientific and Technical Information of China (English)
严文烨
2016-01-01
Platonism has exerted great influence on Romanticism. Wordsworth, as the leading figure of English Romanticism, was inevitably influenced by Plato. Preface to Lyrical Ballads is Wordsworth's declaration of Romanticism. In this essay, the inheritance and innovation of Platonism in Preface to Lyrical Ballads is analyzed from three aspects: mimetic theories, pragmatism and expressive theories.
Duality, Gauge Symmetries, Renormalization Groups and the BKT Transition
José, Jorge V.
2017-03-01
In this chapter, I will briefly review, from my own perspective, the situation within theoretical physics at the beginning of the 1970s, and the advances that played an important role in providing a solid theoretical and experimental foundation for the Berezinskii-Kosterlitz-Thouless theory (BKT). Over this period, it became clear that the Abelian gauge symmetry of the 2D-XY model had to be preserved to get the right phase structure of the model. In previous analyses, this symmetry was broken when using low order calculational approximations. Duality transformations at that time for two-dimensional models with compact gauge symmetries were introduced by José, Kadanoff, Nelson and Kirkpatrick (JKKN). Their goal was to analyze the phase structure and excitations of XY and related models, including symmetry breaking fields which are experimentally important. In a separate context, Migdal had earlier developed an approximate Renormalization Group (RG) algorithm to implement Wilson’s RG for lattice gauge theories. Although Migdal’s RG approach, later extended by Kadanoff, did not produce a true phase transition for the XY model, it almost did asymptotically in terms of a non-perturbative expansion in the coupling constant with an essential singularity. Using these advances, including work done on instantons (vortices), JKKN analyzed the behavior of the spin-spin correlation functions of the 2D XY-model in terms of an expansion in temperature and vortex-pair fugacity. Their analysis led to a perturbative derivation of RG equations for the XY model which are the same as those first derived by Kosterlitz for the two-dimensional Coulomb gas. JKKN’s results gave a theoretical formulation foundation and justification for BKT’s sound physical assumptions and for the validity of their calculational approximations that were, in principle, strictly valid only at very low temperatures, away from the critical TBKT temperature. The theoretical predictions were soon tested
Duality, Gauge Symmetries, Renormalization Groups and the BKT Transition
José, Jorge V.
2013-06-01
In this chapter, I will briefly review, from my own perspective, the situation within theoretical physics at the beginning of the 1970s, and the advances that played an important role in providing a solid theoretical and experimental foundation for the Berezinskii-Kosterlitz-Thouless theory (BKT). Over this period, it became clear that the Abelian gauge symmetry of the 2D-XY model had to be preserved to get the right phase structure of the model. In previous analyses, this symmetry was broken when using low order calculational approximations. Duality transformations at that time for two-dimensional models with compact gauge symmetries were introduced by José, Kadanoff, Nelson and Kirkpatrick (JKKN). Their goal was to analyze the phase structure and excitations of XY and related models, including symmetry breaking fields which are experimentally important. In a separate context, Migdal had earlier developed an approximate Renormalization Group (RG) algorithm to implement Wilson's RG for lattice gauge theories. Although Migdal's RG approach, later extended by Kadanoff, did not produce a true phase transition for the XY model, it almost did asymptotically in terms of a non-perturbative expansion in the coupling constant with an essential singularity. Using these advances, including work done on instantons (vortices), JKKN analyzed the behavior of the spin-spin correlation functions of the 2D XY-model in terms of an expansion in temperature and vortex-pair fugacity. Their analysis led to a perturbative derivation of RG equations for the XY model which are the same as those first derived by Kosterlitz for the two-dimensional Coulomb gas. JKKN's results gave a theoretical formulation foundation and justification for BKT's sound physical assumptions and for the validity of their calculational approximations that were, in principle, strictly valid only at very low temperatures, away from the critical TBKT temperature. The theoretical predictions were soon tested
Gauged Flavor Group with Left-Right Symmetry
Guadagnoli, Diego; Sung, Ilmo
2011-01-01
We construct an anomaly-free extension of the left-right symmetric model, where the maximal flavor group is gauged and anomaly cancellation is guaranteed by adding new vectorlike fermion states. We address the question of the lowest allowed flavor symmetry scale consistent with data. Because of the mechanism recently pointed out by Grinstein et al. tree-level flavor changing neutral currents turn out to play a very weak constraining role. The same occurs, in our model, for electroweak precision observables. The main constraint turns out to come from WR-mediated flavor changing neutral current box diagrams, primarily K - Kbar mixing. In the case where discrete parity symmetry is present at the TeV scale, this constraint implies lower bounds on the mass of vectorlike fermions and flavor bosons of 5 and 10 TeV respectively. However, these limits are weakened under the condition that only SU(2)_R x U(1)_{B-L} is restored at the TeV scale, but not parity. For example, assuming the SU(2) gauge couplings in the rati...
Platonic wholes and quantum ontology
Woszczek, Marek
2015-01-01
The subject of the book is a reconsideration of the internalistic model of composition of the Platonic type, more radical than traditional, post-Aristotelian externalistic compositionism, and its application in the field of the ontology of quantum theory. At the centre of quantum ontology is nonseparability. Quantum wholes are atemporal wholes governed by internalistic logic and they are primitive, global physical entities, requiring an extreme relativization of the fundamental notions of mechanics. That ensures quantum theory to be fully consistent with the relativistic causal structure, with
Symmetries and Group-Invariant Solutions for Transonic Pressure-Gradient Equations
Institute of Scientific and Technical Information of China (English)
王丽真; 黄晴
2011-01-01
Lie symmetry group method is applied to study the transonic pressure-gradient equations in two-dimensional space. Its symmetry groups and corresponding optimal systems are determined, and several classes of irrotational groupinvariant solutions associated to the symmetries are obtained and special case of one-dimensional rarefaction wave is found.
Classification of finite reparametrization symmetry groups in the three-Higgs-doublet model
Ivanov, I P
2012-01-01
Symmetries play a crucial role in electroweak symmetry breaking models with non-minimal Higgs content. Within each class of these models, it is desirable to know which symmetry groups can be implemented via the scalar sector. In N-Higgs-doublet models, this classification problem was solved only for N=2 doublets. Very recently, we suggested a method to classify all realizable finite symmetry groups of Higgs-family transformations in the three-Higgs-doublet model (3HDM). Here, we present this classification in all detail together with an introduction to the theory of solvable groups, which play the key role in our derivation. We also consider generalized-CP symmetries, and discuss the interplay between Higgs-family symmetries and CP-conservation. In particular, we prove that presence of the $Z_4$ symmetry guarantees the explicit CP-conservation of the potential. This work completes classification of finite reparametrization symmetry groups in 3HDM.
Classification of finite reparametrization symmetry groups in the three-Higgs-doublet model
Energy Technology Data Exchange (ETDEWEB)
Ivanov, Igor P. [Universite de Liege, IFPA, Liege (Belgium); Sobolev Institute of Mathematics, Novosibirsk (Russian Federation); Vdovin, E. [Sobolev Institute of Mathematics, Novosibirsk (Russian Federation)
2013-02-15
Symmetries play a crucial role in electroweak symmetry breaking models with non-minimal Higgs content. Within each class of these models, it is desirable to know which symmetry groups can be implemented via the scalar sector. In N-Higgs-doublet models, this classification problem was solved only for N=2 doublets. Very recently, we suggested a method to classify all realizable finite symmetry groups of Higgs-family transformations in the three-Higgs-doublet model (3HDM). Here, we present this classification in all detail together with an introduction to the theory of solvable groups, which play the key role in our derivation. We also consider generalized-CP symmetries, and discuss the interplay between Higgs-family symmetries and CP-conservation. In particular, we prove that presence of the Z{sub 4} symmetry guarantees the explicit CP-conservation of the potential. This work completes classification of finite reparametrization symmetry groups in 3HDM. (orig.)
Classification of finite reparametrization symmetry groups in the three-Higgs-doublet model
Ivanov, Igor P.; Vdovin, E.
2013-02-01
Symmetries play a crucial role in electroweak symmetry breaking models with non-minimal Higgs content. Within each class of these models, it is desirable to know which symmetry groups can be implemented via the scalar sector. In N-Higgs-doublet models, this classification problem was solved only for N=2 doublets. Very recently, we suggested a method to classify all realizable finite symmetry groups of Higgs-family transformations in the three-Higgs-doublet model (3HDM). Here, we present this classification in all detail together with an introduction to the theory of solvable groups, which play the key role in our derivation. We also consider generalized- CP symmetries, and discuss the interplay between Higgs-family symmetries and CP-conservation. In particular, we prove that presence of the ℤ4 symmetry guarantees the explicit CP-conservation of the potential. This work completes classification of finite reparametrization symmetry groups in 3HDM.
Nilpotent Symmetries in Super-Group Field Cosmology
Upadhyay, Sudhaker
2015-01-01
In this paper we study the gauge invariance of the third quantized super-group field cosmology which is a model for multiverse. Further, we propose both the nfinitesimal (usual) as well as the finite superfield-dependent BRST symmetry transformations which leave the effective theory invariant. The effects of finite superfield-dependent BRST transformations on the path integral (so-called void functional in the case of third quantization) are implemented. Within the finite superfield-dependent BRST formulation, the finite superfield-dependent BRST transformations with specific parameter switch the void functional from one gauge to another. We establish this result for the most general gauge with the help of explicit calculations which holds for all possible sets of gauge choices at both the classical and the quantum levels.
Symmetry breaking, subgroup embeddings and the Weyl group
George, Damien P; Thompson, Jayne E; Volkas, Raymond R
2013-01-01
We present a systematic approach to writing adjoint Higgs vacuum expectation values (vevs), which break a symmetry G to differently embedded isomorphic copies of a subgroup belonging to the chain $G \\supset H_1 \\supset ... \\supset H_l $, as linear combinations of each other. Given an adjoint Higgs vacuum expectation value h breaking G \\rightarrow H, a full complement of vevs breaking G to different embeddings of the subgroup H can be generated through the Weyl group orbit of h. An explicit formula for recovering each vev is given. We focus on the case when H stabilizes the highest weight of the lowest dimensional fundamental representation, where the formula is exceedingly simple. We also discuss cases when the Higgs field is not in the adjoint representation and apply these techniques to current research problems, especially in domain-wall brane model building.
Symmetry groups and spiral wave solution of a wave propagation equation
Institute of Scientific and Technical Information of China (English)
张全举; 屈长征
2002-01-01
We study a third-order nonlinear evolution equation, which can be transformed to the modified KdV equation,using the Lie symmetry method. The Lie point symmetries and the one-dimensional optimal system of the symmetryalgebras are determined. Those symmetries are some types of nonlocal symmetries or hidden symmetries of the modifiedKdV equation. The group-invariant solutions, particularly the travelling wave and spiral wave solutions, are discussedin detail, and a type of spiral wave solution which is smooth in the origin is obtained.
EXECUTIVE SUMMARY OF THE SNOWMASS 2001 WORKING GROUP : ELECTROWEAK SYMMETRY BREAKING.
Energy Technology Data Exchange (ETDEWEB)
CARENA,M.; GERDES,D.W.; HABER,H.E.; TURCOT,A.S.; ZERWAS,P.M.
2001-06-30
In this summary report of the 2001 Snowmass Electroweak Symmetry Breaking Working Group, the main candidates for theories of electroweak symmetry breaking are surveyed, and the criteria for distinguishing among the different approaches are discussed. The potential for observing electroweak symmetry breaking phenomena at the upgraded Tevatron and the LHC is described. We emphasize the importance of a high-luminosity e{sup +}e{sup -} linear collider for precision measurements to clarify the underlying electroweak symmetry breaking dynamics. Finally, we note the possible roles of the {mu}{sup +} {mu}{sup -} collider and VLHC for further elucidating the physics of electroweak symmetry breaking.
Dynamical symmetry breaking in chiral gauge theories with direct-product gauge groups
Shi, Yan-Liang; Shrock, Robert
2016-09-01
We analyze patterns of dynamical symmetry breaking in strongly coupled chiral gauge theories with direct-product gauge groups G . If the gauge coupling for a factor group Gi⊂G becomes sufficiently strong, it can produce bilinear fermion condensates that break the Gi symmetry itself and/or break other gauge symmetries Gj⊂G . Our comparative study of a number of strongly coupled direct-product chiral gauge theories elucidates how the patterns of symmetry breaking depend on the structure of G and on the relative sizes of the gauge couplings corresponding to factor groups in the direct product.
Dynamical Symmetry Breaking in Chiral Gauge Theories with Direct-Product Gauge Groups
Shi, Yan-Liang
2016-01-01
We analyze patterns of dynamical symmetry breaking in strongly coupled chiral gauge theories with direct-product gauge groups $G$. If the gauge coupling for a factor group $G_i \\subset G$ becomes sufficiently strong, it can produce bilinear fermion condensates that break the $G_i$ symmetry itself and/or break other gauge symmetries $G_j \\subset G$. Our comparative study of a number of strongly coupled direct-product chiral gauge theories elucidates how the patterns of symmetry breaking depend on the structure of $G$ and on the relative sizes of the gauge couplings corresponding to factor groups in the direct product.
Spontaneous R-symmetry breaking from the renormalization group flow
Amariti, Antonio
2012-01-01
We propose a mechanism of R-symmetry breaking in four-dimensional DSB models based on the RG properties of the coupling constants. By constraining the UV sector, we generate new hierarchies amongst the couplings that allow a spontaneously broken R-symmetry in models with pure chiral fields of R-charges R = 0 and R = 2 only. The result is obtained by a combination of one- and two-loop effects, both at the origin of field space and in the region dominated by leading log potentials.
Noncommutative Integration and Symmetry Algebra of the Dirac Equation on the Lie Groups
Breev, A. I.; Mosman, E. A.
2016-12-01
The algebra of first-order symmetry operators of the Dirac equation on four-dimensional Lie groups with right-invariant metric is investigated. It is shown that the algebra of symmetry operators is in general not a Lie algebra. Noncommutative reduction mediated by spin symmetry operators is investigated. For the Dirac equation on the Lie group SO(2,1) a parametric family of particular solutions obtained by the method of noncommutative integration over a subalgebra containing a spin symmetry operator is constructed.
Platonic solids in $\\mathbb Z^3$
Ionascu, Eugen J
2009-01-01
Extending previous results on a characterization of all equilateral triangle in space having vertices with integer coordinates ("in $\\mathbb Z^3$"), we look at the problem of characterizing all regular polyhedra (Platonic Solids) with the same property. To summarize, we show first that there is no regular icosahedron/ dodecahedron in $\\mathbb Z^3$. On the other hand, there is a finite (6 or 12) class of regular tetrahedra in $\\mathbb Z^3$, associated naturally to each nontrivial solution $(a,b,c,d)$ of the Diophantine equation $a^2+b^2+c^2=3d^2$ and for every nontrivial integer solution $(m,n,k)$ of the equation $m^2-mn+n^2=k^2$. Every regular tetrahedron in $\\mathbb Z^3$ belongs, up to an integer translation and/or rotation, to one of these classes. We then show that each such tetrahedron can be completed to a cube with integer coordinates. The study of regular octahedra is reduced to the cube case via the duality between the two. This work allows one to basically give a description the orthogonal group $O(3...
Virtual and Printed 3D Models for Teaching Crystal Symmetry and Point Groups
Casas, Lluís; Estop, Euge`nia
2015-01-01
Both, virtual and printed 3D crystal models can help students and teachers deal with chemical education topics such as symmetry and point groups. In the present paper, two freely downloadable tools (interactive PDF files and a mobile app) are presented as examples of the application of 3D design to study point-symmetry. The use of 3D printing to…
Using Group Theory to Obtain Eigenvalues of Nonsymmetric Systems by Symmetry Averaging
Directory of Open Access Journals (Sweden)
Marion L. Ellzey
2009-08-01
Full Text Available If the Hamiltonian in the time independent Schrödinger equation, HΨ = EΨ, is invariant under a group of symmetry transformations, the theory of group representations can help obtain the eigenvalues and eigenvectors of H. A finite group that is not a symmetry group of H is nevertheless a symmetry group of an operator Hsym projected from H by the process of symmetry averaging. In this case H = Hsym + HR where HR is the nonsymmetric remainder. Depending on the nature of the remainder, the solutions for the full operator may be obtained by perturbation theory. It is shown here that when H is represented as a matrix [H] over a basis symmetry adapted to the group, the reduced matrix elements of [Hsym] are simple averages of certain elements of [H], providing a substantial enhancement in computational efficiency. A series of examples are given for the smallest molecular graphs. The first is a two vertex graph corresponding to a heteronuclear diatomic molecule. The symmetrized component then corresponds to a homonuclear system. A three vertex system is symmetry averaged in the first case to Cs and in the second case to the nonabelian C3v. These examples illustrate key aspects of the symmetry-averaging process.
Fermat Surface and Group Theory in Symmetry of Rapidity Family in Chiral Potts Model
Roan, Shi-shyr
2013-01-01
The present paper discusses various mathematical aspects about the rapidity symmetry in chiral Potts model (CPM) in the context of algebraic geometry and group theory . We re-analyze the symmetry group of a rapidity curve in $N$-state CPM, explore the universal group structure for all $N$, and further enlarge it to modular symmetries of the complete rapidity family in CPM. As will be shown in the article that all rapidity curves in $N$-state CPM constitute a Fermat hypersurface in $\\PZ^3$ of degree 2N as the natural generalization of the Fermat K3 elliptic surface $(N=2)$, we conduct a thorough algebraic geometry study about the rapidity fibration of Fermat surface and its reduced hyperelliptic fibration via techniques in algebraic surface theory. Symmetries of rapidity family in CPM and hyperelliptic family in $\\tau^{(2)}$-model are exhibited through the geometrical representation of the universal structural group in mathematics.
DEFF Research Database (Denmark)
Olsen, Anne-Marie Eggert
2015-01-01
Artiklen præsenterer i første del (A) det pædagogiske stof fra Platons Staten og Lovene, som Rousseau har læst og fundet inspiration i. Der plæderes for, at Rousseau optager og transponerer såvel principper som konkrete overvejelser uanset den forskelige historiske kontekst og de dermed sammenhæn......Artiklen præsenterer i første del (A) det pædagogiske stof fra Platons Staten og Lovene, som Rousseau har læst og fundet inspiration i. Der plæderes for, at Rousseau optager og transponerer såvel principper som konkrete overvejelser uanset den forskelige historiske kontekst og de dermed...... sammenhængende forskellige udformninger og mål for opdragelsen. I anden del (B) diskuteres Rousseaus ’platonisme’ i mere overordnet filosofisk sammenhæng, og der argumenteres for, at Rousseaus utraditionelle, pædagogisk-filosofiske Platon-læsning dels kan ses at fremdrage underbelyste centrale tematikker i...... Platons filosofi, dels understreger deres stadige aktualitet....
Plato's problem an introduction to mathematical platonism
Panza, M
2013-01-01
What is mathematics about? And how can we have access to the reality it is supposed to describe? The book tells the story of this problem, first raised by Plato, through the views of Aristotle, Proclus, Kant, Frege, Gödel, Benacerraf, up to the most recent debate on mathematical platonism.
Symmetries in a very special relativity and isometric group of Finsler space
Institute of Scientific and Technical Information of China (English)
LI Xin; CHANG Zhe; MO Xiao-Huan
2011-01-01
We present an explicit connection between the symmetries in a Very Special Relativity (VSR) and isometric group of a specific Finsler space. It is shown that the line element that is invariant under the VSR symmetric group is a Finslerian one. The Killing vectors in Finsler space are constructed in a systematic way. The Lie algebras corresponding to the symmetries of VSR are obtained from a geometric famework. The dispersion relation and the Lorentz invariance violation effect in the VSR are discussed.
Symmetries of preon interactions modeled as a finite group
Bellinger, James N.
1997-07-01
I model preon interactions as a finite group. Treating the elements of the group as the bases of a vector space, I examine those linear mappings under which the transformed bases may be treated as members of a group isomorphic to the original. In some cases these mappings are continuous Lie groups.
Symmetries of preon interactions modeled as a finite group
Energy Technology Data Exchange (ETDEWEB)
Bellinger, J.N. [University of Wisconsin at Madison, Madison, Wisconsin 53706 (United States)
1997-07-01
I model preon interactions as a finite group. Treating the elements of the group as the bases of a vector space, I examine those linear mappings under which the transformed bases may be treated as members of a group isomorphic to the original. In some cases these mappings are continuous Lie groups. {copyright} {ital 1997 American Institute of Physics.}
Symmetries and groups in particle physics; Symmetrien und Gruppen in der Teilchenphysik
Energy Technology Data Exchange (ETDEWEB)
Scherer, Stefan [Mainz Univ. (Germany)
2016-07-01
The aim of this book consists of a didactic introduction to the group-theoretical considerations and methods, which have led to an ever deeper understanding of the interactions of the elementary particles. The first three chapters deal primarily with the foundations of the representation theory of primarily finite groups, whereby many results are also transferable to compact Lie groups. In the third chapter we discuss the concept of Lie groups and their connection with Lie algebras. In the remaining chapter it is mainly about the application of group theory in physics. Chapter 4 deals with the groups SO(3) and SU(2), which occur in connection with the description of the angular momentum in quantum mechanics. We discuss the Wigner-Eckar theorem together with some applications. In chapter 5 we are employed to the composition properties of strongly interacting systems, so called hadrons, and discuss extensively the transformation properties of quarks with relation to the special unitary groups. The Noether theorem is generally treated in connection to the conservation laws belonging to the Galilei group and the Poincare group. We confine us in chapter 6 to internal symmetries, but explain for that extensively the application to quantum field theory. Especially an outlook on the effect of symmetries in form of so called Ward identities is granted. In chapter 7 we turn towards the gauge principle and discuss first the construction of quantum electrodynamics. In the following we generalize the gauge principle to non-Abelian groups (Yang-Mills theories) and formulate the quantum chromodynamics (QCD). Especially we take a view of ''random'' global symmetries of QCD, especially the chiral symmetry. In chapter 8 we illuminate the phenomenon of spontaneous symmetry breaking both for global and for local symmetries. In the final chapter we work out the group-theoretical structure of the Standard Model. Finally by means of the group SU(5) we take a view to
Symmetry group and group representations associated with the thermodynamic covariance principle
Sonnino, Giorgio; Evslin, Jarah; Sonnino, Alberto; Steinbrecher, György; Tirapegui, Enrique
2016-10-01
The main objective of this work [previously appeared in literature, the thermodynamical field theory (TFT)] is to determine the nonlinear closure equations (i.e., the flux-force relations) valid for thermodynamic systems out of Onsager's region. The TFT rests upon the concept of equivalence between thermodynamic systems. More precisely, the equivalent character of two alternative descriptions of a thermodynamic system is ensured if, and only if, the two sets of thermodynamic forces are linked with each other by the so-called thermodynamic coordinate transformations (TCT). In this work, we describe the Lie group and the group representations associated to the TCT. The TCT guarantee the validity of the so-called thermodynamic covariance principle (TCP): The nonlinear closure equations, i.e., the flux-force relations, everywhere and in particular outside the Onsager region, must be covariant under TCT. In other terms, the fundamental laws of thermodynamics should be manifestly covariant under transformations between the admissible thermodynamic forces, i.e., under TCT. The TCP ensures the validity of the fundamental theorems for systems far from equilibrium. The symmetry properties of a physical system are intimately related to the conservation laws characterizing that system. Noether's theorem gives a precise description of this relation. We derive the conserved (thermodynamic) currents and, as an example of calculation, a system out of equilibrium (tokamak plasmas) where the validity of TCP imposed at the level of the kinetic equations is also analyzed.
Symmetry group and group representations associated with the thermodynamic covariance principle.
Sonnino, Giorgio; Evslin, Jarah; Sonnino, Alberto; Steinbrecher, György; Tirapegui, Enrique
2016-10-01
The main objective of this work [previously appeared in literature, the thermodynamical field theory (TFT)] is to determine the nonlinear closure equations (i.e., the flux-force relations) valid for thermodynamic systems out of Onsager's region. The TFT rests upon the concept of equivalence between thermodynamic systems. More precisely, the equivalent character of two alternative descriptions of a thermodynamic system is ensured if, and only if, the two sets of thermodynamic forces are linked with each other by the so-called thermodynamic coordinate transformations (TCT). In this work, we describe the Lie group and the group representations associated to the TCT. The TCT guarantee the validity of the so-called thermodynamic covariance principle (TCP): The nonlinear closure equations, i.e., the flux-force relations, everywhere and in particular outside the Onsager region, must be covariant under TCT. In other terms, the fundamental laws of thermodynamics should be manifestly covariant under transformations between the admissible thermodynamic forces, i.e., under TCT. The TCP ensures the validity of the fundamental theorems for systems far from equilibrium. The symmetry properties of a physical system are intimately related to the conservation laws characterizing that system. Noether's theorem gives a precise description of this relation. We derive the conserved (thermodynamic) currents and, as an example of calculation, a system out of equilibrium (tokamak plasmas) where the validity of TCP imposed at the level of the kinetic equations is also analyzed.
On the Physical Reasons for the Extension of Symmetry Groups in Molecular Spectroscopy
Directory of Open Access Journals (Sweden)
Carlo di Lauro
2010-02-01
Full Text Available Several situations of general interest, in which the symmetry groups usually applied to spectroscopy problems need to be extended, are reviewed. It is emphasized that any symmetry group of geometrical operations to be used in Molecular Spectroscopy should be extended for completeness by considering the time reversal operator, as far as the Hamiltonian is invariant with respect to the inversion of the direction of motion. This can explain the degeneracy of pairs of vibrational and rotational states spanning the so-called separably degenerate irreducible representations, in symmetric tops of low symmetry, and Kramers degeneracy in odd electron molecules in the absence of magnetic fields. An extension with account of time reversal is also useful to determine relative phase conventions on vibration-rotation wavefunctions, which render all vibration-rotation matrix elements real. An extension of a molecular symmetry group may be required for molecules which can attain different geometries by large amplitude periodical motions, if such motions are hindered and are not completely free. Special cases involving the internal rotation are discussed in detail. It is observed that the symmetry classification of vibrational modes involving displacements normal to the internal rotation axis is not univocal, but can be done in several ways, which actually correspond to different conventions on the separation of vibration and internal rotation in the adopted basis functions. The symmetry species of the separate vibrational and torsional factors of these functions depend on the adopted convention.
Morse Theory for Flows in Presence of a Symmetry Group.
1984-07-01
n. 2534. [15] J. J. Rotman , An Introduction to Homological Algebra , Academic Press, New York (1979). (16] S. H. Spanier, Algebraic Topology, McGraw... algebra , a method of treating finite groups is described. I ~-- *. --- ptA The responsibility for the wording and views expressed in this descriptive...Aut A. The definition of a G-module A, essentially means that there is an action of G on A which also considers the algebraic structure of A. In
Flexural Mie Resonances: Localized Surface Platonic Modes
Farhat, M; Chen, P Y; Salama, K N; Bagci, H
2016-01-01
Surface plasmons polaritons were thought to exist only in metals near their plasma frequencies. The concept of spoof plasmons extended the realms of plasmonics to domains such as radio frequencies, magnetism, or even acoustic waves. Here, we introduce the concept of localized surface platonic modes (SPMs). We demonstrate that they can be generated on a two-dimensional clamped (or stress-free) cylindrical surface, in a thin elastic plate, with subwavelength corrugations under excitation by an incident flexural plane wave. Our results show that the corrugated rigid surface is elastically equivalent to a cylindrical scatterer with negatively uniform and dispersive flexural rigidity. This, indeed, suggests that plasmonic-like platonic materials can be engineered with potential applications in various areas including earthquake sensing, or elastic imaging and cloaking.
The origin of the division between Middle Platonism and Neoplatonism
DEFF Research Database (Denmark)
Catana, Leo
2013-01-01
The division of Ancient Platonism into Middle Platonism and Neoplatonism is a fairly new one. The conceptual foundation of this division was cemented in Jacob Brucker’s pioneering Historia critica philosophiae (1742-44). In the 1770s and 1780s, the term ‘Neoplatonism’ was coined on the basis...... of Brucker’s analysis. Three historiographical concepts were decisive to Brucker: ‘system of philosophy’, ‘eclecticism’ and ‘syncretism’. By means of these concepts, he characterized Middle Platonism and Neoplatonism as opposing philosophical movements, the former being a genuine form of Platonism...
Quantum groups as generalized gauge symmetries in WZNW models. Part I. The classical model
Hadjiivanov, L.; Furlan, P.
2017-07-01
Wess-Zumino-Novikov-Witten (WZNW) models over compact Lie groups G constitute the best studied class of (two dimensional, 2 D) rational conformal field theories (RCFTs). A WZNW chiral state space is a finite direct sum of integrable representations of the corresponding affine (current) algebra, and the correlation functions of primary fields are monodromy invariant combinations of left times right sector conformal blocks solving the Knizhnik-Zamolodchikov equation. However, even in this very well understood case of 2 D RCFT, the "internal" (gauge) symmetry that governs the ensuing fusion rules remains unclear. On the other hand, the canonical approach to the classical chiral WZNW theory developed by Faddeev, Alekseev, Shatashvili, Gawedzki and Falceto reveals its Poisson-Lie symmetry. After a covariant quantization, the latter gives rise to an associated quantum group symmetry which naturally requires an extension of the state space. This paper contains a review of earlier work on the subject with a special emphasis, in the case G = SU( n), on the emerging chiral "WZNW zero modes" which provide an adequate algebraic description of the internal symmetry structure of the model. Combining further left and right zero modes, one obtains a specific dynamical quantum group, the structure of its Fock representation resembling the axiomatic approach to gauge theories in which a "restricted" quantum group plays the role of a generalized gauge symmetry.
Symmetry group prerequisite for E-infinity in high energy physics
Energy Technology Data Exchange (ETDEWEB)
El Naschie, M.S. [Department of Physics, Alexandria University (United Kingdom); KACST, Riyadh (Saudi Arabia); Department of Astrophysics, Cairo University, Cairo (Egypt)], E-mail: Chaossf@aol.com
2008-01-15
The work addresses the question of extending certain symplectic and exceptional Lie Symmetry groups to the realm of chaotic dynamics. Using a collection of simple examples, the technique of transfinite continuation is illustrated and various physically relevant results are obtained. The paper is intended as an elementary introduction to the use of symmetry groups in transfinite physics and as such is a sequel to a series of previous papers constituting the elementary and advanced mathematical prerequisite for a proper understanding of E-infinity theory.
Painleve analysis and symmetry group for the coupled Zakharov-Kuznetsov equation
Energy Technology Data Exchange (ETDEWEB)
Hu, Heng-Chun, E-mail: hhengchun@163.com [College of Science, University of Shanghai for Science and Technology, Shanghai 200093 (China); Jia, Xiao-Qing; Sang, Ben-Wen [College of Science, University of Shanghai for Science and Technology, Shanghai 200093 (China)
2011-09-12
The Painleve property for the coupled Zakharov-Kuznetsov equation is verified with the WTC approach and new exact solutions of bell-type are constructed from standard truncated expansion. A symmetry transformation group theorem is also given out from a simple direct method. -- Highlights: → Painleve property for coupled Zakharov-Kuznetsov system is verified by WTC method. → Symmetry group for coupled ZK system is given out by a simple direct method. → Bell-type solution for coupled ZK system is constructed from standard truncation.
Similar Symmetries: The Role of Wallpaper Groups in Perceptual Texture Similarity
Directory of Open Access Journals (Sweden)
Fraser Halley
2011-05-01
Full Text Available Periodic patterns and symmetries are striking visual properties that have been used decoratively around the world throughout human history. Periodic patterns can be mathematically classified into one of 17 different Wallpaper groups, and while computational models have been developed which can extract an image's symmetry group, very little work has been done on how humans perceive these patterns. This study presents the results from a grouping experiment using stimuli from the different wallpaper groups. We find that while different images from the same wallpaper group are perceived as similar to one another, not all groups have the same degree of self-similarity. The similarity relationships between wallpaper groups appear to be dominated by rotations.
More on PT-Symmetry in (Generalized Effect Algebras and Partial Groups
Directory of Open Access Journals (Sweden)
J. Paseka
2011-01-01
Full Text Available We continue in the direction of our paper on PT-Symmetry in (Generalized Effect Algebras and Partial Groups. Namely we extend our considerations to the setting of weakly ordered partial groups. In this setting, any operator weakly ordered partial group is a pasting of its partially ordered commutative subgroups of linear operators with a fixed dense domain over bounded operators. Moreover, applications of our approach for generalized effect algebras are mentioned.
de Klerk, E.; Sotirov, R.
2007-01-01
We consider semidefinite programming relaxations of the quadratic assignment problem, and show how to exploit group symmetry in the problem data. Thus we are able to compute the best known lower bounds for several instances of quadratic assignment problems from the problem library: [R.E. Burkard,
Structure of Symmetry Groups via Cartan's Method: Survey of Four Approaches
Directory of Open Access Journals (Sweden)
Oleg I. Morozov
2005-10-01
Full Text Available In this review article we discuss four recent methods for computing Maurer-Cartan structure equations of symmetry groups of differential equations. Examples include solution of the contact equivalence problem for linear hyperbolic equations and finding a contact transformation between the generalized Hunter-Saxton equation and the Euler-Poisson equation.
de Klerk, E.; Sotirov, R.
2007-01-01
We consider semidefinite programming relaxations of the quadratic assignment problem, and show how to exploit group symmetry in the problem data. Thus we are able to compute the best known lower bounds for several instances of quadratic assignment problems from the problem library: [R.E. Burkard, S.
Elementary abelian regular coverings of Platonic maps, Case I: ordinary representations
Jones, Gareth A
2012-01-01
We classify the orientably regular maps which are elementary abelian regular branched coverings of Platonic maps M, in the case where the covering group and the rotation group G of M have coprime orders. The method involves studying the representations of G on certain homology groups of the sphere, punctured at the branch-points. We give a complete classification for branching over faces (or, dually, vertices) of M, and outline how the method extends to other branching patterns.
Directory of Open Access Journals (Sweden)
Alexis De Vos
2011-06-01
Full Text Available Whereas quantum computing circuits follow the symmetries of the unitary Lie group, classical reversible computation circuits follow the symmetries of a finite group, i.e., the symmetric group. We confront the decomposition of an arbitrary classical reversible circuit with w bits and the decomposition of an arbitrary quantum circuit with w qubits. Both decompositions use the control gate as building block, i.e., a circuit transforming only one (qubit, the transformation being controlled by the other w−1 (qubits. We explain why the former circuit can be decomposed into 2w − 1 control gates, whereas the latter circuit needs 2w − 1 control gates. We investigate whether computer circuits, not based on the full unitary group but instead on a subgroup of the unitary group, may be decomposable either into 2w − 1 or into 2w − 1 control gates.
Aoki, Ken-Ichi; Sato, Daisuke
2016-01-01
We analyze the dynamical chiral symmetry breaking in gauge theory with the nonperturbative renormalization group equation (NPRGE), which is a first order nonlinear partial differential equation (PDE). In case that the spontaneous chiral symmetry breaking occurs, the NPRGE encounters some non-analytic singularities at the finite critical scale even though the initial function is continuous and smooth. Therefore there is no usual solution of the PDE beyond the critical scale. In this paper, we newly introduce the notion of a weak solution which is the global solution of the weak NPRGE. We show how to evaluate the physical quantities with the weak solution.
Non-Lie Symmetry Group and New Exact Solutions for the Two-Dimensional KdV-Burgers Equation
Institute of Scientific and Technical Information of China (English)
WANG Hong; TIAN Ying-Hui; CHEN Han-Lin
2011-01-01
@@ By using the modified Clarkson-Kruskal (CK) direct method, we obtain the non-Lie symmetry group of the two-dimensional KdV-Burgers equation.Under some constraint conditions, Lie point symmetry is also obtained.Through the symmetry group, some new exact solutions of the two-dimensional KdV-Burgers equation are found.%By using the modified Clarkson-Kruskal (CK) direct method, we obtain the non-Lie symmetry group of the two-dimensional KdV-Burgers equation. Under some constraint conditions, Lie point symmetry is also obtained.Through the symmetry group, some new exact solutions of the two-dimensional KdV-Burgers equation are found.
Full Symmetry Groups and Exact Solutions to BKP and GKP Equations
Directory of Open Access Journals (Sweden)
Bo Ren
2014-01-01
Full Text Available We investigate the (2+1-dimensional nonlinear BKP and GKP equations with the modified direct CK’s method. Then, we get its Lie point groups and the full symmetry group, and a relationship is constructed between the new solutions and the old one. Based on the relationship, the new solutions can be obtained by using a given solution of the equations.
Ibragimov, Nail H; Kovalev, Vladimir F
2011-01-01
74J30The maximal group of Lie point symmetries of a system of nonlinear equations used in geophysical fluid dynamics is presented. The Lie algebra of this group is infinite-dimensional and involves three arbitrary functions of time. The invariant solution under the rotation and dilation is constructed. Qualitative analysis of the invariant solution is provided and the energy of this solution is presented.
Higashikawa, Sho
2016-01-01
A symmetry broken phase of a system with internal degrees of freedom often features a complex order parameter, which generates a rich variety of topological excitations and topological influence between them, yet the very complexity of the order parameter makes it difficult to treat topological excitations and topological influence in a unified manner. To overcome this problem, we develop a general method to calculate homotopy groups and derive decomposition formulas which express homotopy groups of a quotient space $G/H$ in terms of those of the symmetry $G$ of the system and those of the remaining symmetry $H$ of the state. We apply these formulas to analyze a general monopole and a general three-dimensional skyrmion, and show that their textures are obtained through substitution of the corresponding $\\mathfrak{su}(2)$-subalgebra for the $\\mathfrak{su}(2)$-spin. We also show that a discrete symmetry of $H$ is necessary for the presence of topological influence and find the topological influence on a skyrmio...
Generation of symmetry coordinates for crystals using multiplier representations of the space groups
DEFF Research Database (Denmark)
Hansen, Flemming Yssing
1978-01-01
Symmetry coordinates play an important role in the normal-mode calculations of crystals. It is therefore of great importance to have a general method, which may be applied for any crystal at any wave vector, to generate these. The multiplier representations of the space groups as given by Kovalev...... and the projection-operator technique provide a basis for such a method. The method is illustrated for the nonsymmorphic D36 space group, and the theoretical background for the representations of space groups in general is reviewed and illustrated on the example above. It is desirable to perform the projection...... of symmetry coordinates in such a way that they may be used for as many wave vectors as possible. We discuss how to achieve this goal. The detailed illustrations should make it simple to apply the theory in any other case....
Correlation functions in isotropic and anisotropic turbulence the role of the symmetry group
Arad, I; Procaccia, I; Arad, Itai; L'vov, Victor S.; Procaccia, Itamar
1998-01-01
The theory of fully developed turbulence is usually considered in an idealized homogeneous and isotropic state. Real turbulent flows exhibit the effects of anisotropic forcing. The analysis of correlation functions and structure functions in isotropic and anisotropic situations is facilitated and made rational when performed in terms of the irreducible representations of the relevant symmetry group which is the group of all rotations SO(3). In this paper we firstly consider the needed general theory and explain why we expect different (universal) scaling exponents in the different sectors of the symmetry group. We exemplify the theory context of isotropic turbulence (for third order tensorial structure functions) and in weakly anisotropic turbulence (for the second order structure function). The utility of the resulting expressions for the analysis of experimental data is demonstrated in the context of high Reynolds number measurements of turbulence in the atmosphere.
Symmetry breaking in fluid dynamics: Lie group reducible motions for real fluids
Energy Technology Data Exchange (ETDEWEB)
Holm, D.D.
1976-07-01
The physics of fluids is based on certain kinematical invariance principles, which refer to coordinate systems, dimensions, and Galilean reference frames. Other, thermodynamic, symmetry principles are introduced by the material description. In the present work, the interplay between these two kinds of invariance principles is used to solve for classes of one-dimensional non-steady isentropic motions of a fluid whose equation of state is of Mie-Gruneisen type. Also, the change in profile and attenuation of weak shock waves in a dissipative medium is studied at the level of Burgers' approximation from the viewpoint of its underlying symmetry structure. The mathematical method of approach is based on the theory of infinitesimal Lie groups. Fluid motions are characterized according to inequivalent subgroups of the full invariance group of the flow description and exact group reducible solutions are presented.
[Re]constructing Finite Flavour Groups: Horizontal Symmetry Scans from the Bottom-Up
Talbert, Jim
2014-01-01
We present a novel procedure for identifying discrete, leptonic flavour symmetries, given a class of unitary mixing matrices. By creating explicit 3D representations for generators of residual symmetries in both the charged lepton and neutrino sector, we reconstruct large(r) non-abelian flavour groups using the GAP language for computational finite algebra. We use experimental data to construct only those generators that yield acceptable (or preferable) mixing patterns. Such an approach is advantageous because it 1) can reproduce known groups from other 'top-down' scans while elucidating their origins from residuals, 2) find new previously unconsidered groups, and 3) serve as a powerful model building tool for theorists wishing to explore exotic flavour scenarios. We test our procedure on a generalization of the canonical tri-bimaximal (TBM) form.
Symmetries, Information and Monster Groups before and after the Big Bang
Directory of Open Access Journals (Sweden)
Arturo Tozzi
2016-12-01
Full Text Available The Monster group, the biggest of the sporadic groups, is equipped with the highest known number of dimensions and symmetries. Taking into account variants of the Borsuk–Ulam theorem and a novel topological approach cast in a physical fashion that has the potential to be operationalized, the universe can be conceived as a lower-dimensional manifold encompassed in the Monster group. Our universe might arise from spontaneous dimension decrease and symmetry breaking that occur inside the very structure of the Monster Module. We elucidate how the energetic loss caused by projection from higher to lower dimensions and by the Monster group’s non-abelian features is correlated with the present-day asymmetry in the thermodynamic arrow. By linking the Monster Module to its theoretical physical counterparts, it is then possible to calculate its enthalpy and Lie group trajectories. Our approach also reveals how a symmetry break might lead to a universe based on multi-dimensional string theories and CFT/AdS (anti-de Sitter/conformal field theory correspondence.
Quantum groups as generalized gauge symmetries in WZNW models. Part II. The quantized model
Hadjiivanov, L.; Furlan, P.
2017-07-01
This is the second part of a paper dealing with the "internal" (gauge) symmetry of the Wess-Zumino-Novikov-Witten (WZNW) model on a compact Lie group G. It contains a systematic exposition, for G = SU( n), of the canonical quantization based on the study of the classical model (performed in the first part) following the quantum group symmetric approach first advocated by L.D. Faddeev and collaborators. The internal symmetry of the quantized model is carried by the chiral WZNW zero modes satisfying quadratic exchange relations and an n-linear determinant condition. For generic values of the deformation parameter the Fock representation of the zero modes' algebra gives rise to a model space of U q ( sl( n)). The relevant root of unity case is studied in detail for n = 2 when a "restricted" (finite dimensional) quotient quantum group is shown to appear in a natural way. The module structure of the zero modes' Fock space provides a specific duality with the solutions of the Knizhnik-Zamolodchikov equation for the four point functions of primary fields suggesting the existence of an extended state space of logarithmic CFT type. Combining left and right zero modes (i.e., returning to the 2 D model), the rational CFT structure shows up in a setting reminiscent to covariant quantization of gauge theories in which the restricted quantum group plays the role of a generalized gauge symmetry.
S-Matrices and Quantum Group Symmetry of q-Deformed Sigma Models
Hollowood, Timothy J; Schmidtt, David M
2015-01-01
Recently, several kinds of integrable deformations of the string world sheet theory in the gauge/gravity correspondence have been constructed. One class of these, the q-deformations with q a root of unity, has been shown to be related to a particular discrete deformation of the principal chiral models and (semi-)symmetric space sigma models involving a gauged WZW model. We conjecture a form for the exact S-matrices of the bosonic integrable field theories of this type. The S-matrices imply that the theories have a hidden infinite dimensional affine quantum group symmetry. We provide some evidence, via quantum inverse scattering techniques, that the theories do indeed possess the finite-dimensional part of this quantum group symmetry.
S-matrices and quantum group symmetry of k-deformed sigma models
Hollowood, Timothy J.; Miramontes, J. Luis; Schmidtt, David M.
2016-11-01
Recently, two kinds of integrable deformations of the string world sheet theory in the gauge/gravity correspondence have been constructed (Delduc et al 2014 Phys. Rev. Lett. 112 051601; Hollowood et al 2014 J. Phys. A: Math. Theor. 47 495402). One class of these, the k deformations associated to the more general q deformations but with q={{{e}}}{{i}π /k} a root of unity, has been shown to be related to a particular discrete deformation of the principal chiral models and (semi-)symmetric space sigma models involving a gauged WZW model. We conjecture a form for the exact S-matrices of the bosonic integrable field theories of this type. The S-matrices imply that the theories have a hidden infinite dimensional affine quantum group symmetry. We provide some evidence, via quantum inverse scattering techniques, that the theories do indeed possess the finite-dimensional part of this quantum group symmetry.
CP Symmetry and Lepton Mixing from a Scan of Finite Discrete Groups
Yao, Chang-Yuan
2016-01-01
Including the generalized CP symmetry, we have performed a comprehensive scan of leptonic mixing patterns which can be obtained from finite discrete groups with order less than 2000. Both the semidirect approach and its variant are considered. The lepton mixing matrices which can admit a good agreement with experimental data can be organized into eight different categories up to possible row and column permutations. These viable mixing patterns can be completely obtained from the discrete flavor groups $\\Delta(6n^2)$, $D^{(1)}_{9n,3n}$, $A_5$ and $\\Sigma(168)$ combined with CP symmetry. We perform a detailed analytical and numerical analysis for each possible mixing pattern. The resulting predictions for lepton mixing parameter, neutrinoless double decay and flavored leptogenesis are studied.
The Structure of Reduced Sudoku Grids and the Sudoku Symmetry Group
Directory of Open Access Journals (Sweden)
Siân K. Jones
2012-01-01
Full Text Available A Sudoku grid is a constrained Latin square. In this paper a reduced Sudoku grid is described, the properties of which differ, through necessity, from that of a reduced Latin square. The Sudoku symmetry group is presented and applied to determine a mathematical relationship between the number of reduced Sudoku grids and the total number of Sudoku grids for any size. This relationship simplifies the enumeration of Sudoku grids and an example of the use of this method is given.
Die Aufgabe des Gesetzes bei Solon und Platon
Marti, Urs
2011-01-01
Solon und Platon werden in der Literatur häufig in einem Zug genannt. Bereits Solon habe das Gesetz verstanden als Instrument zur Überwindung einer politischen Unordnung, die aus der mangelnden moralischen Qualifikation der Bürger resultiere. Die verbreitete Ansicht, Solon habe die politische Philosophie Platons vorweggenommen, bedarf der kritischen Prüfung. Tatsächlich versteht Platon unter Politik primär die moralische Erziehung der Bürger, während soziale Konflikte als Ursachen der Unordnu...
Regularities with random interactions in energy centroids defined by group symmetries
Kota, V K B
2005-01-01
Regular structures generated by random interactions in energy centroids defined over irreducible representations (irreps) of some of the group symmetries of the interacting boson models $sd$IBM, $sdg$IBM, $sd$IBM-$T$ and $sd$IBM-$ST$ are studied by deriving trace propagations equations for the centroids. It is found that, with random interactions, the lowest and highest group irreps in general carry most of the probability for the corresponding centroids to be lowest in energy. This generalizes the result known earlier, via numerical diagonalization, for the more complicated fixed spin ($J$) centroids where simple trace propagation is not possible.
Renormalization-group symmetries for solutions of nonlinear boundary value problems
Kovalev, V F
2008-01-01
Approximately 10 years ago, the method of renormalization-group symmetries entered the field of boundary value problems of classical mathematical physics, stemming from the concepts of functional self-similarity and of the Bogoliubov renormalization group treated as a Lie group of continuous transformations. Overwhelmingly dominating practical quantum field theory calculations, the renormalization-group method formed the basis for the discovery of the asymptotic freedom of strong nuclear interactions and underlies the Grand Unification scenario. This paper describes the logical framework of a new algorithm based on the modern theory of transformation groups and presents the most interesting results of application of the method to differential and/or integral equation problems and to problems that involve linear functionals of solutions. Examples from nonlinear optics, kinetic theory, and plasma dynamics are given, where new analytical solutions obtained with this algorithm have allowed describing the singular...
Molecular symmetry and group theory a programmed introduction to chemical applications
Vincent, Alan
2013-01-01
This substantially revised and expanded new edition of the bestselling textbook, addresses the difficulties that can arise with the mathematics that underpins the study of symmetry, and acknowledges that group theory can be a complex concept for students to grasp.Written in a clear, concise manner, the author introduces a series of programmes that help students learn at their own pace and enable to them understand the subject fully. Readers are taken through a series of carefully constructed exercises, designed to simplify the mathematics and give them a full understanding of how this
Michelot, F.
2004-04-01
We underline some inconsistencies in the work [J. Mol. Spectrosc. 219 (2003) 313] concerning symmetry adaptation in cubic groups. Also we show that some rather complicated methods presented can be easily avoided.
Symmetry Groups and Exact Solutions of New (4+1)-Dimensional Fokas Equation
Institute of Scientific and Technical Information of China (English)
YANG Zheng-Zheng; YAN Zhen-Ya
2009-01-01
In this paper, we investigate symmetries of the new (4+1)-dimensional Fokas equation, including point symmetries and the potential symmetries. We firstly employ the algorithmic procedure of computing the point symme-tries. And then we transform the Fokas equation into a potential system and gain the potential symmetries of Fokas equation. Finally, we use the obtained point symmetries and some constructive methods to get some doubly periodic wave solutions and other solutions of the Fokas equation. In particular, some solitary wave solutions are also given.
Cycle symmetry and its causes, Cisco Group (Virgilian and Wolfcampian), Texas
Energy Technology Data Exchange (ETDEWEB)
Yang, W. [Univ. of Texas, Austin, TX (United States). Dept. of Geological Sciences
1996-11-01
181 transgressive-regressive cycles composed of nonmarine and marine carbonate and siliciclastic rocks of the Cisco Group on the Eastern Shelf, Texas, display complex characteristics at both hemicycle and full-cycle scales. They are delineated on the basis of successive changes of depositional environments, stratal boundary relations, and stratigraphic position. Transgressive and regressive stratigraphic environment gradients are defined as the magnitude of environmental shift divided by thickness for each hemicycle. They indicate the rates of lateral environmental shifts during transgression and regression. Cycle symmetry index is defined as the ratio between transgressive and regressive stratigraphic environment gradients. It provides a measure of stratigraphic response to controlling processes. Five Cisco cycle types defined by the type of component lithofacies display the stratigraphic response mainly to noncyclic allogenic and autogenic processes. The cycle types have varying magnitude, thickness, and symmetry. They also vary in lateral extent and in abundance. A process-response model of cyclic sedimentation of the Cisco Group on the Eastern Shelf is established. It emphasizes the interplay between autogenic and allogenic processes at the sub-cycle scale. Understanding interactions among glacio-eustasy, climate, shelf subsidence, sediment supply, and depositional dynamics during various stages of transgression and regression is central to a clearer comprehension of the observed variations in cycle characteristics.
Two dimentional lattice vibrations from direct product representations of symmetry groups
Directory of Open Access Journals (Sweden)
J. N. Boyd
1983-01-01
two dimensional crystals. First, the Born cyclic condition is applied to a double chain composed of coupled linear lattices to obtain a cylindrical arrangement. Then the quadratic Lagrangian function for the system is written in matrix notation. The Lagrangian is diagonalized to yield the natural frequencies of the system. The transformation to achieve the diagonalization was obtained from group theorectic considerations. Next, the techniques developed for the double chain are applied to a square lattice. The square lattice is transformed into the toroidal Ising model. The direct product nature of the symmetry group of the torus reveals the transformation to diagonalize the Lagrangian for the Ising model, and the natural frequencies for the principal directions in the model are obtained in closed form.
Quantum Field Theories with Symmetries in the Wilsonian Exact Renormalization Group
Vian, Federica
1999-01-01
The purpose of the present thesis is the implementation of symmetries in the Wilsonian Exact Renormalization Group (ERG) approach. After recalling how the ERG can be introduced in a general theory (i.e. containing both bosons and fermions, scalars and vectors) and having applied it to the massless scalar theory as an example of how the method works, we discuss the formulation of the Quantum Action Principle (QAP) in the ERG and show that the Slavnov-Taylor identities can be directly derived for the cutoff effective action at any momentum scale. Firstly the QAP is exploited to analyse the breaking of dilatation invariance occurring in the scalar theory in this approach. Then we address SU(N) Yang-Mills theory and extensively treat the key issue of the boundary conditions of the flow equation which, in this case, have also to ensure restoration of symmetry for the physical theory. In case of a chiral gauge theory, we show how the chiral anomaly can be obtained in the ERG. Finally, we extend the ERG formulation ...
Revisiting the Lie-group symmetry method for turbulent channel flow with wall transpiration
Khujadze, George
2016-01-01
The Lie-group-based symmetry analysis, as first proposed in Avsarkisov et al. (2014) and then later modified in Oberlack et al. (2015), to generate invariant solutions in order to predict the scaling behavior of a channel flow with uniform wall transpiration, is revisited. By focusing first on the results obtained in Avsarkisov et al. (2014), we failed to reproduce two key results: (i) For different transpiration rates at a constant Reynolds number, the mean velocity profiles (in deficit form) do not universally collapse onto a single curve as claimed. (ii) The universally proposed logarithmic scaling law in the center of the channel does not match the direct numerical simulation (DNS) data for the presented parameter values. In fact, no universal scaling behavior in the center of the channel can be detected from their DNS data, as it is misleadingly claimed in Avsarkisov et al. (2014). Moreover, we will demonstrate that the assumption of a Reynolds-number independent symmetry analysis is not justified for th...
On symmetry groups of a 2D nonlinear diffusion equation with source
Indian Academy of Sciences (India)
Radica Cimpoiasu
2015-04-01
Symmetry analysis of a 2D nonlinear evolutionary equation with mixed spatial derivative and general source term involving the dependent variable and its spatial derivatives is performed. The source terms for which the equation admits nontrivial Lie symmetries are identified for two different forms of the symmetry operator. In one of these cases, the symmetries do not depend on the form of nonlinearities and in the other case, nonlinearities of power, exponential and trigonometric forms are considered. There are no supplementary nonclassical symmetries for the investigated equation. The results reported here generalize the previous results on the 2D heat equation and the 2D Ricci model.
Group momentum space and Hopf algebra symmetries of point particles coupled to 2+1 gravity
Arzano, Michele; Lotito, Matteo
2014-01-01
We present an in-depth investigation of the $SL(2,\\mathbb{R})$ momentum space describing point particles coupled to Einstein gravity in three space-time dimensions. We introduce different sets of coordinates on the group manifold and discuss their properties under Lorentz transformations. In particular we show how a certain set of coordinates exhibits an upper bound on the energy under deformed Lorentz boosts which saturate at the Planck energy. We discuss how this deformed symmetry framework is generally described by a quantum deformation of the Poincar\\'e group: the quantum double of $SL(2,\\mathbb{R})$. We then illustrate how the space of functions on the group manifold momentum space has a dual representation on a non-commutative space of coordinates via a (quantum) group Fourier transform. In this context we explore the connection between Weyl maps and different notions of (quantum) group Fourier transform appeared in the literature in the past years and establish relations between them. Finally we write ...
Symmetry breaking in the opinion dynamics of a multi-group project organization
Zhu, Zhen-Tao; Zhou, Jing; Li, Ping; Chen, Xing-Guang
2012-10-01
A bounded confidence model of opinion dynamics in multi-group projects is presented in which each group's opinion evolution is driven by two types of forces: (i) the group's cohesive force which tends to restore the opinion back towards the initial status because of its company culture; and (ii) nonlinear coupling forces with other groups which attempt to bring opinions closer due to collaboration willingness. Bifurcation analysis for the case of a two-group project shows a cusp catastrophe phenomenon and three distinctive evolutionary regimes, i.e., a deadlock regime, a convergence regime, and a bifurcation regime in opinion dynamics. The critical value of initial discord between the two groups is derived to discriminate which regime the opinion evolution belongs to. In the case of a three-group project with a symmetric social network, both bifurcation analysis and simulation results demonstrate that if each pair has a high initial discord, instead of symmetrically converging to consensus with the increase of coupling scale as expected by Gabbay's result (Physica A 378 (2007) p. 125 Fig. 5), project organization (PO) may be split into two distinct clusters because of the symmetry breaking phenomenon caused by pitchfork bifurcations, which urges that apart from divergence in participants' interests, nonlinear interaction can also make conflict inevitable in the PO. The effects of two asymmetric level parameters are tested in order to explore the ways of inducing dominant opinion in the whole PO. It is found that the strong influence imposed by a leader group with firm faith on the flexible and open minded follower groups can promote the formation of a positive dominant opinion in the PO.
Symmetry breaking in the opinion dynamics of a multi-group project organization
Institute of Scientific and Technical Information of China (English)
Zhu Zhen-Tao; Zhou Jing; Li Ping; Chen Xing-Guang
2012-01-01
A bounded confidence model of opinion dynamics in multi-group projects is presented in which each group's opinion evolution is driven by two types of forces:(i) the group's cohesive force which tends to restore the opinion back towards the initial status because of its company culture; and (ii) nonlinear coupling forces with other groups which attempt to bring opinions closer due to collaboration willingness.Bifurcation analysis for the case of a two-group project shows a cusp catastrophe phenomenon and three distinctive evolutionary regimes,i.e.,a deadlock regime,a convergence regime,and a bifurcation regime in opinion dynamics.The critical value of initial discord between the two groups is derived to discriminate which regime the opinion evolution belongs to.In the case of a three-group project with a symmetric social network,both bifurcation analysis and simulation results demonstrate that if each pair has a high initial discord,instead of symmetrically converging to consensus with the increase of coupling scale as expected by Gabbay's result (Physica A 378 (2007) p.125 Fig.5),project organization (PO) may be split into two distinct clusters because of the symmetry breaking phenomenon caused by pitchfork bifurcations,which urges that apart from divergence in participants' interests,nonlinear interaction can also make conflict inevitable in the PO.The effects of two asymmetric level parameters are tested in order to explore the ways of inducing dominant opinion in the whole PO.It is found that the strong influence imposed by a leader group with firm faith on the flexible and open minded follower groups can promote the formation of a positive dominant opinion in the PO.
The symmetry group and harmonic potentials of an electrostatic generalized multipole
Institute of Scientific and Technical Information of China (English)
李钰
1995-01-01
The concept of an electrostatic ordinary multipole has been extended to an electrostatic generalized multipole which consists of a pair of close placed electrostatic ordinary multipole and electrostatic round lens. The definition of the M function for an electrostatic ordinary multipole has been extended to that of the M function for an electrostatic generalized multipole. The relation between the symmetry group of anelectrostaticordinary multipole and that of its corresponding electrostatic generalized multipole, and the relation between their constraint relations among their mth partial harmonic potentials have been derived. By analyzing some important electrostatic generalized multipoles, it is concluded that if an electrostatic deflector-multipole and an electrostatic round lens are placed close to each other , one cannot assert that this combined system can always be treated by the aberration theory of a combined focusing-deflection system.
Quinto, A. G.; Ferrari, A. F.; Lehum, A. C.
2016-06-01
In this work, we investigate the consequences of the Renormalization Group Equation (RGE) in the determination of the effective superpotential and the study of Dynamical Symmetry Breaking (DSB) in an N = 1 supersymmetric theory including an Abelian Chern-Simons superfield coupled to N scalar superfields in (2 + 1) dimensional spacetime. The classical Lagrangian presents scale invariance, which is broken by radiative corrections to the effective superpotential. We calculate the effective superpotential up to two-loops by using the RGE and the beta functions and anomalous dimensions known in the literature. We then show how the RGE can be used to improve this calculation, by summing up properly defined series of leading logs (LL), next-to-leading logs (NLL) contributions, and so on... We conclude that even if the RGE improvement procedure can indeed be applied in a supersymmetric model, the effects of the consideration of the RGE are not so dramatic as it happens in the non-supersymmetric case.
Hierarchy of kissing numbers for exceptional Lie symmetry groups in high energy physics
Energy Technology Data Exchange (ETDEWEB)
El Naschie, M.S. [Donghua University, Shanghai (China); Department of Physics University of Alexandria, Alexandria (Egypt)], E-mail: Chaossf@aol.com
2008-01-15
We are constructing a hierarchy of kissing numbers representing singular contact points of hyper-spheres in exceptional Lie symmetry groups lattice arrangement embedded in the 26 dimensional bosonic strings spacetime. That way we find a total number of points and dimensions equal to 548. This is 52 more than the order of E{sub 8}E{sub 8} of heterotic string theory and leads to the prediction of 69 elementary particles at an energy scale under 1 T. In other words, our mathematical model predicts nine more particles than what is currently experimentally known to exist in the standard model of high energy physics namely only 60. The result is thus in full agreement with all our previous theoretical findings.
Institute of Scientific and Technical Information of China (English)
Gao Ya-Jun
2006-01-01
The so-called extended hyperbolic complex (EHC) function method is used to study further the stationary axisymmetric Einstein-Maxwell theory with p Abelian gauge fields (EM-p theory, for short). Two EHC structural Riemann-Hilbert(RH) transformations are constructed and are then shown to give an infinite-dimensional symmetry group of the EM-p theory. This symmetry group is verified to have the structure of semidirect product of Kac-Moody group SU(p + 1, 1) and Virasoro group. Moreover, the infinitesimal forms of these two RH transformations are calculated and found to give exactly the same infinitesimal transformations as in previous author's paper by a different scheme. This demonstrates that the results obtained in the present paper provide some exponentiations of all the infinitesimal symmetry transformations obtained before.
Impact of Platon ETC system on intercity trucking cost
Directory of Open Access Journals (Sweden)
Pogotovkina Natalya
2017-01-01
Full Text Available In 2015 Platon ETC System, a system of charging trucks with gross vehicle weight exceeding 12 tons, was implemented in Russia. The payment is collected as a compensation fo0 the damage caused to the federal public roads. Platon system is an additional source of financing for the road sector. However, its implementation made the carriers face the increasing costs. This paper presents the first results of the system functioning and the problems, associated with it. We consider the foreign systems of truck charging. The results of calculations, which show the effect of the toll collection on the prime cost of road freight transportation, are also presented.
Seiler, Christian; Evers, Ferdinand
2016-10-01
A formalism for electronic-structure calculations is presented that is based on the functional renormalization group (FRG). The traditional FRG has been formulated for systems that exhibit a translational symmetry with an associated Fermi surface, which can provide the organization principle for the renormalization group (RG) procedure. We here advance an alternative formulation, where the RG flow is organized in the energy-domain rather than in k space. This has the advantage that it can also be applied to inhomogeneous matter lacking a band structure, such as disordered metals or molecules. The energy-domain FRG (ɛ FRG) presented here accounts for Fermi-liquid corrections to quasiparticle energies and particle-hole excitations. It goes beyond the state of the art G W -BSE , because in ɛ FRG the Bethe-Salpeter equation (BSE) is solved in a self-consistent manner. An efficient implementation of the approach that has been tested against exact diagonalization calculations and calculations based on the density matrix renormalization group is presented. Similar to the conventional FRG, also the ɛ FRG is able to signalize the vicinity of an instability of the Fermi-liquid fixed point via runaway flow of the corresponding interaction vertex. Embarking upon this fact, in an application of ɛ FRG to the spinless disordered Hubbard model we calculate its phase boundary in the plane spanned by the interaction and disorder strength. Finally, an extension of the approach to finite temperatures and spin S =1 /2 is also given.
Reduction by Lie Group Symmetries in Diffeomorphic Image Registration and Deformation Modelling
Directory of Open Access Journals (Sweden)
Stefan Sommer
2015-05-01
Full Text Available We survey the role of reduction by symmetry in the large deformation diffeomorphic metric mapping framework for registration of a variety of data types (landmarks, curves, surfaces, images and higher-order derivative data. Particle relabelling symmetry allows the equations of motion to be reduced to the Lie algebra allowing the equations to be written purely in terms of the Eulerian velocity field. As a second use of symmetry, the infinite dimensional problem of finding correspondences between objects can be reduced for a range of concrete data types, resulting in compact representations of shape and spatial structure. Using reduction by symmetry, we describe these models in a common theoretical framework that draws on links between the registration problem and geometric mechanics. We outline these constructions and further cases where reduction by symmetry promises new approaches to the registration of complex data types.
Seiler, Christian
2016-01-01
A formalism for electronic-structure calculations is presented that is based on the functional renormalization group (FRG). The traditional FRG has been formulated for systems that exhibit a translational symmetry with an associated Fermi surface, which can provide the organization principle for the renormalization group (RG) procedure. We here advance an alternative formulation, where the RG-flow is organized in the energy-domain rather than in k-space. This has the advantage that it can also be applied to inhomogeneous matter lacking a band-structure, such as disordered metals or molecules. The energy-domain FRG ({\\epsilon}FRG) presented here accounts for Fermi-liquid corrections to quasi-particle energies and particle-hole excitations. It goes beyond the state of the art GW-BSE, because in {\\epsilon}FRG the Bethe-Salpeter equation (BSE) is solved in a self-consistent manner. An efficient implementation of the approach that has been tested against exact diagonalization calculations and calculations based on...
Piiskop Platoni protest saksa okupatsiooni vastu a. 1918 / Piiskop Platon
Platon, Eesti Apostlik-Õigeusu kiriku peapiiskop, 1869-1919
1987-01-01
Piiskop Platon (kodanikunimega Paul Kulbusch) kirjeldab saksa okupatsiooni Eestis ja Lätis, Riia õigeusu kirikute ümberehitamist luteri kirikuteks, preestrite tagakiusamist ja väljasaatmist. A. Piibule Londonisse lääneriikide esindajatele levitamiseks saadetud pöördumise tekstile eelneb Esmo Ridala sissejuhatus ülevaatega piiskop Platoni eluloost
I grandi della fisica da Platone a Heisenberg
Von Weizsäcker, Carl Friedrich
2002-01-01
Parmenide ; Platone ; Aristotele ; Copernico, Keplero, Galilei ; Galileo Galilei ; Cartesio ; Gottfried Wilhelm Leibniz ; Cartesio, Newton, Leibniz, Kant ; Immanuel Kant ; Johann Wolfgang Goethe ; Robert Meyer ; Albert Einstein ; Niels Bohr ; Paul Adrien Maurice Dirac ; Niels Bohr e Werner Heisenberg, un ricordo del 1932 ; Werner Heisenberg ; Heisenberg, fisico e filosofo ; l'interpretazione filosofica della fisica moderna.
Piiskop Platoni protest saksa okupatsiooni vastu a. 1918 / Piiskop Platon
Platon, Eesti Apostlik-Õigeusu kiriku peapiiskop, 1869-1919
1987-01-01
Piiskop Platon (kodanikunimega Paul Kulbusch) kirjeldab saksa okupatsiooni Eestis ja Lätis, Riia õigeusu kirikute ümberehitamist luteri kirikuteks, preestrite tagakiusamist ja väljasaatmist. A. Piibule Londonisse lääneriikide esindajatele levitamiseks saadetud pöördumise tekstile eelneb Esmo Ridala sissejuhatus ülevaatega piiskop Platoni eluloost
Guo, Jian-You; Chen, Shou-Wan; Niu, Zhong-Ming; Li, Dong-Peng; Liu, Quan
2014-02-14
Symmetry is an important and basic topic in physics. The similarity renormalization group theory provides a novel view to study the symmetries hidden in the Dirac Hamiltonian, especially for the deformed system. Based on the similarity renormalization group theory, the contributions from the nonrelativistic term, the spin-orbit term, the dynamical term, the relativistic modification of kinetic energy, and the Darwin term are self-consistently extracted from a general Dirac Hamiltonian and, hence, we get an accurate description for their dependence on the deformation. Taking an axially deformed nucleus as an example, we find that the self-consistent description of the nonrelativistic term, spin-orbit term, and dynamical term is crucial for understanding the relativistic symmetries and their breaking in a deformed nuclear system.
Symmetries, Symmetry Breaking, Gauge Symmetries
Strocchi, Franco
2015-01-01
The concepts of symmetry, symmetry breaking and gauge symmetries are discussed, their operational meaning being displayed by the observables {\\em and} the (physical) states. For infinitely extended systems the states fall into physically disjoint {\\em phases} characterized by their behavior at infinity or boundary conditions, encoded in the ground state, which provide the cause of symmetry breaking without contradicting Curie Principle. Global gauge symmetries, not seen by the observables, are nevertheless displayed by detectable properties of the states (superselected quantum numbers and parastatistics). Local gauge symmetries are not seen also by the physical states; they appear only in non-positive representations of field algebras. Their role at the Lagrangian level is merely to ensure the validity on the physical states of local Gauss laws, obeyed by the currents which generate the corresponding global gauge symmetries; they are responsible for most distinctive physical properties of gauge quantum field ...
Beyer, Florian; Frauendiener, Jörg
2015-01-01
We apply a single patch pseudo-spectral scheme based on integer spin-weighted spherical harmonics presented in [1, 2] to Einstein's equations. The particular hyperbolic reduction of Einstein's equations which we use is obtained by a covariant version of the generalized harmonic formalism and Geroch's symmetry reduction. In this paper we focus on spacetimes with a spatial S3-topology and symmetry group U(1). We discuss analytical and numerical issues related to our implementation. As a test, we reproduce numerically exact inhomogeneous cosmological solutions of the vacuum Einstein field equations obtained in [3].
Wang, Juven; Gu, Zheng-Cheng; Wen, Xiao-Gang
The challenge of identifying symmetry-protected topological states (SPTs) is due to their lack of symmetry-breaking order parameters and intrinsic topological orders. For this reason, it is impossible to formulate SPTs under Ginzburg-Landau theory or probe SPTs via fractionalized bulk excitations and topology-dependent ground state degeneracy. However, the partition functions from path integrals with various symmetry twists are universal SPT invariants, fully characterizing SPTs. In this work, we use gauge fields to represent those symmetry twists in closed spacetimes of any dimensionality and arbitrary topology. This allows us to express the SPT invariants in terms of continuum field theory. We show that SPT invariants of pure gauge actions describe the SPTs predicted by group cohomology, while the mixed gauge-gravity actions describe the beyond-group-cohomology SPTs, recently observed by Kapustin. We find new examples of mixed gauge-gravity actions for U(1) SPTs in 3+1D and 4+1D via the Stiefel-Whitney class and the gravitational Chern-Simons term. [Work based on Phys. Rev. Lett. 114, 031601 (2015) arXiv:1405.7689
A Phase Transformation with no Change in Space Group Symmetry: Octafluoronaphtalene
DEFF Research Database (Denmark)
Pawley, G. S.; Dietrich, O. W.
1975-01-01
, the shear movement being equal to one carbon-carbon bond of the naphthalene skeleton. In this process the molecules reorient, but are still related by the same symmetry operations. This transformation, although not unique, is probably the first of its kind to be discovered in molecular systems....
Jaffé, Hans H
1977-01-01
This book, devoted exclusively to symmetry in chemistry and developed in an essentially nonmathematical way, is a must for students and researchers. Topics include symmetry elements and operations, multiple symmetry operations, multiplication tables and point groups, group theory applications, and crystal symmetry. Extensive appendices provide useful tables.
Energy Technology Data Exchange (ETDEWEB)
Henley, E.M.
1981-09-01
Internal and space-time symmetries are discussed in this group of lectures. The first of the lectures deals with an internal symmetry, or rather two related symmetries called charge independence and charge symmetry. The next two discuss space-time symmetries which also hold approximately, but are broken only by the weak forces; that is, these symmetries hold for both the hadronic and electromagnetic forces. (GHT)
Baena, J D; Marques, R
2007-01-01
In this paper a systematic approach to the design of bulk isotropic magnetic metamaterials is presented. The role of the symmetries of both the constitutive element and the lattice are analyzed. For this purpose it is assumed that the metamaterial is composed by cubic SRR resonators, arranged in a cubic lattice. The minimum symmetries needed to ensure an isotropic behavior are analyzed, and some particular configurations are proposed. Besides, an equivalent circuit model is proposed for the considered cubic SRR resonators. Experiments are carried out in order to validate the proposed theory. We hope that this analysis will pave the way to the design of bulk metamaterials with strong isotropic magnetic response, including negative permeability and left-handed metamaterials.
Account of Nonpolynomial SU(3)-Breaking Effects By Use of Quantum Groups As Flavor Symmetries
Gavrilik, A M
1998-01-01
Using instead of ordinary flavour symmetries SU(n_f) their corresponding quantum (q-deformed) analogs yields new baryon mass sum rules of extreme accuracy. We show, in the 3-flavour case, that such approach accounts for highly nonlinear (nonpolynomial) SU(3)-breaking effects both in the octet and decuplet baryon masses. A version of this approach is considered that involves q-covariant ingredients in the mass operator. The resulting new 'q-deformed' mass relation (q-MR) is simpler than previously derived q-MRs, but requires, for its empirical validity, a fitting to fix the value of the deformation parameter q. Well-known Gell-Mann--Okubo (GMO) octet mass sum rule is found to result not only from usual SU(3), but also from some exotic symmetry corresponding to the q=-1 (i.e., singular) limit of the q-algebra U_q(su_3).
Beyer, F.; Escobar, L.; Frauendiener, J.
2016-02-01
In this paper we consider the single patch pseudospectral scheme for tensorial and spinorial evolution problems on the 2-sphere presented by Beyer et al. [Classical Quantum Gravity 32, 175013 (2015); Classical Quantum Gravity31, 075019 (2014)], which is based on the spin-weighted spherical harmonics transform. We apply and extend this method to Einstein's equations and certain classes of spherical cosmological spacetimes. More specifically, we use the hyperbolic reductions of Einstein's equations obtained in the generalized wave map gauge formalism combined with Geroch's symmetry reduction, and focus on cosmological spacetimes with spatial S3 -topologies and symmetry groups U(1) or U (1 )×U (1 ) . We discuss analytical and numerical issues related to our implementation. We test our code by reproducing the exact inhomogeneous cosmological solutions of the vacuum Einstein field equations obtained by Beyer and Hennig [Classical Quantum Gravity 31, 095010 (2014)].
Lattice Regularization and Symmetries
Hasenfratz, Peter; Von Allmen, R; Allmen, Reto von; Hasenfratz, Peter; Niedermayer, Ferenc
2006-01-01
Finding the relation between the symmetry transformations in the continuum and on the lattice might be a nontrivial task as illustrated by the history of chiral symmetry. Lattice actions induced by a renormalization group procedure inherit all symmetries of the continuum theory. We give a general procedure which gives the corresponding symmetry transformations on the lattice.
Erotic Wisdom and the Socratic Vocation in Plutarch’s Platonic Question 1
Directory of Open Access Journals (Sweden)
Mark Shiffman
2010-11-01
Full Text Available Plutarch's skeptical Platonism is embodied in his understanding of Socrates and Socrates' use of eros, and serves to harmonize his use of the skeptical heritage with his understanding of central Platonic teachings: questioning is the crucial tool in the search for wisdom.
CP and other Symmetries of Symmetries
Trautner, Andreas
2016-01-01
Outer automorphisms of symmetries ("symmetries of symmetries") in relativistic quantum field theories are studied, including charge conjugation (C), space-reflection (P) , and time-reversal (T) transformations. The group theory of outer automorphisms is pedagogically introduced and it is shown that CP transformations are special outer automorphisms of the global, local, and space-time symmetries of a theory. It is shown that certain discrete groups allow for a group theoretical prediction of parameter independent CP violating complex phases with fixed geometrical values. The remainder of this thesis pioneers the study of outer automorphisms which are not related to C, P, or T. It is shown how outer automorphisms, in general, relate symmetry invariants and, in theories with spontaneous symmetry breaking, imply relations between different vacuum expectation values. Thereby, outer automorphisms can give rise to emergent symmetries. An example model with a discrete symmetry and three copies of the Standard Model ...
Low energy phenomena in a model with symmetry group SUSY SO (10) ×△(48)×U(1)
Institute of Scientific and Technical Information of China (English)
周光召; 吴岳良
1996-01-01
Fermion masses and mixing angles including that of neutrinos are studied in a model with symmetry group SUSY S0(10) x4(48) xU(i). Universality of Yukawa coupling of superfields is assumed. The resulting texture of mass matrices in the low energy region depends only on a single coupling constant and VEVs caused by necessary symmetry breaking. 13 parameters involving masses and mixing angles in the quark and charged lepton sector are successfully described by only five parameters with two of them determined by the scales of U(1), SO (10) and SU(5) symmetry breaking compatible with the requirement of grand unification and proton decay. The neutrino masses and mixing angles in the leptonic sector are also determined with the addition of a Majorana coupling term. It is found that LSND, events, atmospheric neutrino deficit and the mass limit put by hot dark matter can be naturally explained. Solar neutrino puzzle can be solved only by introducing sterile neutrino with one additional parameter. More precise me
Flat Zipper-Unfolding Pairs for Platonic Solids
O'Rourke, Joseph
2010-01-01
We show that four of the five Platonic solids' surfaces may be cut open with a Hamiltonian path along edges and unfolded to a polygonal net each of which can "zipper-refold" to a flat doubly covered parallelogram, forming a rather compact representation of the surface. Thus these regular polyhedra have particular flat "zipper pairs." No such zipper pair exists for a dodecahedron, whose Hamiltonian unfoldings are "zip-rigid." This report is primarily an inventory of the possibilities, and raises more questions than it answers.
Chubukov, A. V.
2009-05-01
We analyze antiferromagnetism and superconductivity in novel Fe-based superconductors within the weak-coupling, itinerant model of electron and hole pockets near (0, 0) and ( π, π) in the folded Brillouin zone. We discuss the interaction Hamiltonian, the nesting, the RG flow of the couplings at energies above and below the Fermi energy, and the interplay between SDW magnetism, superconductivity and charge orbital order. We argue that SDW antiferromagnetism wins at zero doping but looses to superconductivity upon doping. We show that the most likely symmetry of the superconducting gap is A1 g in the folded zone. This gap has no nodes on the Fermi surface but changes sign between hole and electron pockets. We also argue that at weak coupling, this pairing predominantly comes not from spin fluctuation exchange but from a direct pair hopping between hole and electron pockets.
Platonic solids back in the sky: Icosahedral inflation
Kang, Jonghee
2015-01-01
We generalize the model of solid inflation to an anisotropic cosmic solid. Barring fine tunings, the observed isotropy of the cosmological background and of the scalar two-point function isolate the icosahedral group as the only possible symmetry group of such a solid. In such a case, higher-point correlation functions---starting with the three-point one---are naturally maximally anisotropic, which makes the standard detection strategies highly inefficient and calls for a dedicated analysis of CMB data. The tensor two-point function can also be highly anisotropic, but only in the presence of sizable higher-derivative couplings.
Van Isacker, P
2010-01-01
The use of dynamical symmetries or spectrum generating algebras for the solution of the nuclear many-body problem is reviewed. General notions of symmetry and dynamical symmetry in quantum mechanics are introduced and illustrated with simple examples such as the SO(4) symmetry of the hydrogen atom and the isospin symmetry in nuclei. Two nuclear models, the shell model and the interacting boson model, are reviewed with particular emphasis on their use of group-theoretical techniques.
Ruf, Armin; Tetaz, Tim; Schott, Brigitte; Joseph, Catherine; Rudolph, Markus G
2016-11-01
Fructose-1,6-bisphosphatase (FBPase) is a key regulator of gluconeogenesis and a potential drug target for type 2 diabetes. FBPase is a homotetramer of 222 symmetry with a major and a minor dimer interface. The dimers connected via the minor interface can rotate with respect to each other, leading to the inactive T-state and active R-state conformations of FBPase. Here, the first crystal structure of human liver FBPase in the R-state conformation is presented, determined at a resolution of 2.2 Å in a tetragonal setting that exhibits an unusual arrangement of noncrystallographic symmetry (NCS) elements. Self-Patterson function analysis and various intensity statistics revealed the presence of pseudo-translation and the absence of twinning. The space group is P41212, but structure determination was also possible in space groups P43212, P4122 and P4322. All solutions have the same arrangement of three C2-symmetric dimers spaced by 1/3 along an NCS axis parallel to the c axis located at (1/4, 1/4, z), which is therefore invisible in a self-rotation function analysis. The solutions in the four space groups are related to one another and emulate a body-centred lattice. If all NCS elements were crystallographic, the space group would be I4122 with a c axis three times shorter and a single FBPase subunit in the asymmetric unit. I4122 is a minimal, non-isomorphic supergroup of the four primitive tetragonal space groups, explaining the space-group ambiguity for this crystal.
Energy Technology Data Exchange (ETDEWEB)
Lorenzen, R.
2007-03-15
Starting from the assumption of modular P{sub 1}CT symmetry in quantum field theory a representation of the universal covering of the Poincar'e group is constructed in terms of pairs of modular conjugations. The modular conjugations are associated with field algebras of unbounded operators localised in wedge regions. It turns out that an essential step consists in characterising the universal covering group of the Lorentz group by pairs of wedge regions, in conjunction with an analysis of its geometrical properties. In this thesis two approaches to this problem are developed in four spacetime dimensions. First a realisation of the universal covering as the quotient space over the set of pairs of wedge regions is presented. In spite of the intuitive definition, the necessary properties of a covering space are not straightforward to prove. But the geometrical properties are easy to handle. The second approach takes advantage of the well-known features of spin groups, given as subgroups of Clifford algebras. Characterising elements of spin groups by pairs of wedge regions is possible in an elegant manner. The geometrical analysis is performed by means of the results achieved in the first approach. These geometrical properties allow for constructing a representation of the universal cover of the Lorentz group in terms of pairs of modular conjugations. For this representation the derivation of the spin-statistics theorem is straightforward, and a PCT operator can be defined. Furthermore, it is possible to transfer the results to nets of field algebras in algebraic quantum field theory with ease. Many of the usual assumptions in quantum field theory like the spectrum condition or the existence of a covariant unitary representation, as well as the assumption on the quantum field to have only finitely many components, are not required. For the standard axioms, the crucial assumption of modular P{sub 1}CT symmetry constitutes no loss of generality because it is a
Mörschel, Philipp; Schmidt, Martin U
2015-01-01
A crystallographic quantum-mechanical/molecular-mechanical model (c-QM/MM model) with full space-group symmetry has been developed for molecular crystals. The lattice energy was calculated by quantum-mechanical methods for short-range interactions and force-field methods for long-range interactions. The quantum-mechanical calculations covered the interactions within the molecule and the interactions of a reference molecule with each of the surrounding 12-15 molecules. The interactions with all other molecules were treated by force-field methods. In each optimization step the energies in the QM and MM shells were calculated separately as single-point energies; after adding both energy contributions, the crystal structure (including the lattice parameters) was optimized accordingly. The space-group symmetry was maintained throughout. Crystal structures with more than one molecule per asymmetric unit, e.g. structures with Z' = 2, hydrates and solvates, have been optimized as well. Test calculations with different quantum-mechanical methods on nine small organic molecules revealed that the density functional theory methods with dispersion correction using the B97-D functional with 6-31G* basis set in combination with the DREIDING force field reproduced the experimental crystal structures with good accuracy. Subsequently the c-QM/MM method was applied to nine compounds from the CCDC blind tests resulting in good energy rankings and excellent geometric accuracies.
The symmetry groups of noncommutative quantum mechanics and coherent state quantization
Energy Technology Data Exchange (ETDEWEB)
Chowdhury, S. Hasibul Hassan; Ali, S. Twareque [Department of Mathematics and Statistics, Concordia University, Montreal, Quebec H3G 1M8 (Canada)
2013-03-15
We explore the group theoretical underpinning of noncommutative quantum mechanics for a system moving on the two-dimensional plane. We show that the pertinent groups for the system are the two-fold central extension of the Galilei group in (2+1)-space-time dimensions and the two-fold extension of the group of translations of R{sup 4}. This latter group is just the standard Weyl-Heisenberg group of standard quantum mechanics with an additional central extension. We also look at a further extension of this group and discuss its significance to noncommutative quantum mechanics. We build unitary irreducible representations of these various groups and construct the associated families of coherent states. A coherent state quantization of the underlying phase space is then carried out, which is shown to lead to exactly the same commutation relations as usually postulated for this model of noncommutative quantum mechanics.
Symmetry, Symmetry Breaking and Topology
Directory of Open Access Journals (Sweden)
Siddhartha Sen
2010-07-01
Full Text Available The ground state of a system with symmetry can be described by a group G. This symmetry group G can be discrete or continuous. Thus for a crystal G is a finite group while for the vacuum state of a grand unified theory G is a continuous Lie group. The ground state symmetry described by G can change spontaneously from G to one of its subgroups H as the external parameters of the system are modified. Such a macroscopic change of the ground state symmetry of a system from G to H correspond to a “phase transition”. Such phase transitions have been extensively studied within a framework due to Landau. A vast range of systems can be described using Landau’s approach, however there are also systems where the framework does not work. Recently there has been growing interest in looking at such non-Landau type of phase transitions. For instance there are several “quantum phase transitions” that are not of the Landau type. In this short review we first describe a refined version of Landau’s approach in which topological ideas are used together with group theory. The combined use of group theory and topological arguments allows us to determine selection rule which forbid transitions from G to certain of its subgroups. We end by making a few brief remarks about non-Landau type of phase transition.
Frewer, Michael
2016-01-01
The study by Oberlack et al. (2006) consists of two main parts: a direct numerical simulation (DNS) of a turbulent plane channel flow with streamwise rotation and a preceding Lie-group symmetry analysis on the two-point correlation equation (TPC) to analytically predict the scaling of the mean velocity profiles for different rotation rates. We will only comment on the latter part, since the DNS result obtained in the former part has already been commented on by Recktenwald et al. (2009), stating that the observed mismatch between DNS and their performed experiment is possibly due to the prescription of periodic boundary conditions on a too small computational domain in the spanwise direction. By revisiting the group analysis part in Oberlack et al. (2006), we will generate more natural scaling laws describing better the mean velocity profiles than the ones proposed. However, due to the statistical closure problem of turbulence, this improvement is illusive. As we will demonstrate, any arbitrary invariant scal...
Parrish, Robert M; Parker, Trent M; Sherrill, C David
2014-10-14
Recently, we introduced an effective atom-pairwise partition of the many-body symmetry-adapted perturbation theory (SAPT) interaction energy decomposition, producing a method known as atomic SAPT (A-SAPT) [Parrish, R. M.; Sherrill, C. D. J. Chem. Phys. 2014, 141, 044115]. A-SAPT provides ab initio atom-pair potentials for force field development and also automatic visualizations of the spatial contributions of noncovalent interactions, but often has difficulty producing chemically useful partitions of the electrostatic energy, due to the buildup of oscillating partial charges on adjacent functional groups. In this work, we substitute chemical functional groups in place of atoms as the relevant local quasiparticles in the partition, resulting in a functional-group-pairwise partition denoted as functional-group SAPT (F-SAPT). F-SAPT assigns integral sets of local occupied electronic orbitals and protons to chemical functional groups and linking σ bonds. Link-bond contributions can be further assigned to chemical functional groups to simplify the analysis. This approach yields a SAPT partition between pairs of functional groups with integral charge (usually neutral), preventing oscillations in the electrostatic partition. F-SAPT qualitatively matches chemical intuition and the cut-and-cap fragmentation technique but additionally yields the quantitative many-body SAPT interaction energy. The conceptual simplicity, chemical utility, and computational efficiency of F-SAPT is demonstrated in the context of phenol dimer, proflavine(+)-DNA intercalation, and a cucurbituril host-guest inclusion complex.
Stokes, Harold T; Campbell, Branton J; van Smaalen, Sander
2011-01-01
A complete table of (3 + 1)D, (3 + 2)D and (3 + 3)D superspace groups (SSGs) has been enumerated that corrects omissions and duplicate entries in previous tables of superspace groups and Bravais classes. The theoretical methods employed are not new, though the implementation is both novel and robust. The paper also describes conventions for assigning a unique one-line symbol for each group in the table. Finally, a new online data repository is introduced that delivers more complete information about each SSG than has been presented previously.
Systematic analysis of finite family symmetry groups and their application to the lepton sector
Ludl, Patrick Otto
2009-01-01
In this work we will investigate Lagrangians of the standard model extended by three right-handed neutrinos, and the consequences of invariance under finite groups G for lepton masses and mixing matrices are studied. The main part of this thesis is the systematic analysis of finite subgroups of SU(3). The analysis of these groups may act as a toolkit for future model building.
Controlling flexural waves in semi-infinite platonic crystals
Haslinger, Stewart G; Movchan, Alexander B; Jones, Ian S; Craster, Richard V
2016-01-01
We address the problem of scattering and transmission of a plane flexural wave through a semi-infinite array of point scatterers/resonators, which take a variety of physically interesting forms. The mathematical model accounts for several classes of point defects, including mass-spring resonators attached to the top surface of the flexural plate and their limiting case of concentrated point masses. We also analyse the special case of resonators attached to opposite faces of the plate. The problem is reduced to a functional equation of the Wiener-Hopf type, whose kernel varies with the type of scatterer considered. A novel approach, which stems from the direct connection between the kernel function of the semi-infinite system and the quasi-periodic Green's functions for corresponding infinite systems, is used to identify special frequency regimes. We thereby demonstrate dynamically anisotropic wave effects in semi-infinite platonic crystals, with particular attention paid to designing systems to exhibit dynami...
Poisson Lie symmetry and D-branes in WZW model on the Heisenberg Lie group $H_4$
Eghbali, A
2015-01-01
We show that the WZW model on the Heisenberg Lie group $H_4$ has Poisson-Lie symmetry only when the dual Lie group is ${ A}_2 \\oplus 2{ A}_1$. In this way, we construct the mutual T-dual sigma models on Drinfel'd double generated by the Heisenberg Lie group $H_4$ and its dual pair, ${ A}_2 \\oplus 2{ A}_1$, as the target space in such a way that the original model is the same as the $H_4$ WZW model. Furthermore, we show that the dual model is conformal up to two loops order. Finally, we discuss $D$-branes and the worldsheet boundary conditions defined by a gluing matrix on the $H_4$ WZW model. Using the duality map obtained from the canonical transformation description of the Poisson-Lie T-duality transformations for the gluing matrix which locally defines the properties of the $D$-brane, we find two different cases of the gluing matrices for the WZW model based on the Heisenberg Lie group $H_4$ and its dual model.
Poisson Lie symmetry and D-branes in WZW model on the Heisenberg Lie group H4
Directory of Open Access Journals (Sweden)
A. Eghbali
2015-10-01
Full Text Available We show that the WZW model on the Heisenberg Lie group H4 has Poisson–Lie symmetry only when the dual Lie group is A2⊕2A1. In this way, we construct the mutual T-dual sigma models on Drinfel'd double generated by the Heisenberg Lie group H4 and its dual pair, A2⊕2A1, as the target space in such a way that the original model is the same as the H4 WZW model. Furthermore, we show that the dual model is conformal up to two-loop order. Finally, we discuss D-branes and the worldsheet boundary conditions defined by a gluing matrix on the H4 WZW model. Using the duality map obtained from the canonical transformation description of the Poisson–Lie T-duality transformations for the gluing matrix which locally defines the properties of the D-brane, we find two different cases of the gluing matrices for the WZW model based on the Heisenberg Lie group H4 and its dual model.
Spin-Anisotropy Commensurable Chains Quantum Group Symmetries and N=2 SUSY
Berkovich, A; Sierra, G
1994-01-01
In this paper we consider a class of the 2D integrable models. These models are higher spin XXZ chains with an extra condition of the commensurability between spin and anisotropy. The mathematics underlying this commensurability is provided by the quantum groups with deformation parameter being an Nth root of unity. Our discussion covers a range of topics including new integrable deformations, thermodynamics, conformal behaviour, S-matrices and magnetization. The emerging picture strongly depends on the N-parity. For the N even case at the commensurable point, S-matrices factorize into N=2 supersymmetric Sine-Gordon matrix and an RSOS piece. The physics of the N odd case is rather different. Here, the supersymmetry does not manifest itself and the bootstrap hypothesis fails. Away from the commensurable point, we find an unusual behaviour. The magnetization of our chains depends on the sign of the external magnetic field.
Approximate and renormgroup symmetries
Energy Technology Data Exchange (ETDEWEB)
Ibragimov, Nail H. [Blekinge Institute of Technology, Karlskrona (Sweden). Dept. of Mathematics Science; Kovalev, Vladimir F. [Russian Academy of Sciences, Moscow (Russian Federation). Inst. of Mathematical Modeling
2009-07-01
''Approximate and Renormgroup Symmetries'' deals with approximate transformation groups, symmetries of integro-differential equations and renormgroup symmetries. It includes a concise and self-contained introduction to basic concepts and methods of Lie group analysis, and provides an easy-to-follow introduction to the theory of approximate transformation groups and symmetries of integro-differential equations. The book is designed for specialists in nonlinear physics - mathematicians and non-mathematicians - interested in methods of applied group analysis for investigating nonlinear problems in physical science and engineering. (orig.)
Symmetry and Condensed Matter Physics
El-Batanouny, M.; Wooten, F.
2008-03-01
Preface; 1. Symmetry and physics; 2. Symmetry and group theory; 3. Group representations: concepts; 4. Group representations: formalism and methodology; 5. Dixon's method for computing group characters; 6. Group action and symmetry projection operators; 7. Construction of the irreducible representations; 8. Product groups and product representations; 9. Induced representations; 10. Crystallographic symmetry and space-groups; 11. Space groups: Irreps; 12. Time-reversal symmetry: color groups and the Onsager relations; 13. Tensors and tensor fields; 14. Electronic properties of solids; 15. Dynamical properties of molecules, solids and surfaces; 16. Experimental measurements and selection rules; 17. Landau's theory of phase transitions; 18. Incommensurate systems and quasi-crystals; References; Bibliography; Index.
Wang, Fa; Zhai, Hui; Ran, Ying; Vishwanath, Ashvin; Lee, Dung-Hai
2009-01-30
We apply the fermion functional renormalization-group method to determine the pairing symmetry and pairing mechanism of the FeAs-Based materials. Within a five band model with pure repulsive interactions, we find an electronic-driven superconducting pairing instability. For the doping and interaction parameters we have examined, extended s wave, whose order parameter takes on opposite sign on the electron and hole pockets, is always the most favorable pairing symmetry. The pairing mechanism is the inter-Fermi-surface Josephson scattering generated by the antiferromagnetic correlation.
Christodoulides, Kyriakos
2014-07-01
We study single and coupled first-order differential equations (ODEs) that admit symmetries with tangent vector fields, which satisfy the N-dimensional Cauchy-Riemann equations. In the two-dimensional case, classes of first-order ODEs which are invariant under Möbius transformations are explored. In the N dimensional case we outline a symmetry analysis method for constructing exact solutions for conformal autonomous systems. A very important aspect of this work is that we propose to extend the traditional technical usage of Lie groups to one that could provide testable predictions and guidelines for model-building and model-validation. The Lie symmetries in this paper are constrained and classified by field theoretical considerations and their phenomenological implications. Our results indicate that conformal transformations are appropriate for elucidating a variety of linear and nonlinear systems which could be used for, or inspire, future applications. The presentation is pragmatic and it is addressed to a wide audience.
Readings of Platonic Virtue Theories from the Middle Ages to the Renaissance
DEFF Research Database (Denmark)
Catana, Leo
2014-01-01
It is commonly known that ancient schools of ethics were revived during the Renaissance: The texts pertaining to Platonic, Aristotelian, Stoic and Epicurean ethics were edited, translated and discussed in this period. It is less known that the Renaissance also witnessed a revival of Plotinian...... ethics, by then perceived as a legitimate form of Platonic ethics. Plotinus’ ethics had been transmitted through the Middle Ages through Macrobius’ Latin treatise In somnium Scipionis I.8, which relied heavily on Plotinus’ student, Porphyry, and his report of Plotinus’ ethics. In this article...... it is argued that the Florentine humanist and philosopher Marsilio Ficino carried on this tradition of Platonic, or rather Plotinian, ethics. He was familiar with Plotinus’ Enneads, since he had had access to it through Greek manuscripts from around 1462; his Latin translation of the Enneads was published...
Efficient methods for solving discrete topology design problems in the PLATO-N project
DEFF Research Database (Denmark)
Canh, Nam Nguyen; Stolpe, Mathias
This paper considers the general multiple load structural topology design problems in the framework of the PLATO-N project. The problems involve a large number of discrete design variables and were modeled as a non-convex mixed 0–1 program. For the class of problems considered, a global optimizat......This paper considers the general multiple load structural topology design problems in the framework of the PLATO-N project. The problems involve a large number of discrete design variables and were modeled as a non-convex mixed 0–1 program. For the class of problems considered, a global...
Johnson, Adam R.
2013-01-01
A molecular orbital (MO) diagram, especially its frontier orbitals, explains the bonding and reactivity for a chemical compound. It is therefore important for students to learn how to construct one. The traditional methods used to derive these diagrams rely on linear algebra techniques to combine ligand orbitals into symmetry-adapted linear…
Groner, Peter
2016-06-01
ERHAM has been used to analyze rotational spectra of many molecules with torsional splitting caused by one or two internal rotors. The gauche form of dimethyl ether-d1 whose equilibrium structure has C1 symmetry is an example of a molecule for which ERHAM could not model additional small splittings resolvable for many transitions, whereas the spectrum of the symmetric (anti, trans) form with a C{_s} equilibrium structure could be analyzed successfully with ERHAM. A more recent example where ERHAM failed is pinacolone CH_3-CO-C(CH_3)_3. In this case, the barriers to internal rotation of the methyl groups within the -C(CH_3)_3 unit are too high to produce observable internal rotation splittings, but the splittings due to the CH_3-CO methyl group could not be modeled correctly with ERHAM nor with any other available program (XIAM, BELGI-Cs, BELGI-C1, RAM36). In the paper, it was speculated that BELGI-Cs-2tops might be able to the job, but arguments against this possibility have also been put forward. The correlation between irreducible representations of groups and their subgroups according to Watson can be used not only to determine the total number of substates (components) to be expected but also to help decide which particular program has a chance for a successful analysis. As it turns out, the number of components of split lines depends on the molecular symmetry at equilibrium in relation to the highest possible symmetry for a given molecular symmetry group. Therefore, for pinacolone, the vibrational ground state is split into 10 torsional substates. P. Groner, J. Mol. Spectrosc. 278 (2012) 52-67. C. Richard et al. A&A 552 (2013), A117. Y. Zhao et al., J. Mol. Spectrosc. 318 (2015) 91-100, with references to all other programs mentioned in the abstract. J. K. G. Watson, Can. J. Physics 43 (1965) 1996-2007.
Nucci, M. C.
2016-09-01
We review some of our recent work devoted to the problem of quantization with preservation of Noether symmetries, finding hidden linearity in superintegrable systems, and showing that nonlocal symmetries are in fact local. In particular, we derive the Schrödinger equation for the isochronous Calogero goldfish model using its relation to Darwin equation. We prove the linearity of a classical superintegrable system on a plane of nonconstant curvature. We find the Lie point symmetries that correspond to the nonlocal symmetries (also reinterpreted as λ-symmetries) of the Riccati chain.
Nicolis, Alberto
2011-01-01
For relativistic quantum field theories, we consider Lorentz breaking, spatially homogeneous field configurations or states that evolve in time along a symmetry direction. We dub this situation "spontaneous symmetry probing" (SSP). We mainly focus on internal symmetries, i.e. on symmetries that commute with the Poincare group. We prove that the fluctuations around SSP states have a Lagrangian that is explicitly time independent, and we provide the field space parameterization that makes this manifest. We show that there is always a gapless Goldstone excitation that perturbs the system in the direction of motion in field space. Perhaps more interestingly, we show that if such a direction is part of a non-Abelian group of symmetries, the Goldstone bosons associated with spontaneously broken generators that do not commute with the SSP one acquire a gap, proportional to the SSP state's "speed". We outline possible applications of this formalism to inflationary cosmology.
Loebbert, Florian
2016-01-01
In these introductory lectures we discuss the topic of Yangian symmetry from various perspectives. Forming the classical counterpart of the Yangian and an extension of ordinary Noether symmetries, first the concept of nonlocal charges in classical, two-dimensional field theory is reviewed. We then define the Yangian algebra following Drinfeld's original motivation to construct solutions to the quantum Yang-Baxter equation. Different realizations of the Yangian and its mathematical role as a Hopf algebra and quantum group are discussed. We demonstrate how the Yangian algebra is implemented in quantum, two-dimensional field theories and how its generators are renormalized. Implications of Yangian symmetry on the two-dimensional scattering matrix are investigated. We furthermore consider the important case of discrete Yangian symmetry realized on integrable spin chains. Finally we give a brief introduction to Yangian symmetry in planar, four-dimensional super Yang-Mills theory and indicate its impact on the dila...
Energy Technology Data Exchange (ETDEWEB)
Blum, Alexander Simon
2009-06-10
This thesis deals with the possibility of describing the flavor sector of the Standard Model of Particle Physics (with neutrino masses), that is the fermion masses and mixing matrices, with a discrete, non-abelian flavor symmetry. In particular, mass independent textures are considered, where one or several of the mixing angles are determined by group theory alone and are independent of the fermion masses. To this end a systematic analysis of a large class of discrete symmetries, the dihedral groups, is analyzed. Mass independent textures originating from such symmetries are described and it is shown that such structures arise naturally from the minimization of scalar potentials, where the scalars are gauge singlet flavons transforming non-trivially only under the flavor group. Two models are constructed from this input, one describing leptons, based on the group D{sub 4}, the other describing quarks and employing the symmetry D{sub 14}. In the latter model it is the quark mixing matrix element V{sub ud} - basically the Cabibbo angle - which is at leading order predicted from group theory. Finally, discrete flavor groups are discussed as subgroups of a continuous gauge symmetry and it is shown that this implies that the original gauge symmetry is broken by fairly large representations. (orig.)
Nomoto, Takuya; Ikeda, Hiroaki
2017-02-01
We present the group-theoretical classification of gap functions in superconductors coexisting with some magnetic order in non-symmorphic magnetic space groups. On the basis of the weak-coupling BCS theory, we show that UCoGe-type ferromagnetic superconductors must have horizontal line nodes on either the kz = 0 or ±π/c plane. Moreover, it is likely that additional Weyl point nodes exist at the axial point. On the other hand, in UPd2Al3-type antiferromagnetic superconductors, gap functions with Ag symmetry possess horizontal line nodes in the antiferromagnetic Brillouin zone boundary perpendicular to the c-axis. In other words, the conventional fully gapped s-wave superconductivity is forbidden in this type of antiferromagnetic superconductor, regardless of the pairing mechanism, as long as the Fermi surface crosses a zone boundary. UCoGe and UPd2Al3 are candidate unconventional superconductors possessing hidden symmetry-protected line nodes, peculiar to non-symmorphic magnetic space groups.
Energy Technology Data Exchange (ETDEWEB)
Secher, Bernard [French Atomic Energy Commission (CEA), Nuclear Energy Division (DEN) (France); CEA Saclay DM2S/SFME/LGLS, Bat. 454, F-91191 Gif-sur-Yvette Cedex (France)], E-mail: bsecher@cea.fr; Belliard, Michel [French Atomic Energy Commission (CEA), Nuclear Energy Division (DEN) (France); CEA Cadarache DER/SSTH/LMDL, Bat. 238, F-13108 Saint-Paul-lez-Durance Cedex (France); Calvin, Christophe [French Atomic Energy Commission (CEA), Nuclear Energy Division (DEN) (France); CEA Saclay DM2S/SERMA/LLPR, Bat. 470, F-91191 Gif-sur-Yvette Cedex (France)
2009-01-15
This paper describes a tool called 'Numerical Platon' developed by the French Atomic Energy Commission (CEA). It provides a freely available (GNU LGPL license) interface for coupling scientific computing applications to various freeware linear solver libraries (essentially PETSc, SuperLU and HyPre), together with some proprietary CEA solvers, for high-performance computers that may be used in industrial software written in various programming languages. This tool was developed as part of considerable efforts by the CEA Nuclear Energy Division in the past years to promote massively parallel software and on-shelf parallel tools to help develop new generation simulation codes. After the presentation of the package architecture and the available algorithms, we show examples of how Numerical Platon is used in sequential and parallel CEA codes. Comparing with in-house solvers, the gain in terms of increases in computation capacities or in terms of parallel performances is notable, without considerable extra development cost.
Platonic topology and CMB fluctuations: Homotopy, anisotropy, and multipole selection rules
Kramer, Peter
2009-01-01
The Cosmic Microwave Background CMB originates from an early stage in the history of the universe. Observed low multipole contributions of CMB fluctuations have motivated the search for selection rules from the underlying topology of 3-space. Everitt (2004) has generated all homotopies for Platonic spherical 3-manifolds by face gluings. We transform the glue generators into isomorphic deck transformations. The deck transformations act on a spherical Platonic 3-manifold as prototile and tile the 3-sphere by its images. A complete set of orthonormal functions on the 3-sphere is spanned by the Wigner harmonic polynomials. For a tetrahedral, two cubic and three octahedral manifolds we construct algebraically linear combinations of Wigner polynomials, invariant under deck transformations and with domain the manifold. We prove boundary conditions on polyhedral faces from homotopy. By algebraic means we pass to a multipole expansion. Assuming random models of the CMB radiation, we derive multipole selection rules, d...
Heuristics of the Platonic Polyhedra for the high Restrictions Reality Research
Directory of Open Access Journals (Sweden)
José Ricardo Díaz Caballero
2013-02-01
Full Text Available In the present work, are exposed concepts, principles and procedures that make up a theory for theheuristical geometrical interpretation of high restrictions reality, based on a thesis where the PlatonicPolyhedra are carriers of a content with a high heuristic potential for the theoretical interpretation ofreality, particularly the high restriction systems , for example the Periodic Table of Chemical Elements,the System of Notes and Tempered Musical Scales and the Universal Genetic Code.
Lovelady, Benjamin C
2015-01-01
According to the Coleman-Mandula theorem, any gauge theory of gravity combined with an internal symmetry based on a Lie group must take the form of a direct product in order to be consistent with basic assumptions of quantum field theory. However, we show that an alternative gauging of a simple group can lead dynamically to a spacetime with compact internal symmetry. The biconformal gauging of the conformal symmetry of n-dim Euclidean space doubles the dimension to give a symplectic manifold. Examining one of the Lagrangian submanifolds in the flat case, we find that in addition to the expected SO(n) connection and curvature, the solder form necessarily becomes Lorentzian. General coordinate invariance gives rise to an SO(n-1,1) connection on the spacetime. The principal fiber bundle character of the original SO(n) guarantees that the two symmetries enter as a direct product, in agreement with the Coleman-Mandula theorem.
Lovelady, Benjamin C.; Wheeler, James T.
2016-04-01
According to the Coleman-Mandula theorem, any gauge theory of gravity combined with an internal symmetry based on a Lie group must take the form of a direct product in order to be consistent with basic assumptions of quantum field theory. However, we show that an alternative gauging of a simple group can lead dynamically to a spacetime with compact internal symmetry. The biconformal gauging of the conformal symmetry of n-dimensional Euclidean space doubles the dimension to give a symplectic manifold. Examining one of the Lagrangian submanifolds in the flat case, we find that in addition to the expected S O (n ) connection and curvature, the solder form necessarily becomes Lorentzian. General coordinate invariance gives rise to an S O (n -1 ,1 ) connection on the spacetime. The principal fiber bundle character of the original S O (n ) guarantees that the two symmetries enter as a direct product, in agreement with the Coleman-Mandula theorem.
'Parabolic' trapped modes and steered Dirac cones in platonic crystals.
McPhedran, R C; Movchan, A B; Movchan, N V; Brun, M; Smith, M J A
2015-05-08
This paper discusses the properties of flexural waves governed by the biharmonic operator, and propagating in a thin plate pinned at doubly periodic sets of points. The emphases are on the design of dispersion surfaces having the Dirac cone topology, and on the related topic of trapped modes in plates for a finite set (cluster) of pinned points. The Dirac cone topologies we exhibit have at least two cones touching at a point in the reciprocal lattice, augmented by another band passing through the point. We show that these Dirac cones can be steered along symmetry lines in the Brillouin zone by varying the aspect ratio of rectangular lattices of pins, and that, as the cones are moved, the involved band surfaces tilt. We link Dirac points with a parabolic profile in their neighbourhood, and the characteristic of this parabolic profile decides the direction of propagation of the trapped mode in finite clusters.
Skala, L.; Jungwirth, P.
1989-10-01
A group symmetry analysis of the Pauli master equation for the excitation energy transfer in the cyclic arrangement of N ( N= 6- 36) antenna Bchl molecules surrounding the bacterial reaction center of Rhodopseudomonas viridis is performed. The group theory allows to find analytic expressions for the most important observables (the antenna and reaction center fluorescence intensities and the quantum yield of the transfer to the charge transfer state) and to express their dependence on N. The time dependence of the fluorescence intensities is given by two exponentials, however, a single-exponential approximation can be used for t> t0 = 4-25 ps. The quantum yield of the excitation energy transfer to the reaction center charge transfer state is high (0.71- 0.98) for the whole range of physically acceptable values of the Förster radius R0 = 46-96 Å.
Voisin, Claire
1999-01-01
This is the English translation of Professor Voisin's book reflecting the discovery of the mirror symmetry phenomenon. The first chapter is devoted to the geometry of Calabi-Yau manifolds, and the second describes, as motivation, the ideas from quantum field theory that led to the discovery of mirror symmetry. The other chapters deal with more specialized aspects of the subject: the work of Candelas, de la Ossa, Greene, and Parkes, based on the fact that under the mirror symmetry hypothesis, the variation of Hodge structure of a Calabi-Yau threefold determines the Gromov-Witten invariants of its mirror; Batyrev's construction, which exhibits the mirror symmetry phenomenon between hypersurfaces of toric Fano varieties, after a combinatorial classification of the latter; the mathematical construction of the Gromov-Witten potential, and the proof of its crucial property (that it satisfies the WDVV equation), which makes it possible to construct a flat connection underlying a variation of Hodge structure in the ...
Häring, Reto Andreas
1993-01-01
The representations of the observable algebra of a low dimensional quantum field theory form the objects of a braided tensor category. The search for gauge symmetry in the theory amounts to finding an algebra which has the same representation category. In this paper we try to establish that every quantum field theory satisfying some basic axioms posseses a weak quasi Hopf algebra as gauge symmetry. The first step is to construct a functor from the representation category to the category of finite dimensional vector spaces. Given such a functor we can use a generalized reconstruction theorem to find the symmetry algebra. It is shown how this symmetry algebra is used to build a gauge covariant field algebra and we investigate the question why this generality is necessary.
Symmetry rules How science and nature are founded on symmetry
Rosen, Joe
2008-01-01
When we use science to describe and understand the world around us, we are in essence grasping nature through symmetry. In fact, modern theoretical physics suggests that symmetry is a, if not the, foundational principle of nature. Emphasizing the concepts, this book leads the reader coherently and comprehensively into the fertile field of symmetry and its applications. Among the most important applications considered are the fundamental forces of nature and the Universe. It is shown that the Universe cannot possess exact symmetry, which is a principle of fundamental significance. Curie's principle - which states that the symmetry of the effect is at least that of the cause - features prominently. An introduction to group theory, the mathematical language of symmetry, is included. This book will convince all interested readers of the importance of symmetry in science. Furthermore, it will serve as valuable background reading for all students in the physical sciences.
Notes on generalized global symmetries in QFT
Sharpe, E
2015-01-01
It was recently argued that quantum field theories possess one-form and higher-form symmetries, labelled `generalized global symmetries.' In this paper, we describe how those higher-form symmetries can be understood mathematically as special cases of more general 2-groups and higher groups, and discuss examples of quantum field theories admitting actions of more general higher groups than merely one-form and higher-form symmetries. We discuss analogues of topological defects for some of these higher symmetry groups, relating some of them to ordinary topological defects. We also discuss topological defects in cases in which the moduli `space' (technically, a stack) admits an action of a higher symmetry group. Finally, we outline a proposal for how certain anomalies might potentially be understood as describing a transmutation of an ordinary group symmetry of the classical theory into a 2-group or higher group symmetry of the quantum theory, which we link to WZW models and bosonization.
Symmetry fractionalization and twist defects
Tarantino, Nicolas; Lindner, Netanel H.; Fidkowski, Lukasz
2016-03-01
Topological order in two-dimensions can be described in terms of deconfined quasiparticle excitations—anyons—and their braiding statistics. However, it has recently been realized that this data does not completely describe the situation in the presence of an unbroken global symmetry. In this case, there can be multiple distinct quantum phases with the same anyons and statistics, but with different patterns of symmetry fractionalization—termed symmetry enriched topological order. When the global symmetry group G, which we take to be discrete, does not change topological superselection sectors—i.e. does not change one type of anyon into a different type of anyon—one can imagine a local version of the action of G around each anyon. This leads to projective representations and a group cohomology description of symmetry fractionalization, with the second cohomology group {H}2(G,{{ A }}{{abelian}}) being the relevant group. In this paper, we treat the general case of a symmetry group G possibly permuting anyon types. We show that despite the lack of a local action of G, one can still make sense of a so-called twisted group cohomology description of symmetry fractionalization, and show how this data is encoded in the associativity of fusion rules of the extrinsic ‘twist’ defects of the symmetry. Furthermore, building on work of Hermele (2014 Phys. Rev. B 90 184418), we construct a wide class of exactly-solvable models which exhibit this twisted symmetry fractionalization, and connect them to our formal framework.
Mir-Kasimov, R. M.
1997-03-01
The Quantum Field Theory (QFT) is considered in which momenta belong to the space of constant nonzero curvature. The conjugated configurational space is quantized space. It is connected with the momentum space by the Fourier expansion in matrix elements of the group of motions of this space. The generators of the translations in the configurational space are differential - difference operators and can be considered as the generators of the q- deformations of the Poincaré group. The deformed character of the translations leads to radical modification of the singularities of the field - theoretical functions. As a result, the S - matrix elements do not contain the non-integrable expressions.
Givental graphs and inversion symmetry
Dunin-Barkowski, P; Spitz, L
2012-01-01
Inversion symmetry is a very non-trivial discrete symmetry of Frobenius manifolds. It was obtained by Dubrovin from one of the elementary Schlesinger transformations of a special ODE associated to Frobenius manifold. In this paper, we review the Givental group action on Frobenius manifolds in terms of Feynman graphs and then we obtain an interpretation of the inversion symmetry in terms of the action of the Givental group. We also consider the implication of this interpretation of the inversion symmetry for the Schlesinger transformations and for the Hamiltonians of the associated principle hierarchy.
Directory of Open Access Journals (Sweden)
Sonja Weiss
2009-07-01
Full Text Available The article presents the leading Platonic doctrines of the embodied soul, examining the relation between their Orphic and Pythagorean roots and Plotinus’ correction of the Neo-Pythagorean pessimism on the one hand, and Gnostic solutions of the problem on the other. The analysis of certain Gnostic passages clearly shows that, in spite of Plotinus’ anti-Gnostic polemic, some of the ideas proposed by the philosopher as an alternative to his opponents’ pessimism are also present in the Gnostic descriptions of the emanation from the first Principle and the multiplication of the Eons. The article focuses on the passages which, avoiding an ethical valuation of the generation and multiplication process, limit the concept of sin to the human domain, where it belongs in Plotinus’ view as well. Moreover, the article endeavours to throw light on some of the most controversial themes, which were to remain irreconcilable despite a number of tenets shared by both sides.
2+1-Gravity and The Embedding its Dynamical Symmetry and Para-Supersymmetry into SO(4,c) Group
Jafarizadeh, M A; Moayedi, S K
1999-01-01
Some special solutions of the Einstein-Maxwell action with a non-negative cosmological constant and a very heavy point mass particle have been obtained. The solutions correspond to static spacetime of locally constant curvature in its spatial part and a constant magnetic field of a magnetic monopole together with deficit of angle at the location of point mass. The quantum mechanics of a point particle in these spacetimes in the absence of angular deficit has been solved algebraically both relativistically and non-relativistically. It has been also shown that these 2-dimensional Hamiltonians have the degeneracy group of GL(2,c) type and para-supersymmetry of arbitrary order or shape invariance, which is originated from a SO(4,c) group.
Horizontal Symmetry: Bottom Up and Top Down
Lam, C S
2011-01-01
A group-theoretical connection between horizontal symmetry $\\G$ and fermion mixing is established, and applied to neutrino mixing. The group-theoretical approach is consistent with a dynamical theory based on $U(1)\\times \\G$, but the dynamical theory can be used to pick out the most stable mixing that purely group-theoretical considerations cannot. A symmetry common to leptons and quarks is also discussed. This higher symmetry picks $A_4$ over $S_4$ to be the preferred symmetry for leptons.
El Triangulo de Platon y El Factor Gnomonico: Una aplicacion a los oraculos de Herodoto
Perez-Enriquez, Raul
2013-01-01
A modification to the gnomonic factor using the concept of triangle of Plato is presented. With the aid of the platonic gnomonic factor (fgp) as we called it, we find that the oracles mentioned by Herodotus in his History, Dodona in Greece and Ammon in Oasis Siwa, Libya, were placed there because the noon shadow of Sun of a gnomon formed, back in 2500BC, the triangle of Plato the former, and the Egyptian sacred triangle the latter. This means that both concepts were known by Egyptians form Th...
Attanucci, Frank J.; Losse, John
2008-01-01
In a first calculus course, it is not unusual for students to encounter the theorems which state: If f is an even (odd) differentiable function, then its derivative is odd (even). In our paper, we prove some theorems which show how the symmetry of a continuous function f with respect to (i) the vertical line: x = a or (ii) with respect to the…
SYMMETRY IN WORLD TRADE NETWORK
Institute of Scientific and Technical Information of China (English)
Hui WANG; Guangle YAN; Yanghua XIAO
2009-01-01
Symmetry of the world trade network provides a novel perspective to understand the world-wide trading system. However, symmetry in the world trade network (WTN) has been rarely studied so far. In this paper, the authors systematically explore the symmetry in WTN. The authors construct WTN in 2005 and explore the size and structure of its automorphism group, through which the authors find that WTN is symmetric, particularly, locally symmetric to a certain degree. Furthermore, the authors work out the symmetric motifs of WTN and investigate the structure and function of the symmetric motifs, coming to the conclusion that local symmetry will have great effect on the stability of the WTN and that continuous symmetry-breakings will generate complexity and diversity of the trade network. Finally, utilizing the local symmetry of the network, the authors work out the quotient of WTN, which is the structural skeleton dominating stability and evolution of WTN.
Symmetry of crystals and molecules
Ladd, Mark
2014-01-01
This book successfully combines a thorough treatment of molecular and crystalline symmetry with a simple and informal writing style. By means of familiar examples the author helps to provide the reader with those conceptual tools necessary for the development of a clear understanding of what are often regarded as 'difficult' topics. Christopher Hammond, University of Leeds This book should tell you everything you need to know about crystal and molecular symmetry. Ladd adopts an integrated approach so that the relationships between crystal symmetry, molecular symmetry and features of chemical interest are maintained and reinforced. The theoretical aspects of bonding and symmetry are also well represented, as are symmetry-dependent physical properties and the applications of group theory. The comprehensive coverage will make this book a valuable resource for a broad range of readers.
Legré, J.-P.; Albinet, G.; Firpo, J.-L.; Tremblay, A.-M. S.
1984-11-01
This paper is concerned with the liquid-expanded (LE) -liquid-condensed (LC) transition in monolayers of amphiphilic molecules at the air-water interface. A model, which can be mapped into the Blume-Emery-Griffiths Hamiltonian, has been considered before within the (mean-field) Bragg-Williams approximation and it gave results which could be successfully compared with experiment. The LE-LC transition has been associated with a chiral-symmetry breaking of the hydrocarbon-chain defects. This model is treated here with a Migdal-Kadanoff approximate position-space renormalization group. Renormalization-group flows are consistent with those obtained by previous authors. The connection between experimental and Hamiltonian parameters is easiest for a particular choice of ensemble, which turns out to be rather subtle for this problem. As in the work of Lavis, Southern, and Bell, isotherms in the surface-pressure-molecular-area plane do not show a signature of the LE-LC transition. The better agreement between experiments (showing a compressibility jump at the LE-LC transition) and mean-field theory suggests that in these cases long-range forces depending on the nature of the polar head and on the water substrate pH are responsible for the jump.
Quantum entanglement and symmetry
Energy Technology Data Exchange (ETDEWEB)
Chruscinski, D; Kossakowski, A [Institute of Physics, Nicolaus Copernicus University, Grudziadzka 5/7, 87-100 Torun (Poland)
2007-11-15
One of the main problem in Quantum Information Theory is to test whether a given state of a composite quantum system is entangled or separable. It turns out that within a class of states invariant under the action of the symmetry group this problem considerably simplifies. We analyze multipartite invariant states and the corresponding symmetric quantum channels.
Quantum entanglement and symmetry
Chruściński, D.; Kossakowski, A.
2007-11-01
One of the main problem in Quantum Information Theory is to test whether a given state of a composite quantum system is entangled or separable. It turns out that within a class of states invariant under the action of the symmetry group this problem considerably simplifies. We analyze multipartite invariant states and the corresponding symmetric quantum channels.
El Triangulo de Platon y El Factor Gnomonico: Una aplicacion a los oraculos de Herodoto
Perez-Enriquez, Raul
2013-01-01
A modification to the gnomonic factor using the concept of triangle of Plato is presented. With the aid of the platonic gnomonic factor (fgp) as we called it, we find that the oracles mentioned by Herodotus in his History, Dodona in Greece and Ammon in Oasis Siwa, Libya, were placed there because the noon shadow of Sun of a gnomon formed, back in 2500BC, the triangle of Plato the former, and the Egyptian sacred triangle the latter. This means that both concepts were known by Egyptians form Thebes long before they were formalized by the Greeks. The right angled triangle concept is an idealization, as said by D. Magdolen, of an astronomical observation; i. e. it is the shadow cast by a gnomon. ----- Se presenta una modificacion al factor gnomonico usando el concepto de triangulo de Platon. Con la ayuda de lo que llamamos factor gnomonico platonico (fgp) nosotros encontramos que los oraculos mencionados por Herodoto en su Historia, Dodona en Grecia, y Ammon en el Oasis Siwa, Libia, fueron ubicados ahi porque, ha...
Khudaverdian, H M
2016-01-01
We notice that one of the Diophantine equations, $knm=2kn+2km+2nm$, arising in the universality originated Diophantine classification of simple Lie algebras, has interesting interpretations for two different sets of signs of variables. In both cases it describes "regular polyhedrons" with $k$ edges in each vertex, $n$ edges of each face, with total number of edges $|m|$, and Euler characteristics $\\chi=\\pm 2$. In the case of negative $m$ this equation corresponds to $\\chi=2$ and describes true regular polyhedrons, Platonic solids. The case with positive $m$ corresponds to Euler characteristic $\\chi=-2$ and describes the so called equivelar maps (charts) on the surface of genus $2$. In the former case there are two routes from Platonic solids to simple Lie algebras - abovementioned Diophantine classification and McKay correspondence. We compare them for all solutions of this type, and find coincidence in the case of icosahedron (dodecahedron), corresponding to $E_8$ algebra. In the case of positive $k$, $n$ an...
Labudde, D; Leitner, D; Krüger, M; Oschkinat, H
2003-01-01
The algorithm PLATON is able to assign sets of chemical shifts derived from a single residue to amino acid types with its secondary structure (amino acid species). A subsequent ranking procedure using optionally two different penalty functions yields predictions for possible amino acid species for the given set of chemical shifts. This was demonstrated in the case of the alpha-spectrin SH3 domain and applied to 9 further protein data sets taken from the BioMagRes database. A database consisting of reference chemical shift patterns (reference CSPs) was generated from assigned chemical shifts of proteins with known 3D-structure. This reference CSP database is used in our approach for extracting distributions of amino acid types with their most likely secondary structure elements (namely alpha-helix, beta-sheet, and coil) for single amino acids by comparison with query CSPs. Results obtained for the 10 investigated proteins indicates that the percentage of correct amino acid species in the first three positions in the ranking list, ranges from 71.4% to 93.2% for the more favorable penalty function. Where only the top result of the ranking list for these 10 proteins is considered, 36.5% to 83.1% of the amino acid species are correctly predicted. The main advantage of our approach, over other methods that rely on average chemical shift values is the ability to increase database content by incorporating newly derived CSPs, and therefore to improve PLATON's performance over time.
Flavour from accidental symmetries
Energy Technology Data Exchange (ETDEWEB)
Ferretti, Luca [SISSA/ISAS and INFN, I-34013 Trieste (Italy); King, Stephen F. [School of Physics and Astronomy, University of Southampton, Southampton, SO17 1BJ (United Kingdom); Romanino, Andrea [SISSA/ISAS and INFN, I-34013 Trieste (Italy)
2006-11-15
We consider a new approach to fermion masses and mixings in which no special 'horizontal' dynamics is invoked to account for the hierarchical pattern of charged fermion masses and for the peculiar features of neutrino masses. The hierarchy follows from the vertical, family-independent structure of the model, in particular from the breaking pattern of the Pati-Salam group. The lightness of the first two fermion families can be related to two family symmetries emerging in this context as accidental symmetries.
Arzano, Michele; Kowalski-Glikman, Jerzy
2016-09-01
We construct discrete symmetry transformations for deformed relativistic kinematics based on group valued momenta. We focus on the specific example of κ-deformations of the Poincaré algebra with associated momenta living on (a sub-manifold of) de Sitter space. Our approach relies on the description of quantum states constructed from deformed kinematics and the observable charges associated with them. The results we present provide the first step towards the analysis of experimental bounds on the deformation parameter κ to be derived via precision measurements of discrete symmetries and CPT.
Directory of Open Access Journals (Sweden)
Kirstin Peters
2010-11-01
Full Text Available A well-known result by Palamidessi tells us that πmix (the π-calculus with mixed choice is more expressive than πsep (its subset with only separate choice. The proof of this result argues with their different expressive power concerning leader election in symmetric networks. Later on, Gorla offered an arguably simpler proof that, instead of leader election in symmetric networks, employed the reducibility of incestual processes (mixed choices that include both enabled senders and receivers for the same channel when running two copies in parallel. In both proofs, the role of breaking (initial symmetries is more or less apparent. In this paper, we shed more light on this role by re-proving the above result - based on a proper formalization of what it means to break symmetries without referring to another layer of the distinguishing problem domain of leader election. Both Palamidessi and Gorla rephrased their results by stating that there is no uniform and reasonable encoding from πmix into πsep. We indicate how the respective proofs can be adapted and exhibit the consequences of varying notions of uniformity and reasonableness. In each case, the ability to break initial symmetries turns out to be essential.
Loebbert, Florian
2016-08-01
In these introductory lectures we discuss the topic of Yangian symmetry from various perspectives. Forming the classical counterpart of the Yangian and an extension of ordinary Noether symmetries, first the concept of nonlocal charges in classical, two-dimensional field theory is reviewed. We then define the Yangian algebra following Drinfel’d's original motivation to construct solutions to the quantum Yang-Baxter equation. Different realizations of the Yangian and its mathematical role as a Hopf algebra and quantum group are discussed. We demonstrate how the Yangian algebra is implemented in quantum, two-dimensional field theories and how its generators are renormalized. Implications of Yangian symmetry on the two-dimensional scattering matrix are investigated. We furthermore consider the important case of discrete Yangian symmetry realized on integrable spin chains. Finally we give a brief introduction to Yangian symmetry in planar, four-dimensional super Yang-Mills theory and indicate its impact on the dilatation operator and tree-level scattering amplitudes. These lectures are illustrated by several examples, in particular the two-dimensional chiral Gross-Neveu model, the Heisenberg spin chain and { N }=4 superconformal Yang-Mills theory in four dimensions.
Weiss, Asia; Whiteley, Walter
2014-01-01
This book contains recent contributions to the fields of rigidity and symmetry with two primary focuses: to present the mathematically rigorous treatment of rigidity of structures, and to explore the interaction of geometry, algebra, and combinatorics. Overall, the book shows how researchers from diverse backgrounds explore connections among the various discrete structures with symmetry as the unifying theme. Contributions present recent trends and advances in discrete geometry, particularly in the theory of polytopes. The rapid development of abstract polytope theory has resulted in a rich theory featuring an attractive interplay of methods and tools from discrete geometry, group theory, classical geometry, hyperbolic geometry and topology. The volume will also be a valuable source as an introduction to the ideas of both combinatorial and geometric rigidity theory and its applications, incorporating the surprising impact of symmetry. It will appeal to students at both the advanced undergraduate and gradu...
Binary Tetrahedral Flavor Symmetry
Eby, David A
2013-01-01
A study of the T' Model and its variants utilizing Binary Tetrahedral Flavor Symmetry. We begin with a description of the historical context and motivations for this theory, together with some conceptual background for added clarity, and an account of our theory's inception in previous works. Our model endeavors to bridge two categories of particles, leptons and quarks, a unification made possible by the inclusion of additional Higgs particles, shared between the two fermion sectors and creating a single coherent system. This is achieved through the use of the Binary Tetrahedral symmetry group and an investigation of the Tribimaximal symmetry evidenced by neutrinos. Our work details perturbations and extensions of this T' Model as we apply our framework to neutrino mixing, quark mixing, unification, and dark matter. Where possible, we evaluate model predictions against experimental results and find excellent matching with the atmospheric and reactor neutrino mixing angles, an accurate prediction of the Cabibb...
Symmetries of Ginsparg-Wilson Chiral Fermions
Mandula, Jeffrey E
2009-01-01
The group structure of the variant chiral symmetry discovered by Luscher in the Ginsparg-Wilson description of lattice chiral fermions is analyzed. It is shown that the group contains an infinite number of linearly independent symmetry generators, and the Lie algebra is given explicitly. CP is an automorphism of this extended chiral group, and the CP transformation properties of the symmetry generators are found. The group has an infinite-parameter subgroup, and the factor group whose elements are its cosets is isomorphic to the continuum chiral symmetry group. Features of the currents associated with these symmetries are discussed, including the fact that some different, non-commuting symmetry generators lead to the same Noether current. These are universal features of lattice chiral fermions based on the Ginsparg-Wilson relation; they occur in the overlap, domain-wall, and perfect-action formulations. In a solvable example - free overlap fermions - these non-canonical elements of lattice chiral symmetry are...
Institute of Scientific and Technical Information of China (English)
刘官厅; 范天佑
2003-01-01
The complex method of the plane elasticity in 2D quasicrystal with point group 10 mm tenfold rotational symmetry is established. First displacement potential function in the quasicrystal is represented by four analytic functions. Then by utilizing the properties of analytic function and through a great deal of derivation, the complex representations of stresses and displacements components of phonon fields and phason fields in the quasicrystal are given, which are the theoretical foundation for this method. From this theory, and by the help of conformal transformations in the theory of complex function, the problems of elliptic hole in the quasicrystal are solved. Its special cases are the solutions of well-known crack problem. Meanwhile, the results show that even if under the self-counterbalance force in the quasicrystal plane with elliptic hole, the stress components of phonon fields are also related to material constants of the quasicrystal when the phonon fields and phason fields are coupled, which is another distinctive difference from the properties of classical elastic theory. Besides, the present work is generalization and application of the complex method in the classical elastic theory established by Muskhelishvili to 2D quasicrystal. As in the classical elastic theory, if only conformal transformation from the quasicrystal plane to unit circle is found, any holey and crack problem in the quasicrystal plane could be solved.
Mei Symmetry and Noether Symmetry of the Relativistic Variable Mass System
Institute of Scientific and Technical Information of China (English)
FANG Jian-Hui
2004-01-01
The definition and criterion of the Mei symmetry of a relativistic variable mass system are given. The relation between the Mei symmetry and the Noether symmetry of the system is found under infinitesimal transformations of groups. The conserved quantities to which the Mei symmetry and Noether symmetry of the system lead are obtained.An example is given to illustrate the application of the result.
Discrete symmetries in the MSSM
Energy Technology Data Exchange (ETDEWEB)
Schieren, Roland
2010-12-02
The use of discrete symmetries, especially abelian ones, in physics beyond the standard model of particle physics is discussed. A method is developed how a general, abelian, discrete symmetry can be obtained via spontaneous symmetry breaking. In addition, anomalies are treated in the path integral approach with special attention to anomaly cancellation via the Green-Schwarz mechanism. All this is applied to the minimal supersymmetric standard model. A unique Z{sup R}{sub 4} symmetry is discovered which solves the {mu}-problem as well as problems with proton decay and allows to embed the standard model gauge group into a simple group, i.e. the Z{sup R}{sub 4} is compatible with grand unification. Also the flavor problem in the context of minimal flavor violation is addressed. Finally, a string theory model is presented which exhibits the mentioned Z{sup R}{sub 4} symmetry and other desirable features. (orig.)
Painlevé property, symmetries and symmetry reductions of the coupled Burgers system
Institute of Scientific and Technical Information of China (English)
Lian Zeng-Ju; Chen Li-Li; Lou Sen-Yue
2005-01-01
The Painlevé property, inverse recursion operator, infinite number of symmetries and Lie symmetry reductions of the coupled Burgers equation are given explicitly. Three sets of infinitely many symmetries of the considered model are obtained by acting the recursion operator and the inverse recursion operator on the trivial symmetries such as the identity transformation, the space translation and the scaling transformation respectively. These symmetries constitute an infinite dimensional Lie algebra while its finite dimensional Lie point symmetry subalgebra is used to find possible symmetry reductions and then the group invariant solutions.
Non-Crystallographic Symmetry in Packing Spaces
Directory of Open Access Journals (Sweden)
Valery G. Rau
2013-01-01
Full Text Available In the following, isomorphism of an arbitrary finite group of symmetry, non-crystallographic symmetry (quaternion groups, Pauli matrices groups, and other abstract subgroups, in addition to the permutation group, are considered. Application of finite groups of permutations to the packing space determines space tilings by policubes (polyominoes and forms a structure. Such an approach establishes the computer design of abstract groups of symmetry. Every finite discrete model of the real structure is an element of symmetry groups, including non-crystallographic ones. The set packing spaces of the same order N characterizes discrete deformation transformations of the structure.
Symmetry and quantum mechanics
Corry, Scott
2016-01-01
This book offers an introduction to quantum mechanics for professionals, students, and others in the field of mathematics who have a minimal background in physics with an understanding of linear algebra and group theory. It covers such topics as Lie groups, algebras and their representations, and analysis (Hilbert space, distributions, the spectral Theorem, and the Stone-Von Neumann Theorem). The book emphasizes the role of symmetry and is useful to physicists as it provides a mathematical introduction to the topic.
Symmetry Non-restoration at High Temperature
Rius, N
1998-01-01
We discuss the (non)-restoration of global and local symmetries at high temperature. First, we analyze a two-scalar model with $Z_2 \\times Z_2$ symmetry using the exact renormalization group. We conclude that inverse symmetry breaking is possible in this kind of models within the perturbative regime. Regarding local symmetries, we consider the $SU(2) \\otimes U(1)$ gauge symmetry and focus on the case of a strongly interacting scalar sector. Employing a model-independent chiral Lagrangian we find indications of symmetry restoration.
Westphal, Eduard; Gallardo, Hugo; Caramori, Giovanni Finoto; Sebastián, Nerea; Tamba, Maria-Gabriela; Eremin, Alexey; Kawauchi, Susumu; Prehm, Marko; Tschierske, Carsten
2016-06-01
Two isomeric achiral bent-core liquid crystals involving a 4-cyanoresorcinol core and containing a carbosilane unit as nanosegregating segment were synthesized and were shown to form ferroelectric liquid-crystalline phases. Inversion of the direction of one of the COO groups in these molecules leads to a distinct distribution of the electrostatic potential along the surface of the molecule and to a strong change of the molecular dipole moments. Thus, a distinct degree of segregation of the carbosilane units and consequent modification of the phase structure and coherence length of polar order result. For the compound with larger dipole moment (CN1) segregation of the carbosilane units is suppressed, and this compound forms paraelectric SmA and SmC phases; polar order is only achieved after transition to a new LC phase, namely, the ferroelectric leaning phase (SmCLs PS ) with the unique feature that tilt direction and polar direction coincide. The isomeric compound CN2 with a smaller dipole moment forms separate layers of the carbosilane groups and shows a randomized polar SmA phase (SmAPAR ) and ferroelectric polydomain SmCs PS phases with orthogonal combination of tilt and polar direction and much higher polarizations. Thus, surprisingly, the compound with the smaller molecular dipole moment shows increased polar order in the LC phases. Besides ferroelectricity, mirror-symmetry breaking with formation of a conglomerate of macroscopic chiral domains was observed in one of the SmC phases of CN1. These investigations contribute to the general understanding of the development of polar order and chirality in soft matter.
Gauging without Initial Symmetry
Kotov, Alexei
2016-01-01
The gauge principle is at the heart of a good part of fundamental physics: Starting with a group G of so-called rigid symmetries of a functional defined over space-time Sigma, the original functional is extended appropriately by additional Lie(G)-valued 1-form gauge fields so as to lift the symmetry to Maps(Sigma,G). Physically relevant quantities are then to be obtained as the quotient of the solutions to the Euler-Lagrange equations by these gauge symmetries. In this article we show that one can construct a gauge theory for a standard sigma model in arbitrary space-time dimensions where the target metric is not invariant with respect to any rigid symmetry group, but satisfies a much weaker condition: It is sufficient to find a collection of vector fields v_a on the target M satisfying the extended Killing equation v_{a(i;j)}=0 for some connection acting on the index a. For regular foliations this is equivalent to merely requiring the distribution orthogonal to the leaves to be invariant with respect to leaf...
Peters, Kirstin
2010-01-01
A well-known result by Palamidessi tells us that {\\pi}mix (the {\\pi}-calculus with mixed choice) is more expressive than {\\pi}sep (its subset with only separate choice). The proof of this result argues with their different expressive power concerning leader election in symmetric networks. Later on, Gorla of- fered an arguably simpler proof that, instead of leader election in symmetric networks, employed the reducibility of "incestual" processes (mixed choices that include both enabled senders and receivers for the same channel) when running two copies in parallel. In both proofs, the role of breaking (ini- tial) symmetries is more or less apparent. In this paper, we shed more light on this role by re-proving the above result-based on a proper formalization of what it means to break symmetries-without referring to another layer of the distinguishing problem domain of leader election. Both Palamidessi and Gorla rephrased their results by stating that there is no uniform and reason- able encoding from {\\pi}mix i...
Peters, Kirstin; 10.4204/EPTCS.41.10
2010-01-01
A well-known result by Palamidessi tells us that \\pimix (the \\pi-calculus with mixed choice) is more expressive than \\pisep (its subset with only separate choice). The proof of this result argues with their different expressive power concerning leader election in symmetric networks. Later on, Gorla offered an arguably simpler proof that, instead of leader election in symmetric networks, employed the reducibility of incestual processes (mixed choices that include both enabled senders and receivers for the same channel) when running two copies in parallel. In both proofs, the role of breaking (initial) symmetries is more or less apparent. In this paper, we shed more light on this role by re-proving the above result - based on a proper formalization of what it means to break symmetries without referring to another layer of the distinguishing problem domain of leader election. Both Palamidessi and Gorla rephrased their results by stating that there is no uniform and reasonable encoding from \\pimix into \\pisep. We...
Symmetries in multi-Higgs-doublet models
Ivanov, I P
2012-01-01
We report the recent progress in understanding of symmetries which can be implemented in the scalar sector of electroweak symmetry breaking models with several Higgs doublets. In particular we present the list of finite reparametrization symmetry groups which can appear in the three-Higgs-doublet models.
Gauge origin of discrete flavor symmetries in heterotic orbifolds
Directory of Open Access Journals (Sweden)
Florian Beye
2014-09-01
Full Text Available We show that non-Abelian discrete symmetries in orbifold string models have a gauge origin. This can be understood when looking at the vicinity of a symmetry enhanced point in moduli space. At such an enhanced point, orbifold fixed points are characterized by an enhanced gauge symmetry. This gauge symmetry can be broken to a discrete subgroup by a nontrivial vacuum expectation value of the Kähler modulus T. Using this mechanism it is shown that the Δ(54 non-Abelian discrete symmetry group originates from a SU(3 gauge symmetry, whereas the D4 symmetry group is obtained from a SU(2 gauge symmetry.
Rainer Knab, Platons Siebter Brief. Einleitung, Text, Übersetzung, Kommentar
Brisson, Luc
2016-01-01
Cette traduction commentée de la septième Lettre attribuée à Platon est un objet étrange. On y trouve imprimé le texte édité par Burnet en 1905, mais on ne trouve rien sur l’édition de Souilhé aux Belles Lettres en 1926 ni celle de J. Moore-Blunt chez Teubner en 1985. De surcroît, la bibliographie qui clôt le volume fait montre d’incroyables faiblesses en ce qui concerne les traductions et les commentaires utilisés. Dans l’introduction, R. Knab admet, mais sans apporter d’arguments nouveaux,...
Efficient methods for solving discrete topology design problems in the PLATO-N project
DEFF Research Database (Denmark)
Canh, Nam Nguyen; Stolpe, Mathias
This paper considers the general multiple load structural topology design problems in the framework of the PLATO-N project. The problems involve a large number of discrete design variables and were modeled as a non-convex mixed 0–1 program. For the class of problems considered, a global...... optimization method based on the branch-and-cut concept was developed and implemented. In the method a large number of continuous relaxations were solved. We also present an algorithm for generating cuts to strengthen the quality of the relaxations. Several heuristics were also investigated to obtain efficient...... algorithms. The branch and cut method is used to solve benchmark examples which can be used to validate other methods and heuristics....
Queen Christina’s esoteric interests as a background to her Platonic Academies
Directory of Open Access Journals (Sweden)
Susanna Åkerman
2008-01-01
Full Text Available In 1681 the blind quietist, Francois Malaval, stated that Queen Christina of Sweden late in life had ‘given up’ [Hermes] Trismegistos and the Platonists, in favour of the Church fathers. The statement does not explain what role the Church fathers were to play in her last years, but it does show that Christina really had been interested in the rather elitist and esoteric doctrine of Hermetic Platonic Christianity. In this article the author looks at her library to show the depth of this Hermetic involvement. Her interest serves as a background to her life as ex-queen in Italy after her famous abdication from the Swedish throne in 1654, when she was 27 years old.
Structure and binding in crystals of cage-like molecules: hexamine and platonic hydrocarbons
Berland, Kristian; 10.1063/1.3366652
2010-01-01
In this paper, we show that first-principle calculations using a van der Waals density functional (vdW-DF), [Phys. Rev. Lett. $\\mathbf{92}$, 246401 (2004)] permits determination of molecular crystal structure. We study the crystal structures of hexamine and the platonic hydrocarbons (cubane and dodecahedrane). The calculated lattice parameters and cohesion energy agree well with experiments. Further, we examine the asymptotic accounts of the van der Waals forces by comparing full vdW-DF with asymptotic atom-based pair potentials extracted from vdW-DF. The character of the binding differ in the two cases, with vdW-DF giving a significant enhancement at intermediate and relevant binding separations. We analyze consequences of this result for methods such as DFT-D, and question DFT-D's transferability over the full range of separations.
Hermeneutics and the philosophy of medicine: Hans-Georg Gadamer's platonic metaphor.
Lingiardi, V; Grieco, A
1999-09-01
Taking as our starting point Plato's metaphor of the doctor as philosopher we reflect on some aspects of the epistemological status of medicine. The framework to this paper is the hermeneutics of Hans-Georg Gadamer which shows the paradoxical nature of Western medicine in choosing the body-object as its investigative starting point, while in actual fact dealing with subjects. Gadamer proposes a model of medicine as the art of understanding and dialogue, which is capable of bringing together its various constituent parts, i.e. knowledge, knowing how to do and knowing how to be, in medical practice and in the physician's training. The paper concludes with a brief discussion of the dyadic figure of the physician as Platonic "master of the living totality" and wounded healer, capable of activating the patient's self-healing capacity.
Symmetry of tetrahydroxycalix[4]arenes
Directory of Open Access Journals (Sweden)
M. GHORBANI
2006-10-01
Full Text Available Graph theory provides an elegant and natural representation of molecular symmetry and the resulting group expressed in terms of permutations is isomorphic to the permutation-inversion group of Longuet-Higgins. In this paper, using the group theory package GAP, the character table and the automorphism group of the Euclidean graph of tetrahydroxycalix[4]arenes were computed.
Symmetries of Massive and Massless Neutrinos
Kim, Y S
2016-01-01
Wigner's little groups are subgroups of the Lorentz group dictating the internal space-time symmetries of massive and massless particles. These little groups are like O(3) and E(2) for massive and massless particles respectively. While the geometry of the O(3) symmetry is familiar to us, the geometry of the flat plane cannot explain the E(2)-like symmetry for massless particles. However, the geometry of a circular cylinder can explain the symmetry with the helicity and gauge degrees of freedom. It is shown further that the symmetry of the massless particle can be obtained as a zero-mass limit of O(3)-like symmetry for massive particles. It is shown further that the polarization of massless neutrinos is a consequence of gauge invariance, while the symmetry of massive neutrinos is still like O(3).
Symmetry constraints on many-body localization
Potter, Andrew C.; Vasseur, Romain
2016-12-01
We derive general constraints on the existence of many-body localized (MBL) phases in the presence of global symmetries, and show that MBL is not possible with symmetry groups that protect multiplets (e.g., all non-Abelian symmetry groups). Based on simple representation theoretic considerations, we derive general Mermin-Wagner-type principles governing the possible alternative fates of nonequilibrium dynamics in isolated, strongly disordered quantum systems. Our results rule out the existence of MBL symmetry-protected topological phases with non-Abelian symmetry groups, as well as time-reversal symmetry-protected electronic topological insulators, and in fact all fermion topological insulators and superconductors in the 10-fold way classification. Moreover, extending our arguments to systems with intrinsic topological order, we rule out MBL phases with non-Abelian anyons as well as certain classes of symmetry-enriched topological orders.
Inverse semigroups the theory of partial symmetries
Lawson, Mark V
1998-01-01
Symmetry is one of the most important organising principles in the natural sciences. The mathematical theory of symmetry has long been associated with group theory, but it is a basic premise of this book that there are aspects of symmetry which are more faithfully represented by a generalization of groups called inverse semigroups. The theory of inverse semigroups is described from its origins in the foundations of differential geometry through to its most recent applications in combinatorial group theory, and the theory tilings.
Symmetry and symmetry breaking in particle physics
Tsou, ST
1998-01-01
Symmetry, in particular gauge symmetry, is a fundamental principle in theoretical physics. It is intimately connected to the geometry of fibre bundles. A refinement to the gauge principle, known as ``spontaneous symmetry breaking'', leads to one of the most successful theories in modern particle physics. In this short talk, I shall try to give a taste of this beautiful and exciting concept.
Directory of Open Access Journals (Sweden)
Maria Chiara Pievatolo
2011-05-01
Full Text Available Secondo alcune fonti antiche il sofista Protagora, ormai anziano, fu accusato, come Socrate, di empietà e trovò la morte lasciando Atene, forse per sfuggire al processo o forse perché bandito dalla città. Contro questa tradizione sembra militare la testimonianza di Platone, secondo la quale, almeno in apparenza, Protagora, a differenza di altri intellettuali, non si [...
Dynamical symmetries of the Kepler problem
Cariglia, Marco
2013-01-01
This work originates from a first year undergraduate research project on hidden symmetries of the dynamics for classical Hamiltonian systems, under the program 'Jovens talentos para a Ciencia' of Brazilian funding agency Capes. For pedagogical reasons the main subject chosen was Kepler's problem of motion under a central potential, since it is a completely solved system. It is well known that for this problem the group of dynamical symmetries is strictly larger than the isometry group O(3), the extra symmetries corresponding to hidden symmetries of the dynamics. By taking the point of view of examining the group action of the dynamical symmetries on the allowed trajectories, it is possible to teach in the same project basic elements of as many important subjects in physics as: Hamiltonian formalism, hidden symmetries, integrable systems, group theory, and the use of manifolds.
Yale, Paul B
2012-01-01
This book is an introduction to the geometry of Euclidean, affine, and projective spaces with special emphasis on the important groups of symmetries of these spaces. The two major objectives of the text are to introduce the main ideas of affine and projective spaces and to develop facility in handling transformations and groups of transformations. Since there are many good texts on affine and projective planes, the author has concentrated on the n-dimensional cases.Designed to be used in advanced undergraduate mathematics or physics courses, the book focuses on ""practical geometry,"" emphasi
Nonlocalization of Nonlocal Symmetry and Symmetry Reductions of the Burgers Equation
Institute of Scientific and Technical Information of China (English)
金艳; 贾曼; 楼森岳
2012-01-01
Symmetry reduction method is one of the best ways to find exact solutions. In this paper, we study the possibility of symmetry reductions of the well known Burgers equation including the nonlocal symmetry. The related new group Jnvariant solutions are obtained. Especially, the interactions among solitons, Airy waves, and Kummer waves are explicitly given.
Perception of Mirror Symmetry in Autism Spectrum Disorders
Falter, Christine M.; Bailey, Anthony J.
2012-01-01
Gestalt grouping in autism spectrum disorders (ASD) is selectively impaired for certain organization principles but for not others. Symmetry is a fundamental Gestalt principle characterizing many biological shapes. Sensitivity to symmetry was tested using the Picture Symmetry Test, which requires finding symmetry lines on pictures. Individuals…
A platonic solid templating Archimedean solid: an unprecedented nanometre-sized Ag37 cluster
Li, Xiao-Yu; Su, Hai-Feng; Yu, Kai; Tan, Yuan-Zhi; Wang, Xing-Po; Zhao, Ya-Qin; Sun, Di; Zheng, Lan-Sun
2015-04-01
The spontaneous formation of discrete spherical nanosized molecules is prevalent in nature, but the authentic structural mimicry of such highly symmetric polyhedra from edge sharing of regular polygons has remained elusive. Here we present a novel ball-shaped {(HNEt3)[Ag37S4(SC6H4tBu)24(CF3COO)6(H2O)12]} cluster (1) that is assembled via a one-pot process from polymeric {(HNEt3)2[Ag10(SC6H4tBu)12]}n and CF3COOAg. Single crystal X-ray analysis confirmed that 1 is a Td symmetric spherical molecule with a [Ag36(SC6H4tBu)24] anion shell enwrapping a AgS4 tetrahedron. The shell topology of 1 belongs to one of 13 Archimedean solids, a truncated tetrahedron with four edge-shared hexagons and trigons, which are supported by a AgS4 Platonic solid in the core. Interestingly, the cluster emits green luminescence centered at 515 nm at room temperature. Our investigations have provided a promising synthetic protocol for a high-nuclearity silver cluster based on underlying geometrical principles.The spontaneous formation of discrete spherical nanosized molecules is prevalent in nature, but the authentic structural mimicry of such highly symmetric polyhedra from edge sharing of regular polygons has remained elusive. Here we present a novel ball-shaped {(HNEt3)[Ag37S4(SC6H4tBu)24(CF3COO)6(H2O)12]} cluster (1) that is assembled via a one-pot process from polymeric {(HNEt3)2[Ag10(SC6H4tBu)12]}n and CF3COOAg. Single crystal X-ray analysis confirmed that 1 is a Td symmetric spherical molecule with a [Ag36(SC6H4tBu)24] anion shell enwrapping a AgS4 tetrahedron. The shell topology of 1 belongs to one of 13 Archimedean solids, a truncated tetrahedron with four edge-shared hexagons and trigons, which are supported by a AgS4 Platonic solid in the core. Interestingly, the cluster emits green luminescence centered at 515 nm at room temperature. Our investigations have provided a promising synthetic protocol for a high-nuclearity silver cluster based on underlying geometrical principles
External symmetry in general relativity
Cotaescu, I I
2000-01-01
We propose a generalization of the isometry transformations to the geometric context of the field theories with spin where the local frames are explicitly involved. We define the external symmetry transformations as isometries combined with suitable tetrad gauge transformations and we show that these form a group which is locally isomorphic with the isometry one. We point out that the symmetry transformations that leave invariant the equations of the fields with spin have generators with specific spin terms which represent new physical observables. The examples we present are the generators of the central symmetry and those of the maximal symmetries of the de Sitter and anti-de Sitter spacetimes derived in different tetrad gauge fixings. Pacs: 04.20.Cv, 04.62.+v, 11.30.-j
Deriving diffeomorphism symmetry
Kleppe, Astri
2014-01-01
In an earlier article, we have "derived" space, as a part of the Random Dynamics project. In order to get locality we need to obtain reparametrization symmetry, or equivalently, diffeomorphism symmetry. There we sketched a procedure for how to get locality by first obtaining reparametrization symmetry, or equivalently, diffeomorphism symmetry. This is the object of the present article.
On structuralism, and the poststructuralistic condition in Deleuze, inverter of Platonism
Directory of Open Access Journals (Sweden)
Manuel Altamirano
2016-11-01
Full Text Available Focusing on Gilles Deleuze´s second stage of thought, specially his work of inversion of Platonism, we´ll show why the concept of structure is so important, as well as its conditions and functioning, and how this characterization has an impact on central concepts such as identity or difference. That way we´ll understand the idealistic character of Deleuze´s philosophy, thus a different kind of Plato´s idealism. We´ll take into consideration, also, the realm of the “problematic”, and the “ideal game”. We´ll evaluate the six necessary criteria of what Deleuze calls an “Idea”. Given the conditions we´ll establish trough this revision, we´ll be able to conclude that Deleuze overtakes structuralism and embraces poststructuralism. This last affirmation will be argued trough a comparison between Delezue´s poststructuralism and the basics of more classical, Lévi-Straus´s structuralism
Directory of Open Access Journals (Sweden)
Mikhailova N. V.
2015-01-01
Full Text Available The author of the work proposes a philosophical and methodological interpretation of the mathematical objects, using the system triad of the main directions of substantiation of mathematics: the formalism of Hilbert, Brouwer’s intuitionism and Godel’s Platonism. The need for these directions in the concept of substantiation of mathematics from the point of view of the current state of the philosophy of mathematics is shown on the mathematical examples. The philosophical and methodological analysis of objects of mathematics has never been unambiguous, therefore in this paper the results of studies of philosophers, logicians and mathematicians, in which the problem of substantiation is explicated in the context of trends in the development of mathematics, are used. Their professional view on philosophical characteristics of the objects of mathematics contributes to the identification of the unity of all mathematical knowledge maintaining the initial mathematical base of knowledge and revealing new ways of integrating the directions of substantiation in the philosophy of mathematics. The practical problem of substantiation of mathematics is realized through the elaboration of metatheoretical knowledge under the paradigm shift in the philosophy of mathematics to the productive direction from analysis to synthesis.
Platonism, cartesianism and Hegel’s thought in the Matrix Trilogy
Directory of Open Access Journals (Sweden)
Milidrag Predrag
2013-01-01
Full Text Available In this article I will try to interpret changes in Neo, the main character in The Matrix Trilogy, against the background of the ideas of Plato and Descartes, as well as Hegel’s from his Philosophy of History and The Phenomenology of Spirit. Although “philosophical” The Matrix Trilogy is not long-winded and boring film: instead of talking endlessly, the characters are working ceaselessly, and that work is changing them. Contrary to widespread opinion, this interpretation does not find the presence of Descartes’ hyperbolic doubt in the first part of trilogy, but first film sees as a pure Platonism. Nevertheless, there are the Cartesian motifs (e.g. dualism, freeing mind from preconceived opinions, acquiring different habits of belief. The result of the first film is the position of Hegelian unhappy consciousness. This is just a preparation for the key moment of whole Trilogy that is the dialogue between Neo and Architect. Neo’s decision to chose to save Trinity is interpreted in Hegel’s terms of the infinite right of the subject to satisfy himself in his activity and work; because of that, this, sixth Neo is new. After showing the differences in the objectives of Neo and Agent Smith, and transformations of the objectives of humans, the third part of the article analyzes the very end of the Matrix Revolutions, using Marx’s ideas, with some references to Plato and Nietzsche.
Expel poetry from life and society, exile poets. Modern interpretations of the Platonic postulate
Directory of Open Access Journals (Sweden)
Krystyna Bartol
2012-01-01
Full Text Available This article is a critical review of the most important modern interpretations of the Platonic postulate of expelling poets from the polis, formulated in two works of the thinker, the Republic and the Laws. The reflections presented in the article focus on two fundamental questions, namely the reasons behind Plato’s refusal to allow poets into his ideal state and, secondly, the aim he was going to attain by expelling artists from the community of citizens. To try to explain the reasons behind these statements, so embarrassing to present-day readers of Plato, involves considerations of Plato’s concept of the nature of poetry (art as flawed, defective and secondary reflection of the sensual world, as well as of ethical questions (art as a perfidious tool to facilitate malevolent designs towards human characters. Any investigation as to the intentions of the philosophers that preceded the formulation of the postulate concentrates thus inevitably on his vision of utopian realism. It further aims to provide sufficient arguments that Plato, oscillating in his presentation between authoritarian diagnosis and protreptic provocation, makes recipients redefine the mutual relationship between literature and philosophy.
Une histoire de la lumière de Platon au photon
Maitte, Bernard
2015-01-01
De la sensation commune à la compréhension scientifique, nos idées sur la nature et les propriétés de la lumière ont connu un long cheminement depuis les théories de Platon jusqu'à la maîtrise du photon. L'Antiquité, la civilisation arabo-islamique, la Renaissance européenne et sa révolution scientifique, puis la science classique du me siècle, les avancées modernes enfin, autant de moments dans la riche histoire de nos connaissances sur la lumière. Ce livre décrit l'élaboration tourmentée des idées, tant philosophiques que scientifiques, qui ont scandé cette histoire, tirant profit des succès comme des échecs, des efforts comme des renoncements. "En regardant d'un oeil critique l'histoire de la lumière, nous pourrons accéder à notre tour à cette logique savoureuse et amère que l'on appelle Science." La première édition de ce livre, ici considérablement augmentée, a obtenu le prix Jean-Rostand du meilleur ouvrage de vulgarisation scientifique.
Ultra-large supramolecular coordination cages composed of endohedral Archimedean and Platonic bodies
Byrne, Kevin; Zubair, Muhammad; Zhu, Nianyong; Zhou, Xiao-Ping; Fox, Daniel S.; Zhang, Hongzhou; Twamley, Brendan; Lennox, Matthew J.; Düren, Tina; Schmitt, Wolfgang
2017-05-01
Pioneered by Lehn, Cram, Peterson and Breslow, supramolecular chemistry concepts have evolved providing fundamental knowledge of the relationships between the structures and reactivities of organized molecules. A particular fascinating class of metallo-supramolecular molecules are hollow coordination cages that provide cavities of molecular dimensions promoting applications in diverse areas including catalysis, enzyme mimetics and material science. Here we report the synthesis of coordination cages with exceptional cross-sectional diameters that are composed of multiple sub-cages providing numerous distinctive binding sites through labile coordination solvent molecules. The building principles, involving Archimedean and Platonic bodies, renders these supramolecular keplerates as a class of cages whose composition and topological aspects compare to characteristics of edge-transitive {Cu2} MOFs with A3X4 stoichiometry. The nature of the cavities in these double-shell metal-organic polyhedra and their inner/outer binding sites provide perspectives for post-synthetic functionalizations, separations and catalysis. Transmission electron microscopy studies demonstrate that single molecules are experimentally accessible.
Notes on generalized global symmetries in QFT
Energy Technology Data Exchange (ETDEWEB)
Sharpe, Eric [Department of Physics MC 0435, 850 West Campus Drive, Virginia Tech, Blacksburg, VA (United States)
2015-11-15
It was recently argued that quantum field theories possess one-form and higher-form symmetries, labelled 'generalized global symmetries.' In this paper, we describe how those higher-form symmetries can be understood mathematically as special cases of more general 2-groups and higher groups, and discuss examples of quantum field theories admitting actions of more general higher groups than merely one-form and higher-form symmetries. We discuss analogues of topological defects for some of these higher symmetry groups, relating some of them to ordinary topological defects. We also discuss topological defects in cases in which the moduli 'space' (technically, a stack) admits an action of a higher symmetry group. Finally, we outline a proposal for how certain anomalies might potentially be understood as describing a transmutation of an ordinary group symmetry of the classical theory into a 2-group or higher group symmetry of the quantum theory, which we link to WZW models and bosonization. (copyright 2015 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Cubic Icosahedra? A Problem in Assigning Symmetry
Lloyd, D. R.
2010-01-01
There is a standard convention that the icosahedral groups are classified separately from the cubic groups, but these two symmetry types have been conflated as "cubic" in some chemistry textbooks. In this note, the connection between cubic and icosahedral symmetries is examined, using a simple pictorial model. It is shown that octahedral and…
SASS: a symmetry adapted stochastic search algorithm exploiting site symmetry.
Wheeler, Steven E; Schleyer, Paul V R; Schaefer, Henry F
2007-03-14
A simple symmetry adapted search algorithm (SASS) exploiting point group symmetry increases the efficiency of systematic explorations of complex quantum mechanical potential energy surfaces. In contrast to previously described stochastic approaches, which do not employ symmetry, candidate structures are generated within simple point groups, such as C2, Cs, and C2v. This facilitates efficient sampling of the 3N-6 Pople's dimensional configuration space and increases the speed and effectiveness of quantum chemical geometry optimizations. Pople's concept of framework groups [J. Am. Chem. Soc. 102, 4615 (1980)] is used to partition the configuration space into structures spanning all possible distributions of sets of symmetry equivalent atoms. This provides an efficient means of computing all structures of a given symmetry with minimum redundancy. This approach also is advantageous for generating initial structures for global optimizations via genetic algorithm and other stochastic global search techniques. Application of the SASS method is illustrated by locating 14 low-lying stationary points on the cc-pwCVDZ ROCCSD(T) potential energy surface of Li5H2. The global minimum structure is identified, along with many unique, nonintuitive, energetically favorable isomers.
论英国文艺复兴时期的新柏拉图主义图景%Neo-Platonic Variations in Renaissance England
Institute of Scientific and Technical Information of China (English)
潘先利
2012-01-01
Neo-Platonic variations in Renaissance England is a promising arena for further scholarly exploration. A platonic landscape is outlined with explicit British features： John Colet＇s idea in Christian image, Thomas Moore＇s Platonic Utopian train of thought and John Dee＇s Christian-Platonic numerology and magic--all construct a blueprint of Platonic cosmos.%英国文艺复兴时期的新柏拉图主义在当时是一股不可忽略的知性力量，但其形成性研究还是一个学术冷门。主要考证该思潮的本土化变体，尤其聚焦约翰·克里特的基督教理式模型、托马斯·莫尔结合了柏拉图古典社会完美观念和古罗马修辞策略的鸟托邦思想、约翰·迪的基督教一柏拉图式数字命理哲学和神秘主义魔法理论等具有英国风貌的新柏拉图主义宇宙图景。
Quantum mechanics. Symmetries. 5. corr. ed.; Quantenmechanik. Symmetrien
Energy Technology Data Exchange (ETDEWEB)
Greiner, Walter [Frankfurt Univ. (Germany). Frankfurt Inst. for Advanced Studies; Mueller, Berndt [Duke Univ., Durham, NC (United States). Dept. of Physics
2014-07-01
The volume quantum mechanics treats the as elegant as mighty theory of the symmetry groups and their application in quantum mechanics and the theory of the elementary particles. By means of many examples and problems with worked-out solutions the application of the fundamental principles to realistic problems is elucidated. The themes are symmetries in quantum mechanics, representations of the algebra of the angular momentum operators as generators of the SO(3) group. fundamental properties of Lie groups as mathematical supplement, symmetry groups and their physical meaning, thr isospin group, the hypercharge, quarks and the symmetry group SU(3), representations of the permutation group and Young diagrams, group characters as mathematical supplement, charm and the symmetry group SU(4), Cartan-Weyl claasification as mathematical supplement, special discrete symmetries, dynamical symmetries and the hydrogen atom, non-compact Lie groups as mathematical supplement, a proof of Racah's theorem.
Beyond bilateral symmetry: geometric morphometric methods for any type of symmetry
Directory of Open Access Journals (Sweden)
Klingenberg Christian
2011-09-01
Full Text Available Abstract Background Studies of symmetric structures have made important contributions to evolutionary biology, for example, by using fluctuating asymmetry as a measure of developmental instability or for investigating the mechanisms of morphological integration. Most analyses of symmetry and asymmetry have focused on organisms or parts with bilateral symmetry. This is not the only type of symmetry in biological shapes, however, because a multitude of other types of symmetry exists in plants and animals. For instance, some organisms have two axes of reflection symmetry (biradial symmetry; e.g. many algae, corals and flowers or rotational symmetry (e.g. sea urchins and many flowers. So far, there is no general method for the shape analysis of these types of symmetry. Results We generalize the morphometric methods currently used for the shape analysis of bilaterally symmetric objects so that they can be used for analyzing any type of symmetry. Our framework uses a mathematical definition of symmetry based on the theory of symmetry groups. This approach can be used to divide shape variation into a component of symmetric variation among individuals and one or more components of asymmetry. We illustrate this approach with data from a colonial coral that has ambiguous symmetry and thus can be analyzed in multiple ways. Our results demonstrate that asymmetric variation predominates in this dataset and that its amount depends on the type of symmetry considered in the analysis. Conclusions The framework for analyzing symmetry and asymmetry is suitable for studying structures with any type of symmetry in two or three dimensions. Studies of complex symmetries are promising for many contexts in evolutionary biology, such as fluctuating asymmetry, because these structures can potentially provide more information than structures with bilateral symmetry.
Mathieu Moonshine and Symmetry Surfing
Gaberdiel, Matthias R; Paul, Hynek
2016-01-01
Mathieu Moonshine, the observation that the Fourier coefficients of the elliptic genus on K3 can be interpreted as dimensions of representations of the Mathieu group M24, has been proven abstractly, but a conceptual understanding in terms of a representation of the Mathieu group on the BPS states, is missing. Some time ago, Taormina and Wendland showed that such an action can be naturally defined on the lowest non-trivial BPS states, using the idea of `symmetry surfing', i.e., by combining the symmetries of different K3 sigma models. In this paper we find non-trivial evidence that this construction can be generalized to all BPS states.
Symposium Symmetries in Science XIII
Gruber, Bruno J; Yoshinaga, Naotaka; Symmetries in Science XI
2005-01-01
This book is a collection of reviews and essays about the recent developments in the area of Symmetries and applications of Group Theory. Contributions have been written mostly at the graduate level but some are accessible to advanced undergraduates. The book is of interest to a wide audience and covers a broad range of topics with a strong degree of thematical unity. The book is part of a Series of books on Symmetries in Science and may be compared to the published Proceedings of the Colloquia on Group Theoretical Methods in Physics. Here, however, prevails a distinguished character for presenting extended reviews on present applications to Science, not restricted to Theoretical Physics.
Ermolenko, Alexander E; Perepada, Elena A
2007-01-01
The paper contains a description of basic regularities in the manifestation of symmetry of human structural organization and its ontogenetic and phylogenetic development. A concept of macrobiocrystalloid with inherent complex symmetry is proposed for the description of the human organism in its integrity. The symmetry can be characterized as two-plane radial (quadrilateral), where the planar symmetry is predominant while the layout of organs of radial symmetry is subordinated to it. Out of the two planes of symmetry (sagittal and horizontal), the sagittal plane is predominant. The symmetry of the chromosome, of the embrio at the early stages of cell cleavage as well as of some organs and systems in their phylogenetic development is described. An hypothesis is postulated that the two-plane symmetry is formed by two mechanisms: a) the impact of morphogenetic fields of the whole crystalloid organism during embriogenesis and, b) genetic mechanisms of the development of chromosomes having two-plane symmetry.
Noether symmetry and Lie symmetry of discrete holonomic systems with dependent coordinates
Institute of Scientific and Technical Information of China (English)
Shi Shen-Yang; Huang Xiao-Hong
2008-01-01
The Noether symmetry,the Lie symmetry and the conserved quantity of discrete holonomic systems with dependent coordinates are investigated in this paper.The Noether symmetry provides a discrete Noether identity and a conserved qu中antity of the system.The invariance of discrete motion equations under infinitesimal transformation groups is defined as the Lie symmetry,and the condition of obtaining the Noether conserved quantity from the Lie symmetry is also presented.An example is discussed to show the applications of the results.
Directory of Open Access Journals (Sweden)
Tetsuo Deguchi
2011-06-01
Full Text Available We show some symmetry relations among the correlation functions of the integrable higher-spin XXX and XXZ spin chains, where we explicitly evaluate the multiple integrals representing the one-point functions in the spin-1 case. We review the multiple-integral representations of correlation functions for the integrable higher-spin XXZ chains derived in a region of the massless regime including the anti-ferromagnetic point. Here we make use of the gauge transformations between the symmetric and asymmetric R-matrices, which correspond to the principal and homogeneous gradings, respectively, and we send the inhomogeneous parameters to the set of complete 2s-strings. We also give a numerical support for the analytical expression of the one-point functions in the spin-1 case.
Brading, Katherine; Castellani, Elena
2010-01-01
Preface; Copyright acknowledgements; List of contributors; 1. Introduction; Part I. Continuous Symmetries: 2. Classic texts: extracts from Weyl and Wigner; 3. Review paper: On the significance of continuous symmetry to the foundations of physics C. Martin; 4. The philosophical roots of the gauge principle: Weyl and transcendental phenomenological idealism T. Ryckman; 5. Symmetries and Noether's theorems K. A. Brading and H. R. Brown; 6. General covariance, gauge theories, and the Kretschmann objection J. Norton; 7. The interpretation of gauge symmetry M. Redhead; 8. Tracking down gauge: an ode to the constrained Hamiltonian formalism J. Earman; 9. Time-dependent symmetries: the link between gauge symmetries and indeterminism D. Wallace; 10. A fourth way to the Aharanov-Bohm effect A. Nounou; Part II. Discrete Symmetries: 11. Classic texts: extracts from Lebniz, Kant and Black; 12. Review paper: Understanding permutation symmetry S. French and D. Rickles; 13. Quarticles and the identity of discernibles N. Hugget; 14. Review paper: Handedness, parity violation, and the reality of space O. Pooley; 15. Mirror symmetry: what is it for a relational space to be orientable? N. Huggett; 16. Physics and Leibniz's principles S. Saunders; Part III. Symmetry Breaking: 17: Classic texts: extracts from Curie and Weyl; 18. Extract from G. Jona-Lasinio: Cross-fertilization in theoretical physics: the case of condensed matter and particle physics G. Jona-Lasinio; 19. Review paper: On the meaning of symmetry breaking E. Castellani; 20. Rough guide to spontaneous symmetry breaking J. Earman; 21. Spontaneous symmetry breaking: theoretical arguments and philosophical problems M. Morrison; Part IV. General Interpretative Issues: 22. Classic texts: extracts from Wigner; 23. Symmetry as a guide to superfluous theoretical structure J. Ismael and B. van Fraassen; 24. Notes on symmetries G. Belot; 25. Symmetry, objectivity, and design P. Kosso; 26. Symmetry and equivalence E. Castellani.
Rosensteel, George
1995-01-01
Riemann ellipsoids model rotating galaxies when the galactic velocity field is a linear function of the Cartesian coordinates of the galactic masses. In nuclear physics, the kinetic energy in the linear velocity field approximation is known as the collective kinetic energy. But, the linear approximation neglects intrinsic degrees of freedom associated with nonlinear velocity fields. To remove this limitation, the theory of symplectic dynamical symmetry is developed for classical systems. A classical phase space for a self-gravitating symplectic system is a co-adjoint orbit of the noncompact group SP(3,R). The degenerate co-adjoint orbit is the 12 dimensional homogeneous space Sp(3,R)/U(3), where the maximal compact subgroup U(3) is the symmetry group of the harmonic oscillator. The Hamiltonian equations of motion on each orbit form a Lax system X = (X,F), where X and F are elements of the symplectic Lie algebra. The elements of the matrix X are the generators of the symplectic Lie algebra, viz., the one-body collective quadratic functions of the positions and momenta of the galactic masses. The matrix F is composed from the self-gravitating potential energy, the angular velocity, and the hydostatic pressure. Solutions to the hamiltonian dynamical system on Sp(3,R)/U(3) are given by symplectic isospectral deformations. The Casimirs of Sp(3,R), equal to the traces of powers of X, are conserved quantities.
Rašin, Andrija
1994-01-01
We discuss the idea of approximate flavor symmetries. Relations between approximate flavor symmetries and natural flavor conservation and democracy models is explored. Implications for neutrino physics are also discussed.
Directory of Open Access Journals (Sweden)
Joe Rosen
2005-12-01
Full Text Available Abstract: The symmetry principle is described in this paper. The full details are given in the book: J. Rosen, Symmetry in Science: An Introduction to the General Theory (Springer-Verlag, New York, 1995.
Localization of Nonlocal Symmetries and Symmetry Reductions of Burgers Equation
Wu, Jian-Wen; Lou, Sen-Yue; Yu, Jun
2017-05-01
The nonlocal symmetries of the Burgers equation are explicitly given by the truncated Painlevé method. The auto-Bäcklund transformation and group invariant solutions are obtained via the localization procedure for the nonlocal residual symmetries. Furthermore, the interaction solutions of the solition-Kummer waves and the solition-Airy waves are obtained. Supported by the Global Change Research Program China under Grant No. 2015CB953904, the National Natural Science Foundations of China under Grant Nos. 11435005, 11175092, and 11205092, Shanghai Knowledge Service Platform for Trustworthy Internet of Things under Grant No. ZF1213, and K. C. Wong Magna Fund in Ningbo University
Institute of Scientific and Technical Information of China (English)
王琳; 高敏娜
2014-01-01
The background of Captain Corelli’s Mandolin is based on World War II. When the war provoked on the Greek Is-land, the Greeks fight against the Italian Fascist and live a tough life with their love. This article mainly talks about the essence of the Platonic love revealed in the book. By analyzing the description about homosexuality and heterosexuality in the book, this ar-ticle acclaims the essence of the Platonic love-the noble abstention of lust-based love and the truth, kindness and beauty of love.
Energy Technology Data Exchange (ETDEWEB)
Nilles, Hans Peter [Bonn Univ. (Germany). Bethe Center for Theoretical Physics; Bonn Univ. (Germany). Physikalisches Inst.; Ratz, Michael [Technische Univ. Muenchen, Garching (Germany). Physik-Department; Vaudrevange, Patrick K.S. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
2012-04-15
Discrete (family) symmetries might play an important role in models of elementary particle physics. We discuss the origin of such symmetries in the framework of consistent ultraviolet completions of the standard model in field and string theory. The symmetries can arise due to special geometrical properties of extra compact dimensions and the localization of fields in this geometrical landscape. We also comment on anomaly constraints for discrete symmetries.
Neutrinos and flavor symmetries
Tanimoto, Morimitsu
2015-07-01
We discuss the recent progress of flavor models with the non-Abelian discrete symmetry in the lepton sector focusing on the θ13 and CP violating phase. In both direct approach and indirect approach of the flavor symmetry, the non-vanishing θ13 is predictable. The flavor symmetry with the generalised CP symmetry can also predicts the CP violating phase. We show the phenomenological analyses of neutrino mixing for the typical flavor models.
Neutrinos and flavor symmetries
Energy Technology Data Exchange (ETDEWEB)
Tanimoto, Morimitsu
2015-07-15
We discuss the recent progress of flavor models with the non-Abelian discrete symmetry in the lepton sector focusing on the θ{sub 13} and CP violating phase. In both direct approach and indirect approach of the flavor symmetry, the non-vanishing θ{sub 13} is predictable. The flavor symmetry with the generalised CP symmetry can also predicts the CP violating phase. We show the phenomenological analyses of neutrino mixing for the typical flavor models.
On the origin of neutrino flavour symmetry
King, Stephen F
2009-01-01
We study classes of models which are based on some discrete family symmetry which is completely broken such that the observed neutrino flavour symmetry emerges indirectly as an accidental symmetry. For such "indirect" models we discuss the D-term flavon vacuum alignments which are required for such an accidental flavour symmetry consistent with tri-bimaximal lepton mixing to emerge. We identify large classes of suitable discrete family symmetries, namely the $\\Delta(3n^2)$ and $\\Delta(6n^2)$ groups, together with other examples such as $Z_7\\rtimes Z_3$. In such indirect models the implementation of the type I see-saw mechanism is straightforward using constrained sequential dominance. However the accidental neutrino flavour symmetry may be easily violated, for example leading to a large reactor angle, while maintaining accurately the tri-bimaximal solar and atmospheric predictions.
Maniplexes: Part 1: Maps, Polytopes, Symmetry and Operators
Directory of Open Access Journals (Sweden)
Steve Wilson
2012-04-01
Full Text Available This paper introduces the idea of a maniplex, a common generalization of map and of polytope. The paper then discusses operators, orientability, symmetry and the action of the symmetry group.
Geometric Approach to Lie Symmetry of Discrete Time Toda Equation
Institute of Scientific and Technical Information of China (English)
JIA Xiao-Yu; WANG Na
2009-01-01
By using the extended Harrison and Estabrook geometric approach,we investigate the Lie symmetry of discrete time Toda equation from the geometric point of view.Its one-dimensional continuous symmetry group is presented.
Lie Point Symmetries of Differential-Difference Equations
Institute of Scientific and Technical Information of China (English)
DING Wei; TANG Xiao-Yan
2004-01-01
In this paper, the classical Lie group approach is extended to find some Lie point symmetries of differentialdifference equations. It reveals that the obtained Lie point symmetries can constitute a Kac-Moody-Virasoro algebra.
On Gauging Symmetry of Modular Categories
Cui, Shawn X.; Galindo, César; Plavnik, Julia Yael; Wang, Zhenghan
2016-05-01
Topological order of a topological phase of matter in two spacial dimensions is encoded by a unitary modular (tensor) category (UMC). A group symmetry of the topological phase induces a group symmetry of its corresponding UMC. Gauging is a well-known theoretical tool to promote a global symmetry to a local gauge symmetry. We give a mathematical formulation of gauging in terms of higher category formalism. Roughly, given a UMC with a symmetry group G, gauging is a 2-step process: first extend the UMC to a G-crossed braided fusion category and then take the equivariantization of the resulting category. Gauging can tell whether or not two enriched topological phases of matter are different, and also provides a way to construct new UMCs out of old ones. We derive a formula for the {H^4} -obstruction, prove some properties of gauging, and carry out gauging for two concrete examples.
On Gauging Symmetry of Modular Categories
Cui, Shawn X.; Galindo, César; Plavnik, Julia Yael; Wang, Zhenghan
2016-12-01
Topological order of a topological phase of matter in two spacial dimensions is encoded by a unitary modular (tensor) category (UMC). A group symmetry of the topological phase induces a group symmetry of its corresponding UMC. Gauging is a well-known theoretical tool to promote a global symmetry to a local gauge symmetry. We give a mathematical formulation of gauging in terms of higher category formalism. Roughly, given a UMC with a symmetry group G, gauging is a 2-step process: first extend the UMC to a G-crossed braided fusion category and then take the equivariantization of the resulting category. Gauging can tell whether or not two enriched topological phases of matter are different, and also provides a way to construct new UMCs out of old ones. We derive a formula for the {H^4}-obstruction, prove some properties of gauging, and carry out gauging for two concrete examples.
Polynomial Graphs and Symmetry
Goehle, Geoff; Kobayashi, Mitsuo
2013-01-01
Most quadratic functions are not even, but every parabola has symmetry with respect to some vertical line. Similarly, every cubic has rotational symmetry with respect to some point, though most cubics are not odd. We show that every polynomial has at most one point of symmetry and give conditions under which the polynomial has rotational or…
Polynomial Graphs and Symmetry
Goehle, Geoff; Kobayashi, Mitsuo
2013-01-01
Most quadratic functions are not even, but every parabola has symmetry with respect to some vertical line. Similarly, every cubic has rotational symmetry with respect to some point, though most cubics are not odd. We show that every polynomial has at most one point of symmetry and give conditions under which the polynomial has rotational or…
Chiral symmetry and chiral-symmetry breaking
Energy Technology Data Exchange (ETDEWEB)
Peskin, M.E.
1982-12-01
These lectures concern the dynamics of fermions in strong interaction with gauge fields. Systems of fermions coupled by gauge forces have a very rich structure of global symmetries, which are called chiral symmetries. These lectures will focus on the realization of chiral symmetries and the causes and consequences of thier spontaneous breaking. A brief introduction to the basic formalism and concepts of chiral symmetry breaking is given, then some explicit calculations of chiral symmetry breaking in gauge theories are given, treating first parity-invariant and then chiral models. These calculations are meant to be illustrative rather than accurate; they make use of unjustified mathematical approximations which serve to make the physics more clear. Some formal constraints on chiral symmetry breaking are discussed which illuminate and extend the results of our more explicit analysis. Finally, a brief review of the phenomenological theory of chiral symmetry breaking is presented, and some applications of this theory to problems in weak-interaction physics are discussed. (WHK)
Dynamical gauge symmetry breaking on the lattice
Energy Technology Data Exchange (ETDEWEB)
Farakos, K.; Koutsoumbas, G.; Zoupanos, G. (National Research Centre for the Physical Sciences Democritos, Athens (Greece))
1990-10-11
We study, using lattice techniques, the dynamical symmetry breaking of a three-dimensional theory that mimics the electroweak sector of the standard model. We show that in the strong coupling limit of a QCD-like theory the fermion condensates which are produced induce dynamical symmetry breaking of the sector corresponding to the electroweak gauge group. (orig.).
de Leeuw, Marius; Moriyama, Sanefumi; Regelskis, Vidas; Torrielli, Alessandro
2012-01-01
We discuss special quantum group (secret) symmetries of the integrable system associated to the AdS/CFT correspondence. These symmetries have by now been observed in a variety of forms, including the spectral problem, the boundary scattering problem, n-point amplitudes, the pure-spinor formulation and quantum affine deformations.
Hidden flavor symmetries of SO(10 GUT
Directory of Open Access Journals (Sweden)
Borut Bajc
2016-08-01
Full Text Available The Yukawa interactions of the SO(10 GUT with fermions in 16-plets (as well as with singlets have certain intrinsic (“built-in” symmetries which do not depend on the model parameters. Thus, the symmetric Yukawa interactions of the 10 and 126 dimensional Higgses have intrinsic discrete Z2×Z2 symmetries, while the antisymmetric Yukawa interactions of the 120 dimensional Higgs have a continuous SU(2 symmetry. The couplings of SO(10 singlet fermions with fermionic 16-plets have U(13 symmetry. We consider a possibility that some elements of these intrinsic symmetries are the residual symmetries, which originate from the (spontaneous breaking of a larger symmetry group Gf. Such an embedding leads to the determination of certain elements of the relative mixing matrix U between the matrices of Yukawa couplings Y10, Y126, Y120, and consequently, to restrictions of masses and mixings of quarks and leptons. We explore the consequences of such embedding using the symmetry group conditions. We show how unitarity emerges from group properties and obtain the conditions it imposes on the parameters of embedding. We find that in some cases the predicted values of elements of U are compatible with the existing data fits. In the supersymmetric version of SO(10 such results are renormalization group invariant.
Hidden flavor symmetries of SO(10) GUT
Bajc, Borut; Smirnov, Alexei Yu.
2016-08-01
The Yukawa interactions of the SO(10) GUT with fermions in 16-plets (as well as with singlets) have certain intrinsic ("built-in") symmetries which do not depend on the model parameters. Thus, the symmetric Yukawa interactions of the 10 and 126 dimensional Higgses have intrinsic discrete Z2 ×Z2 symmetries, while the antisymmetric Yukawa interactions of the 120 dimensional Higgs have a continuous SU(2) symmetry. The couplings of SO(10) singlet fermions with fermionic 16-plets have U(1) 3 symmetry. We consider a possibility that some elements of these intrinsic symmetries are the residual symmetries, which originate from the (spontaneous) breaking of a larger symmetry group Gf. Such an embedding leads to the determination of certain elements of the relative mixing matrix U between the matrices of Yukawa couplings Y10, Y126, Y120, and consequently, to restrictions of masses and mixings of quarks and leptons. We explore the consequences of such embedding using the symmetry group conditions. We show how unitarity emerges from group properties and obtain the conditions it imposes on the parameters of embedding. We find that in some cases the predicted values of elements of U are compatible with the existing data fits. In the supersymmetric version of SO(10) such results are renormalization group invariant.
Applications of chiral symmetry
Energy Technology Data Exchange (ETDEWEB)
Pisarski, R.D.
1995-03-01
The author discusses several topics in the applications of chiral symmetry at nonzero temperature. First, where does the rho go? The answer: up. The restoration of chiral symmetry at a temperature T{sub {chi}} implies that the {rho} and a{sub 1} vector mesons are degenerate in mass. In a gauged linear sigma model the {rho} mass increases with temperature, m{sub {rho}}(T{sub {chi}}) > m{sub {rho}}(0). The author conjectures that at T{sub {chi}} the thermal {rho} - a{sub 1}, peak is relatively high, at about {approximately}1 GeV, with a width approximately that at zero temperature (up to standard kinematic factors). The {omega} meson also increases in mass, nearly degenerate with the {rho}, but its width grows dramatically with temperature, increasing to at least {approximately}100 MeV by T{sub {chi}}. The author also stresses how utterly remarkable the principle of vector meson dominance is, when viewed from the modern perspective of the renormalization group. Secondly, he discusses the possible appearance of disoriented chiral condensates from {open_quotes}quenched{close_quotes} heavy ion collisions. It appears difficult to obtain large domains of disoriented chiral condensates in the standard two flavor model. This leads to the last topic, which is the phase diagram for QCD with three flavors, and its proximity to the chiral critical point. QCD may be very near this chiral critical point, and one might thereby generated large domains of disoriented chiral condensates.
Energy Technology Data Exchange (ETDEWEB)
El Naschie, M.S. [King Abdul Aziz City of Science and Technology, Riyadh (Saudi Arabia)
2007-04-15
The notion of a particle-like state emerging from a symmetry breaking is given five corresponding pictures. We start from a geometrical picture in two dimensions involving a modular curve constructed using 336 triangles. The same number of building blocks is found again, this time as 336 contact points in the ten dimensional space of super string theory in the context of the largest kissing number of lattice sphere packing. The next corresponding representation is an abstract one pertinent to the order of the simple linear Lie group SL(2, n) in seven dimensions (n = 7) which leads to 336 symmetries. Subsequently a tensorial picture is given using the Riemannian tensor of relativity theory but this time in an eight dimensional space (n = 8) for which the number of independent components is again 336. Finally we use a physical string theory related picture in the 12 dimensions of F theory to find 336 moduli space dimensions representing the instanton cells of our theory. It is evident that the five preceding pictures are ten fold interconnected and exchangeable. This additional mental freedom does not only enhance the feeling of understanding, but also facilitates the easy recognition of complex mathematical relations and its connection to the physical concepts.
Directory of Open Access Journals (Sweden)
Mauro Bonazzi
2013-05-01
Full Text Available The chapters dedicated to Parmenides and Plato play a decisive role in the composition strategy of the Adversus Colotem, since this is where Plutarch most clearly defines the background dualist thesis that will help demonstrate that Platonism is superior to Epicurism. By showing Parmenides too as a dualist engaged in distinguishing between the sensible and the intelligible world, Plutarch structures a history of ancient philosophy entirely focused on Plato. These chapters also bear witness of another centre of interest, namely Aristoteles (§ 14, who, despite the criticism he aimed at the theory of ideas, is not completely refuted, but rather used as a possible ally against epicurean materialists, Plutarch’s true bête noire.Les chapitres consacrés à Parménide et Platon jouent un rôle décisif dans la stratégie de composition de l’Adversus Colotem : c’est là en effet que Plutarque définit de la manière la plus claire la thèse dualiste de fond qui va servir à démontrer la supériorité du platonisme sur l’épicurisme. En présentant Parménide lui aussi comme un dualiste occupé à distinguer entre monde sensible et monde intelligible, Plutarque articule une histoire de la philosophie antique entièrement centrée sur Platon. Les chapitres témoignent ensuite d’un autre centre d’intérêt, avec la mention d’Aristote (§ 14, lequel, malgré les critiques qu’il adresse à la théorie des idées, n’est pas complètement réfuté, mais plutôt utilisé comme un allié possible contre les matérialistes épicuriens, la véritable « bête noire » de Plutarque.I capitoli dedicati a Parmenide e Platone giocano un ruolo decisivo nella strategia compositiva dell’Adversus Colotem: è qui infatti che Plutarco delinea nel modo più chiaro la tesi dualistica di fondo che servirà a dimostrare la superiorità del platonismo sull’epicureismo. Presentando anche Parmenide come un dualista, impegnato a distinguere tra mondo
Hidden Symmetries of Stochastic Models
Directory of Open Access Journals (Sweden)
Boyka Aneva
2007-05-01
Full Text Available In the matrix product states approach to $n$ species diffusion processes the stationary probability distribution is expressed as a matrix product state with respect to a quadratic algebra determined by the dynamics of the process. The quadratic algebra defines a noncommutative space with a $SU_q(n$ quantum group action as its symmetry. Boundary processes amount to the appearance of parameter dependent linear terms in the algebraic relations and lead to a reduction of the $SU_q(n$ symmetry. We argue that the boundary operators of the asymmetric simple exclusion process generate a tridiagonal algebra whose irriducible representations are expressed in terms of the Askey-Wilson polynomials. The Askey-Wilson algebra arises as a symmetry of the boundary problem and allows to solve the model exactly.
Bouwknegt, P G
1995-01-01
W-symmetry is an extension of conformal symmetry in two dimensions. Since its introduction in 1985, W-symmetry has become one of the central notions in the study of two-dimensional conformal field theory. The mathematical structures that underlie W-symmetry are so-called W-algebras, which are higher-spin extensions of the Virasoro algebra. This book contains a collection of papers on W-symmetry, covering the period from 1985 through 1993. Its main focus is the construction of W-algebras and their representation theory. A recurrent theme is the intimate connection between W-algebras and affine
Cheng, Meng; Zaletel, Michael; Barkeshli, Maissam; Vishwanath, Ashvin; Bonderson, Parsa
2016-10-01
The Lieb-Schultz-Mattis theorem and its higher-dimensional generalizations by Oshikawa and Hastings require that translationally invariant 2D spin systems with a half-integer spin per unit cell must either have a continuum of low energy excitations, spontaneously break some symmetries, or exhibit topological order with anyonic excitations. We establish a connection between these constraints and a remarkably similar set of constraints at the surface of a 3D interacting topological insulator. This, combined with recent work on symmetry-enriched topological phases with on-site unitary symmetries, enables us to develop a framework for understanding the structure of symmetry-enriched topological phases with both translational and on-site unitary symmetries, including the effective theory of symmetry defects. This framework places stringent constraints on the possible types of symmetry fractionalization that can occur in 2D systems whose unit cell contains fractional spin, fractional charge, or a projective representation of the symmetry group. As a concrete application, we determine when a topological phase must possess a "spinon" excitation, even in cases when spin rotational invariance is broken down to a discrete subgroup by the crystal structure. We also describe the phenomena of "anyonic spin-orbit coupling," which may arise from the interplay of translational and on-site symmetries. These include the possibility of on-site symmetry defect branch lines carrying topological charge per unit length and lattice dislocations inducing degeneracies protected by on-site symmetry.
L’ORALITÀ A SCUOLA, DA PLATONE AL PORTFOLIO EUROPEO DELLE LINGUE
Directory of Open Access Journals (Sweden)
Alberto A. Sobrero
2010-09-01
Full Text Available L'oralità risulta primaria rispetto alla scrittura sia per quanto riguarda la razza umana (filogenesi sia per quanto riguarda lo sviluppo individuale (ontogenesi, tuttavia essa ha sempre goduto di minor prestigio della scrittura. Nella prima parte di questo articolo sono ricostruiti i diversi momenti in cui questa gerarchia è stata fondata e si è affermata stabilmente: dai contrasti epocali tra Socrate e Platone da una parte e i Sofisti dall'altra all'affermazione della centralità della scrittura da parte di Aristotele e degli aristotelici; fino, poi, all'Illuminismo, in cui l'oralità veniva ormai identificata con l'inciviltà, la rozzezza e l'arretratezza, posizione che in qualche misura permane ancora oggi. Nella seconda parte dell'articolo si ricostruisce il graduale recupero del valore dell'oralità nell'insegnamento linguistico, attraverso un'analisi dei programmi scolastici italiani, dalla Legge Casati del 1859 ai Programmi della scuola media e di quella elementare rispettivamente del 1979 e del 1985, alle più recenti "Indicazioni Moratti e infine alle "Indicazioni Fioroni". In queste ultime si sottolinea la necessità di finalizzare l'insegnamento dell'oralità anche a scopi interculturali più ampi, prioritari nella società attuale, quali il rispetto e la promozione delle differenze linguistiche e culturali, lo sviluppo del plurilinguismo; la centralità e l'autonomia dell'apprendente. Historically, the oral tradition has been more important than writing, both in human history (philogenesis and in individual, personal history (onthogenesis, but it has always had far less prestige. The first part of this paper surveys important moments in the formation and establishment of this hierarchy, starting from the fundamental contrast between the Sophists on the one hand, and Socrates and Plato from the other, to the centrality of Aristotle and Aristotelianism, up to the Age of Enlightenment and the identification between orality
Symmetries of partial differential equations
Gaussier, Hervé; Merker, Joël
2004-01-01
We establish a link between the study of completely integrable systems of partial differential equations and the study of generic submanifolds in C^n. Using the recent developments of Cauchy-Riemann geometry we provide the set of symmetries of such a system with a Lie group structure. Finally we determine the precise upper bound of the dimension of this Lie group for some specific systems of partial differential equations.
Dynamics symmetries of Hamiltonian system on time scales
Energy Technology Data Exchange (ETDEWEB)
Peng, Keke, E-mail: pengkeke88@126.com; Luo, Yiping, E-mail: zjstulyp@126.com [Department of Physics, Zhejiang Sci-Tech University, Hangzhou 310018 (China)
2014-04-15
In this paper, the dynamics symmetries of Hamiltonian system on time scales are studied. We study the symmetries and quantities based on the calculation of variation and Lie transformation group. Particular focus lies in: the Noether symmetry leads to the Noether conserved quantity and the Lie symmetry leads to the Noether conserved quantity if the infinitesimal transformations satisfy the structure equation. As the new application of result, at end of the article, we give a simple example of Noether symmetry and Lie symmetry on time scales.
Dynamics symmetries of Hamiltonian system on time scales
Peng, Keke; Luo, Yiping
2014-04-01
In this paper, the dynamics symmetries of Hamiltonian system on time scales are studied. We study the symmetries and quantities based on the calculation of variation and Lie transformation group. Particular focus lies in: the Noether symmetry leads to the Noether conserved quantity and the Lie symmetry leads to the Noether conserved quantity if the infinitesimal transformations satisfy the structure equation. As the new application of result, at end of the article, we give a simple example of Noether symmetry and Lie symmetry on time scales.
Energy Technology Data Exchange (ETDEWEB)
Heeck, Julian
2013-04-15
Augmenting the Standard Model by three right-handed neutrinos allows for an anomaly-free gauge group extension G{sub max}=U(1){sub B−L}×U(1){sub L{sub e−L{sub μ}}}×U(1){sub L{sub μ−L{sub τ}}}. Simple U(1) subgroups of G{sub max} can be used to impose structure on the righthanded neutrino mass matrix, which then propagates to the active neutrino mass matrix via the seesaw mechanism. We show how this framework can be used to gauge the approximate lepton-number symmetries behind the normal, inverted, and quasidegenerate neutrino mass spectrum, and also how to generate texture-zeros and vanishing minors in the neutrino mass matrix, leading to testable relations among mixing parameters.
PREFACE: Symmetries in Science XIV
Schuch, Dieter; Ramek, Michael
2010-04-01
Symmetries Logo This volume of the proceedings "Symmetries in Science XIV" is dedicated to the memory of our colleagues and dear friends Marcos Moshinsky and Yuriĭ Smirnov who regularly participated in these Symposia and were a great inspiration to many. We shall miss them. Dieter Schuch and Michael Ramek The international symposium "Symmetries in Science XIV" held at Collegium Mehrerau in Bregenz, Austria from July 19-24, 2009, attended by 32 scientists from 11 countries, was an experiment, performed by theoreticians. Aim of this experiment was to find out if the desire to revive or even continue this conference series was stronger than the very restricted pecuniary boundary conditions. It obviously was! After its establishment by Bruno Gruber in 1979, the biennial series settled in the very stimulating atmosphere of the monastery Mehrerau, which provided the ideal environment for a limited number of invited participants to exchange ideas, without parallel sessions, and pursue deeper discussions (at the latest in the evening at "Gasthof Lamm"). When the conference series terminated in 2003, former participants were quite disappointed. Meeting again at several (larger) conferences in subsequent years, there were repeated expressions of "the lack of a Bregenz-type meeting in our field nowadays" and the question of a possible "revitalization", even without external funding. After some hesitation, but also driven by our own desire to reinstate the series, we consulted Bruno who not only approved wholeheartedly but also offered his full support. It all finally led to the symposium in July 2009. The atmosphere was really like in the "good old days" and the interesting and thought-provoking presentations culminated in the publication of these Proceedings. We are grateful to Carl Bender for establishing contact with IOP making it possible for us to publish these Proceedings in the Journal of Physics Conference Series. A majority of the participants contributed to these
Large neutrino mixing from large discrete symmetries
Energy Technology Data Exchange (ETDEWEB)
Neder, Thomas; King, Stephen F.; Stuart, Alexander J. [School of Physics and Astronomy, University of Southampton (United Kingdom)
2013-07-01
Several finite groups that are candidates for a flavor symmetry of leptons are investigated. Promising candidates are amongst others the groups Δ(150) and Δ(600). The group theory of these groups as well as results for the lepton mixing parameters resulting from these groups are presented.
Hidden flavor symmetries of SO(10) GUT
Bajc, Borut
2016-01-01
The Yukawa interactions of the SO(10) GUT with fermions in 16-plets (as well as with singlets) have certain intrinsic ("built-in") symmetries which do not depend on the model parameters. Thus, the symmetric Yukawa interactions of the 10 and 126 dimensional Higgses have intrinsic discrete $Z_2\\times Z_2$ symmetries, while the antisymmetric Yukawa interactions of the 120 dimensional Higgs have a continuous SU(2) symmetry. The couplings of SO(10) singlet fermions with fermionic 16-plets have $U(1)^3$ symmetry. We consider a possibility that some elements of these intrinsic symmetries are the residual symmetries, which originate from the (spontaneous) breaking of a larger symmetry group $G_f$. Such an embedding leads to the determination of certain elements of the relative mixing matrix $U$ between the matrices of Yukawa couplings $Y_{10}$, $Y_{126}$, $Y_{120}$, and consequently, to restrictions of masses and mixings of quarks and leptons. We explore the consequences of such embedding using the symmetry group con...
ON THE NOETHER SYMMETRY AND LIE SYMMETRY OF MECHANICAL SYSTEMS
Institute of Scientific and Technical Information of China (English)
梅凤翔; 郑改华
2002-01-01
The Noether symmetry is an invariance of Hamilton action under infinitesimal transformations of time and the coordinates. The Lie symmetry is an invariance of the differential equations of motion under the transformations. In this paper, the relation between these two symmetries is proved definitely and firstly for mechanical systems. The results indicate that all the Noether symmetries are Lie symmetries for Lagrangian systems meanwhile a Noether symmetry is a Lie symmetry for the general holonomic or nonholonomic systems provided that some conditions hold.
Quantized Response and Topological Magnetic Insulators with Inversion Symmetry
Turner, A.M.; Zhang, Y.; Mong, R.S.K.; Vishwanath, A.
2012-01-01
We study three-dimensional insulators with inversion symmetry in which other point group symmetries, such as time reversal, are generically absent. We find that certain information about such materials’ behavior is determined by just the eigenvalues under inversion symmetry of occupied states at
Quantized Response and Topological Magnetic Insulators with Inversion Symmetry
Turner, A.M.; Zhang, Y.; Mong, R.S.K.; Vishwanath, A.
2012-01-01
We study three-dimensional insulators with inversion symmetry in which other point group symmetries, such as time reversal, are generically absent. We find that certain information about such materials’ behavior is determined by just the eigenvalues under inversion symmetry of occupied states at tim
Leptonic Dirac CP Violation Predictions from Residual Discrete Symmetries
Girardi, I; Stuart, Alexander J; Titov, A V
2016-01-01
Assuming that the observed pattern of 3-neutrino mixing is related to the existence of a (lepton) flavour symmetry, corresponding to a non-Abelian discrete symmetry group $G_f$, and that $G_f$ is broken to specific residual symmetries $G_e$ and $G_\
Anomalous Symmetry Fractionalization and Surface Topological Order
Directory of Open Access Journals (Sweden)
Xie Chen
2015-10-01
Full Text Available In addition to possessing fractional statistics, anyon excitations of a 2D topologically ordered state can realize symmetry in distinct ways, leading to a variety of symmetry-enriched topological (SET phases. While the symmetry fractionalization must be consistent with the fusion and braiding rules of the anyons, not all ostensibly consistent symmetry fractionalizations can be realized in 2D systems. Instead, certain “anomalous” SETs can only occur on the surface of a 3D symmetry-protected topological (SPT phase. In this paper, we describe a procedure for determining whether a SET of a discrete, on-site, unitary symmetry group G is anomalous or not. The basic idea is to gauge the symmetry and expose the anomaly as an obstruction to a consistent topological theory combining both the original anyons and the gauge fluxes. Utilizing a result of Etingof, Nikshych, and Ostrik, we point out that a class of obstructions is captured by the fourth cohomology group H^{4}(G,U(1, which also precisely labels the set of 3D SPT phases, with symmetry group G. An explicit procedure for calculating the cohomology data from a SET is given, with the corresponding physical intuition explained. We thus establish a general bulk-boundary correspondence between the anomalous SET and the 3D bulk SPT whose surface termination realizes it. We illustrate this idea using the chiral spin liquid [U(1_{2}] topological order with a reduced symmetry Z_{2}×Z_{2}⊂SO(3, which can act on the semion quasiparticle in an anomalous way. We construct exactly solved 3D SPT models realizing the anomalous surface terminations and demonstrate that they are nontrivial by computing three-loop braiding statistics. Possible extensions to antiunitary symmetries are also discussed.
The zonal satellite problem. III Symmetries
Directory of Open Access Journals (Sweden)
Mioc V.
2002-01-01
Full Text Available The two-body problem associated with a force field described by a potential of the form U =Sum(k=1,n ak/rk (r = distance between particles, ak = real parameters is resumed from the only standpoint of symmetries. Such symmetries, expressed in Hamiltonian coordinates, or in standard polar coordinates, are recovered for McGehee-type coordinates of both collision-blow-up and infinity-blow-up kind. They form diffeomorphic commutative groups endowed with a Boolean structure. Expressed in Levi-Civita’s coordinates, the problem exhibits a larger group of symmetries, also commutative and presenting a Boolean structure.
From physical symmetries to emergent gauge symmetries
Energy Technology Data Exchange (ETDEWEB)
Barceló, Carlos [Instituto de Astrofísica de Andalucía (IAA-CSIC),Glorieta de la Astronomía, 18008 Granada (Spain); Carballo-Rubio, Raúl [Instituto de Astrofísica de Andalucía (IAA-CSIC), Glorieta de la Astronomía, 18008 Granada (Spain); Laboratory for Quantum Gravity & Strings,Department of Mathematics & Applied Mathematics, University of Cape Town,Private Bag, Rondebosch 7701 (South Africa); Di Filippo, Francesco [Instituto de Astrofísica de Andalucía (IAA-CSIC), Glorieta de la Astronomía, 18008 Granada (Spain); Dipartamento di Scienze Fisiche “E.R. Caianiello”, Università di Salerno,I-84081 Fisciano (Italy); Garay, Luis J. [Departamento de Física Teórica II, Universidad Complutense de Madrid, 28040 Madrid (Spain); Instituto de Estructura de la Materia (IEM-CSIC), Serrano 121, 28006 Madrid (Spain)
2016-10-17
Gauge symmetries indicate redundancies in the description of the relevant degrees of freedom of a given field theory and restrict the nature of observable quantities. One of the problems faced by emergent theories of relativistic fields is to understand how gauge symmetries can show up in systems that contain no trace of these symmetries at a more fundamental level. In this paper we start a systematic study aimed to establish a satisfactory mathematical and physical picture of this issue, dealing first with abelian field theories. We discuss how the trivialization, due to the decoupling and lack of excitation of some degrees of freedom, of the Noether currents associated with physical symmetries leads to emergent gauge symmetries in specific situations. An example of a relativistic field theory of a vector field is worked out in detail in order to make explicit how this mechanism works and to clarify the physics behind it. The interplay of these ideas with well-known results of importance to the emergent gravity program, such as the Weinberg-Witten theorem, are discussed.
From physical symmetries to emergent gauge symmetries
Barceló, Carlos; Carballo-Rubio, Raúl; Di Filippo, Francesco; Garay, Luis J.
2016-10-01
Gauge symmetries indicate redundancies in the description of the relevant degrees of freedom of a given field theory and restrict the nature of observable quantities. One of the problems faced by emergent theories of relativistic fields is to understand how gauge symmetries can show up in systems that contain no trace of these symmetries at a more fundamental level. In this paper we start a systematic study aimed to establish a satisfactory mathematical and physical picture of this issue, dealing first with abelian field theories. We discuss how the trivialization, due to the decoupling and lack of excitation of some degrees of freedom, of the Noether currents associated with physical symmetries leads to emergent gauge symmetries in specific situations. An example of a relativistic field theory of a vector field is worked out in detail in order to make explicit how this mechanism works and to clarify the physics behind it. The interplay of these ideas with well-known results of importance to the emergent gravity program, such as the Weinberg-Witten theorem, are discussed.
From physical symmetries to emergent gauge symmetries
Barceló, Carlos; Di Filippo, Francesco; Garay, Luis J
2016-01-01
Gauge symmetries indicate redundancies in the description of the relevant degrees of freedom of a given field theory and restrict the nature of observable quantities. One of the problems faced by emergent theories of relativistic fields is to understand how gauge symmetries can show up in systems that contain no trace of these symmetries at a more fundamental level. In this paper we start a systematic study aimed to establish a satisfactory mathematical and physical picture of this issue, dealing first with abelian field theories. We discuss how the trivialization, due to the decoupling and lack of excitation of some degrees of freedom, of the Noether currents associated with physical symmetries leads to emergent gauge symmetries in specific situations. An example of a relativistic field theory of a vector field is worked out in detail in order to make explicit how this mechanism works and to clarify the physics behind it. The interplay of these ideas with well-known results of importance to the emergent grav...
Optimization leads to symmetry
Institute of Scientific and Technical Information of China (English)
Chenghong WANG; Yuqian GUO; Daizhan CHENG
2004-01-01
The science of complexity studies the behavior and properties of complex systems in nature and human society.Particular interest has been put on their certain simple common properties.Symmetry is one of such properties.Symmetric phenomena can be found in many complex systems.The purpose of this paper is to reveal the internal reason of the symmetry.Using some physical systems and geometric objects,the paper shows that many symmetries are caused by optimization under certain criteria.It has also been revealed that an evolutional process may lead to symmetry.
Symmetries in atmospheric sciences
Bihlo, Alexander
2009-01-01
Selected applications of symmetry methods in the atmospheric sciences are reviewed briefly. In particular, focus is put on the utilisation of the classical Lie symmetry approach to derive classes of exact solutions from atmospheric models. This is illustrated with the barotropic vorticity equation. Moreover, the possibility for construction of partially-invariant solutions is discussed for this model. A further point is a discussion of using symmetries for relating different classes of differential equations. This is illustrated with the spherical and the potential vorticity equation. Finally, discrete symmetries are used to derive the minimal finite-mode version of the vorticity equation first discussed by E. Lorenz (1960) in a sound mathematical fashion.
Applications of Symmetry Methods to the Theory of Plasma Physics
Giampaolo Cicogna; Francesco Ceccherini; Francesco Pegoraro
2006-01-01
The theory of plasma physics offers a number of nontrivial examples of partial differential equations, which can be successfully treated with symmetry methods. We propose three different examples which may illustrate the reciprocal advantage of this "interaction" between plasma physics and symmetry techniques. The examples include, in particular, the complete symmetry analysis of system of two PDE's, with the determination of some conditional and partial symmetries, the construction of group-...
S4 as a natural flavor symmetry for lepton mixing
Bazzocchi, Federica
2008-01-01
Group theoretical motivations seem to indicate the discrete symmetry S4 as the minimal flavour symmetry compatible with tribimaximal neutrino mixing. We prove in a model independent way that indeed S4 can realize exact TriBimaximal mixing through different symmetry breaking patterns. We present two models in which lepton TriBimaximal mixing is realized in different ways and for each one we discuss the superpotential that leads to the correct breaking of the flavor symmetry.
Bregestovski, Piotr
2012-01-01
On May 10th 2010 Platon Grigorevitch Kostyuk sadly left us at the age of 85. He was a talented scientist, a brilliant experimenter, an outstanding organizer of science and an excellent teacher. Platon Kostyuk was born in 1924 in Kiev, Ukraine. He obtained a double education: a graduate of the Kiev University Department of Biology in 1946 and the Kiev Medical Institute in 1949, he became a pioneer in neuroscience, the first in the Soviet Union to use microelectrodes for intracellular recording of electrical signals in neurons. Despite the difficulties for international travel for those living behind the Iron Curtain, he was able to present his work at the International Congress of Physiology in Buenos Aires in 1959 and here met Prof. John Eccles who invited him to work at the University of Canberra in Australia in 1960–1961. This was the start of an outstanding international career, complementing his creative achievements in the Soviet Union. In 1966 P.G. Kostyuk became director of the Bogomoletz Institute of Physiology in Kiev, which he headed for nearly 45 years. Under his direction this Institute became a leading centre for neuroscience, renowned not only in the Soviet Union but also internationally. New directions of research were developed in cell physiology, molecular biophysics and neurophysiology. Several important discoveries were made including the development of a method for intracellular perfusion, evidence for a calcium-dependent conductance in nerve cells and the discovery of new types of ion channels. Elected to the Ukraine Academy of Science in 1969 and Grand Academician of the Soviet Academy of Science in 1974, Kostyuk has also been honoured by many international societies. He is the author of more than 650 articles, 17 monographs and 7 discoveries and was the creator and editor of two scientific journals: "Neurophysiology" and "Neuroscience". The outstanding career and multifaceted activities of Academician Platon Kostyuk form a pyramid of
Ermakov's Superintegrable Toy and Nonlocal Symmetries
Leach, P. G. L.; Karasu Kalkanli, A.; Nucci, M. C.; Andriopoulos, K.
2005-11-01
We investigate the symmetry properties of a pair of Ermakov equations. The system is superintegrable and yet possesses only three Lie point symmetries with the algebra sl(2, R). The number of point symmetries is insufficient and the algebra unsuitable for the complete specification of the system. We use the method of reduction of order to reduce the nonlinear fourth-order system to a third-order system comprising a linear second-order equation and a conservation law. We obtain the representation of the complete symmetry group from this system. Four of the required symmetries are nonlocal and the algebra is the direct sum of a one-dimensional Abelian algebra with the semidirect sum of a two-dimensional solvable algebra with a two-dimensional Abelian algebra. The problem illustrates the difficulties which can arise in very elementary systems. Our treatment demonstrates the existence of possible routes to overcome these problems in a systematic fashion.
Ermakov's Superintegrable Toy and Nonlocal Symmetries
Directory of Open Access Journals (Sweden)
P.G.L. Leach
2005-11-01
Full Text Available We investigate the symmetry properties of a pair of Ermakov equations. The system is superintegrable and yet possesses only three Lie point symmetries with the algebra sl(2, R. The number of point symmetries is insufficient and the algebra unsuitable for the complete specification of the system. We use the method of reduction of order to reduce the nonlinear fourth-order system to a third-order system comprising a linear second-order equation and a conservation law. We obtain the representation of the complete symmetry group from this system. Four of the required symmetries are nonlocal and the algebra is the direct sum of a one-dimensional Abelian algebra with the semidirect sum of a two-dimensional solvable algebra with a two-dimensional Abelian algebra. The problem illustrates the difficulties which can arise in very elementary systems. Our treatment demonstrates the existence of possible routes to overcome these problems in a systematic fashion.
Symmetry in critical random Boolean network dynamics
Hossein, Shabnam; Reichl, Matthew D.; Bassler, Kevin E.
2014-04-01
Using Boolean networks as prototypical examples, the role of symmetry in the dynamics of heterogeneous complex systems is explored. We show that symmetry of the dynamics, especially in critical states, is a controlling feature that can be used both to greatly simplify analysis and to characterize different types of dynamics. Symmetry in Boolean networks is found by determining the frequency at which the various Boolean output functions occur. There are classes of functions that consist of Boolean functions that behave similarly. These classes are orbits of the controlling symmetry group. We find that the symmetry that controls the critical random Boolean networks is expressed through the frequency by which output functions are utilized by nodes that remain active on dynamical attractors. This symmetry preserves canalization, a form of network robustness. We compare it to a different symmetry known to control the dynamics of an evolutionary process that allows Boolean networks to organize into a critical state. Our results demonstrate the usefulness and power of using the symmetry of the behavior of the nodes to characterize complex network dynamics, and introduce an alternative approach to the analysis of heterogeneous complex systems.
Symmetry in Critical Random Boolean Networks Dynamics
Bassler, Kevin E.; Hossein, Shabnam
2014-03-01
Using Boolean networks as prototypical examples, the role of symmetry in the dynamics of heterogeneous complex systems is explored. We show that symmetry of the dynamics, especially in critical states, is a controlling feature that can be used to both greatly simplify analysis and to characterize different types of dynamics. Symmetry in Boolean networks is found by determining the frequency at which the various Boolean output functions occur. Classes of functions occur at the same frequency. These classes are orbits of the controlling symmetry group. We find the nature of the symmetry that controls the dynamics of critical random Boolean networks by determining the frequency of output functions utilized by nodes that remain active on dynamical attractors. This symmetry preserves canalization, a form of network robustness. We compare it to a different symmetry known to control the dynamics of an evolutionary process that allows Boolean networks to organize into a critical state. Our results demonstrate the usefulness and power of using symmetry to characterize complex network dynamics, and introduce a novel approach to the analysis of heterogeneous complex systems. This work was supported by the NSF through grants DMR-0908286 and DMR-1206839, and by the AFSOR and DARPA through grant FA9550-12-1-0405.
Symmetry in critical random Boolean network dynamics.
Hossein, Shabnam; Reichl, Matthew D; Bassler, Kevin E
2014-04-01
Using Boolean networks as prototypical examples, the role of symmetry in the dynamics of heterogeneous complex systems is explored. We show that symmetry of the dynamics, especially in critical states, is a controlling feature that can be used both to greatly simplify analysis and to characterize different types of dynamics. Symmetry in Boolean networks is found by determining the frequency at which the various Boolean output functions occur. There are classes of functions that consist of Boolean functions that behave similarly. These classes are orbits of the controlling symmetry group. We find that the symmetry that controls the critical random Boolean networks is expressed through the frequency by which output functions are utilized by nodes that remain active on dynamical attractors. This symmetry preserves canalization, a form of network robustness. We compare it to a different symmetry known to control the dynamics of an evolutionary process that allows Boolean networks to organize into a critical state. Our results demonstrate the usefulness and power of using the symmetry of the behavior of the nodes to characterize complex network dynamics, and introduce an alternative approach to the analysis of heterogeneous complex systems.
Artificial Neural Networks, Symmetries and Differential Evolution
Urfalioglu, Onay
2010-01-01
Neuroevolution is an active and growing research field, especially in times of increasingly parallel computing architectures. Learning methods for Artificial Neural Networks (ANN) can be divided into two groups. Neuroevolution is mainly based on Monte-Carlo techniques and belongs to the group of global search methods, whereas other methods such as backpropagation belong to the group of local search methods. ANN's comprise important symmetry properties, which can influence Monte-Carlo methods. On the other hand, local search methods are generally unaffected by these symmetries. In the literature, dealing with the symmetries is generally reported as being not effective or even yielding inferior results. In this paper, we introduce the so called Minimum Global Optimum Proximity principle derived from theoretical considerations for effective symmetry breaking, applied to offline supervised learning. Using Differential Evolution (DE), which is a popular and robust evolutionary global optimization method, we experi...
An Analysis of the Agency and Providence in Platonic, Aristotelian and Avicennan Metaphysics
Directory of Open Access Journals (Sweden)
S. Mahdi Emamijomeh
2014-01-01
Full Text Available The questions as to whether the cosmic order of this world is based on action/agent or not? And if an agent is involved and the world and what it contains have to be seen as action, could we declare the cosmic order a providential order? are among the problems which have always occupied the mind of philosophers. Reading through Platonic corpse leads us to the conclusion that he has founded his metaphysics upon the very idea of world of ideas. According to his works and words, Plato is a proponent of the theory of ideas. As a matter of fact, Plato's metaphysics lies in the theory of ideas. Plato illustrates the general makeup of the world of ideas and the way sensible objects stand in relation with the beings dwelling in the latter world by the well-known cave allegory in the seventh book of Republic. In his view, whatever we find around ourselves not only are not authentic realities but rather they are merely shadows of the truth. Every phenomenon has an essence or reality which is known as its form. The idea of Good overshadows the other ideas insofar as these latter ideas or forms are seen as the effects of the former. It seems we can take God, the One, Absolute Good, Absolute Beauty and Good in itself as expressions of the same reality which Plato has used in different contexts through his works. Along these terms some other notions have also been brought up like intellect, divine intellect, Demiurge, ideas and the particulars of material world. By explaining Plato's taking of these notions and terms, we believe, one can discover Platonic ontological system. In Republic, Plato argues that God is the creator of ideal bed and all other things, and he is the creator of intelligible entities (ideas. The One or reality as a whole not only contains ideas but the spirit too. The One is the final principle and the source of ideas and is beyond all human attributes. Having said these, it is not clear how reason gets itself related to the
An Analysis of the Agency and Providence in Platonic, Aristotelian and Avicennan Metaphysics
Directory of Open Access Journals (Sweden)
Vahideh Hadad
2013-12-01
Full Text Available The questions as to whether the cosmic order of this world is based on action/agent or not? And if an agent is involved and the world and what it contains have to be seen as action, could we declare the cosmic order a providential order? are among the problems which have always occupied the mind of philosophers. Reading through Platonic corpse leads us to the conclusion that he has founded his metaphysics upon the very idea of world of ideas. According to his works and words, Plato is a proponent of the theory of ideas. As a matter of fact, Plato's metaphysics lies in the theory of ideas. Plato illustrates the general makeup of the world of ideas and the way sensible objects stand in relation with the beings dwelling in the latter world by the well-known cave allegory in the seventh book of Republic. In his view, whatever we find around ourselves not only are not authentic realities but rather they are merely shadows of the truth. Every phenomenon has an essence or reality which is known as its form. The idea of Good overshadows the other ideas insofar as these latter ideas or forms are seen as the effects of the former. It seems we can take God, the One, Absolute Good, Absolute Beauty and Good in itself as expressions of the same reality which Plato has used in different contexts through his works. Along these terms some other notions have also been brought up like intellect, divine intellect, Demiurge, ideas and the particulars of material world. By explaining Plato's taking of these notions and terms, we believe, one can discover Platonic ontological system. In Republic, Plato argues that God is the creator of ideal bed and all other things, and he is the creator of intelligible entities (ideas. The One or reality as a whole not only contains ideas but the spirit too. The One is the final principle and the source of ideas and is beyond all human attributes. Having said these, it is not clear how reason gets itself related to the
Symbolic Detection of Permutation and Parity Symmetries of Evolution Equations
Alghamdi, Moataz
2017-06-18
We introduce a symbolic computational approach to detecting all permutation and parity symmetries in any general evolution equation, and to generating associated invariant polynomials, from given monomials, under the action of these symmetries. Traditionally, discrete point symmetries of differential equations are systemically found by solving complicated nonlinear systems of partial differential equations; in the presence of Lie symmetries, the process can be simplified further. Here, we show how to find parity- and permutation-type discrete symmetries purely based on algebraic calculations. Furthermore, we show that such symmetries always form groups, thereby allowing for the generation of new group-invariant conserved quantities from known conserved quantities. This work also contains an implementation of the said results in Mathematica. In addition, it includes, as a motivation for this work, an investigation of the connection between variational symmetries, described by local Lie groups, and conserved quantities in Hamiltonian systems.
Marchis, Iuliana
2009-01-01
Symmetry is one of the fundamental concepts in Geometry. It is a Mathematical concept, which can be very well connected with Art and Ethnography. The aim of the article is to show how to link the geometrical concept symmetry with interculturality. For this mosaics from different countries are used.
2016-01-01
The Symmetry Festival is a science and art program series, the most important periodic event (see its history) to bring together scientists, artists, educators and practitioners interested in symmetry (its roots, what is behind, applications, etc.), or in the consequences of its absence.
Schaft, A.J. van der
1987-01-01
It is argued that the existence of symmetries may simplify, as in classical mechanics, the solution of optimal control problems. A procedure for obtaining symmetries for the optimal Hamiltonian resulting from the Maximum Principle is given; this avoids the actual calculation of the optimal
Dirac neutrinos from flavor symmetry
Aranda, Alfredo; Morisi, S; Peinado, E; Valle, J W F
2013-01-01
We present a model where Majorana neutrino mass terms are forbidden by the flavor symmetry group Delta(27). Neutrinos are Dirac fermions and their masses arise in the same way as that of the charged fermions, due to very small Yukawa couplings. The model fits current neutrino oscillation data and correlates the octant of the atmospheric angle with the magnitude of the lightest neutrino mass, with maximal mixing excluded for any neutrino mass
Denton, Michael J; Marshall, Craig J; Legge, Michael
2002-12-07
Before the Darwinian revolution many biologists considered organic forms to be determined by natural law like atoms or crystals and therefore necessary, intrinsic and immutable features of the world order, which will occur throughout the cosmos wherever there is life. The search for the natural determinants of organic form-the celebrated "Laws of Form"-was seen as one of the major tasks of biology. After Darwin, this Platonic conception of form was abandoned and natural selection, not natural law, was increasingly seen to be the main, if not the exclusive, determinant of organic form. However, in the case of one class of very important organic forms-the basic protein folds-advances in protein chemistry since the early 1970s have revealed that they represent a finite set of natural forms, determined by a number of generative constructional rules, like those which govern the formation of atoms or crystals, in which functional adaptations are clearly secondary modifications of primary "givens of physics." The folds are evidently determined by natural law, not natural selection, and are "lawful forms" in the Platonic and pre-Darwinian sense of the word, which are bound to occur everywhere in the universe where the same 20 amino acids are used for their construction. We argue that this is a major discovery which has many important implications regarding the origin of proteins, the origin of life and the fundamental nature of organic form. We speculate that it is unlikely that the folds will prove to be the only case in nature where a set of complex organic forms is determined by natural law, and suggest that natural law may have played a far greater role in the origin and evolution of life than is currently assumed.
Partial Dynamical Symmetry as an Intermediate Symmetry Structure
Leviatan, A
2003-01-01
We introduce the notion of a partial dynamical symmetry for which a prescribed symmetry is neither exact nor completely broken. We survey the different types of partial dynamical symmetries and present empirical examples in each category.
Mei Symmetry and Lie Symmetry of Relativistic Hamiltonian System
Institute of Scientific and Technical Information of China (English)
FANG Jian-Hui; YAN Xiang-Hong; LI Hong; CHEN Pei-Sheng
2004-01-01
The Mei symmetry and the Lie symmetry of the relativistic Hamiltonian system are studied. The definition and criterion of the Mei symmetry and the Lie symmetry of the relativistic Hamiltonian system are given. The relationship between them is found. The conserved quantities which the Mei symmetry and the Lie symmetry lead to are obtained.An example is given to illustrate the application of the result.
Leviatan, A
2010-01-01
This overview focuses on the notion of partial dynamical symmetry (PDS), for which a prescribed symmetry is obeyed by a subset of solvable eigenstates, but is not shared by the Hamiltonian. General algorithms are presented to identify interactions, of a given order, with such intermediate-symmetry structure. Explicit bosonic and fermionic Hamiltonians with PDS are constructed in the framework of models based on spectrum generating algebras. PDSs of various types are shown to be relevant to nuclear spectroscopy, quantum phase transitions and systems with mixed chaotic and regular dynamics.
Schwichtenberg, Jakob
2015-01-01
This is a textbook that derives the fundamental theories of physics from symmetry. It starts by introducing, in a completely self-contained way, all mathematical tools needed to use symmetry ideas in physics. Thereafter, these tools are put into action and by using symmetry constraints, the fundamental equations of Quantum Mechanics, Quantum Field Theory, Electromagnetism, and Classical Mechanics are derived. As a result, the reader is able to understand the basic assumptions behind, and the connections between the modern theories of physics. The book concludes with first applications of the previously derived equations.
CP symmetry in optical systems
Dana, Brenda; Malomed, Boris A
2015-01-01
We introduce a model of a dual-core optical waveguide with opposite signs of the group-velocity-dispersion (GVD) in the two cores, and a phase-velocity mismatch between them. The coupler is embedded into an active host medium, which provides for the linear coupling of a gain-loss type between the two cores. The same system can be derived, without phenomenological assumptions, by considering the three-wave propagation in a medium with the quadratic nonlinearity, provided that the depletion of the second-harmonic pump is negligible. This linear system offers an optical realization of the charge-parity ($\\mathcal{CP}$) symmetry, while the addition of the intra-core cubic nonlinearity breaks the symmetry. By means of direct simulations and analytical approximations, it is demonstrated that the linear system generates expanding Gaussian states, while the nonlinear one gives rise to broad oscillating solitons, as well as a general family of stable stationary gap solitons.
Lepton mixing and discrete symmetries
Hernandez, D.; Smirnov, A. Yu.
2012-09-01
The pattern of lepton mixing can emerge from breaking a flavor symmetry in different ways in the neutrino and charged lepton Yukawa sectors. In this framework, we derive the model-independent conditions imposed on the mixing matrix by the structure of discrete groups of the von Dyck type which include A4, S4, and A5. We show that, in general, these conditions lead to at least two equations for the mixing parameters (angles and CP phase δ). These constraints, which correspond to unbroken residual symmetries, are consistent with nonzero 13 mixing and deviations from maximal 2-3 mixing. For the simplest case, which leads to an S4 model and reproduces the allowed values of the mixing angles, we predict δ=(90°-120°).
Applications of Symmetry Methods to the Theory of Plasma Physics
Directory of Open Access Journals (Sweden)
Giampaolo Cicogna
2006-02-01
Full Text Available The theory of plasma physics offers a number of nontrivial examples of partial differential equations, which can be successfully treated with symmetry methods. We propose three different examples which may illustrate the reciprocal advantage of this "interaction" between plasma physics and symmetry techniques. The examples include, in particular, the complete symmetry analysis of system of two PDE's, with the determination of some conditional and partial symmetries, the construction of group-invariant solutions, and the symmetry classification of a nonlinear PDE.
Golubitsky, Martin
2012-04-01
Many gaits of four-legged animals are described by symmetry. For example, when a horse paces it moves both left legs in unison and then both right legs and so on. The motion is described by two symmetries: Interchange front and back legs, and swap left and right legs with a half-period phase shift. Biologists postulate the existence of a central pattern generator (CPG) in the neuronal system that sends periodic signals to the legs. CPGs can be thought of as electrical circuits that produce periodic signals and can be modeled by systems with symmetry. In this lecture we discuss animal gaits; use gait symmetries to construct a simplest CPG architecture that naturally produces quadrupedal gait rhythms; and make several testable predictions about gaits.
Gauge symmetry from decoupling
Energy Technology Data Exchange (ETDEWEB)
Wetterich, C., E-mail: c.wetterich@thphys.uni-heidelberg.de
2017-02-15
Gauge symmetries emerge from a redundant description of the effective action for light degrees of freedom after the decoupling of heavy modes. This redundant description avoids the use of explicit constraints in configuration space. For non-linear constraints the gauge symmetries are non-linear. In a quantum field theory setting the gauge symmetries are local and can describe Yang–Mills theories or quantum gravity. We formulate gauge invariant fields that correspond to the non-linear light degrees of freedom. In the context of functional renormalization gauge symmetries can emerge if the flow generates or preserves large mass-like terms for the heavy degrees of freedom. They correspond to a particular form of gauge fixing terms in quantum field theories.
Gauge symmetry from decoupling
Directory of Open Access Journals (Sweden)
C. Wetterich
2017-02-01
Full Text Available Gauge symmetries emerge from a redundant description of the effective action for light degrees of freedom after the decoupling of heavy modes. This redundant description avoids the use of explicit constraints in configuration space. For non-linear constraints the gauge symmetries are non-linear. In a quantum field theory setting the gauge symmetries are local and can describe Yang–Mills theories or quantum gravity. We formulate gauge invariant fields that correspond to the non-linear light degrees of freedom. In the context of functional renormalization gauge symmetries can emerge if the flow generates or preserves large mass-like terms for the heavy degrees of freedom. They correspond to a particular form of gauge fixing terms in quantum field theories.
CPT Symmetry Without Hermiticity
Mannheim, Philip D
2016-01-01
In the literature the $CPT$ theorem has only been established for Hamiltonians that are Hermitian. Here we extend the $CPT$ theorem to quantum field theories with non-Hermitian Hamiltonians. Our derivation is a quite minimal one as it requires only the time independent evolution of scalar products and invariance under complex Lorentz transformations. The first of these requirements does not force the Hamiltonian to be Hermitian. Rather, it forces its eigenvalues to either be real or to appear in complex conjugate pairs, forces the eigenvectors of such conjugate pairs to be conjugates of each other, and forces the Hamiltonian to admit of an antilinear symmetry. The latter requirement then forces this antilinear symmetry to be $CPT$, with Hermiticity of a Hamiltonian thus only being a sufficient condition for $CPT$ symmetry and not a necessary one. $CPT$ symmetry thus has primacy over Hermiticity, and it rather than Hermiticity should be taken as a guiding principle for constructing quantum theories. With confo...
Gauge symmetry from decoupling
Wetterich, C.
2017-02-01
Gauge symmetries emerge from a redundant description of the effective action for light degrees of freedom after the decoupling of heavy modes. This redundant description avoids the use of explicit constraints in configuration space. For non-linear constraints the gauge symmetries are non-linear. In a quantum field theory setting the gauge symmetries are local and can describe Yang-Mills theories or quantum gravity. We formulate gauge invariant fields that correspond to the non-linear light degrees of freedom. In the context of functional renormalization gauge symmetries can emerge if the flow generates or preserves large mass-like terms for the heavy degrees of freedom. They correspond to a particular form of gauge fixing terms in quantum field theories.
L’anagogie poétique. Un dialogue entre Virgile et Platon
Directory of Open Access Journals (Sweden)
Jelena Pilipović
2010-02-01
Full Text Available Établir des relations constructives entre la poésie de Virgile et certains aspects de la pensée platonicienne constitue le but de notre recherche, dont le texte présenté ici propose une esquisse. Cette recherche n’est fondée ni sur la notion d’influence ni sur celle d’analogie – la première exigeant une approche historique et biographique, la deuxième présupposant un parallélisme entre les deux œuvres antiques –, mais sur la notion de participation constructive. La notion pivot qui permet de défendre cette idée est le concept d’anagogie. L’anagogie ou l’ascension, décrite dans les textes originaux de Platon d’une manière plutôt poétique que théorétique (Phèdre, Symposion, sera incorporée dans le système philosophique de l’époque médioplatonicienne (Didaskalos d’Alkinoos : étant établi le télos suprême de l’existence humaine, elle représente la pénétration de l’âme dans le domaine éïdétique surpassant le monde sensible. Reflétée dans la structure autant que dans le corpus thématique de l’œuvre virgilienne, l’anagogie peut être proclamée comme l’un de ses principes créatifs. Sur le plan structural, la poétique de polysémie et l’idéal des significations cachées forment une hiérarchie sémantique, grâce à laquelle l’acte de lire devient une sorte d’ascension à travers le texte. La forme polysémique graduelle du texte virgilien est le fruit et l’objet central de cet article.The aim of this paper is to establish constructive relations between Virgilian poetry and some aspects of Plato’s thought. The research is based neither on the notion of influence, demanding a historical-biographical approach, nor on the notion of analogy, the two opera not being equal and their relation being causality instead of similarity, but on the notion of constructive participation. The key-point in defending this idea is, consequently, the concept of anagogy. Anagogy, or the
Superconductivity and symmetry breaking
Energy Technology Data Exchange (ETDEWEB)
Sarasua, L.G., E-mail: sarasua@fisica.edu.uy [Instituto de Fisica, Facultad de Ciencias, Universidad de la Republica, Montevideo (Uruguay)
2012-02-15
In the present work we consider the relation between superconductivity and spontaneous gauge symmetry breaking (SGBS). We show that ODLRO does not require in principle SBGS, even in the presence of particle number fluctuations, by examining exact solutions of a fermionic pairing model. The criteria become equivalent if a symmetry breaking field is allowed, which can be attributed to the interaction with the environment. However, superconducting states without SBGS are not forbidden.
Hamhalter, Jan; Turilova, Ekaterina
2017-02-01
Quantum symmetries of spectral lattices are studied. Basic properties of spectral order on A W ∗-algebras are summarized. Connection between projection and spectral automorphisms is clarified by showing that, under mild conditions, any spectral automorphism is a composition of function calculus and Jordan ∗-automorphism. Complete description of quantum spectral symmetries on Type I and Type II A W ∗-factors are completely described.
Baldo, M.; Burgio, G. F.
2016-11-01
The nuclear symmetry energy characterizes the variation of the binding energy as the neutron to proton ratio of a nuclear system is varied. This is one of the most important features of nuclear physics in general, since it is just related to the two component nature of the nuclear systems. As such it is one of the most relevant physical parameters that affect the physics of many phenomena and nuclear processes. This review paper presents a survey of the role and relevance of the nuclear symmetry energy in different fields of research and of the accuracy of its determination from the phenomenology and from the microscopic many-body theory. In recent years, a great interest was devoted not only to the Nuclear Matter symmetry energy at saturation density but also to its whole density dependence, which is an essential ingredient for our understanding of many phenomena. We analyze the nuclear symmetry energy in different realms of nuclear physics and astrophysics. In particular we consider the nuclear symmetry energy in relation to nuclear structure, astrophysics of Neutron Stars and supernovae, and heavy ion collision experiments, trying to elucidate the connections of these different fields on the basis of the symmetry energy peculiarities. The interplay between experimental and observational data and theoretical developments is stressed. The expected future developments and improvements are schematically addressed, together with most demanded experimental and theoretical advances for the next few years.
Nonlocal Symmetries and Exact Solutions for PIB Equation
Xin, Xiang-Peng; Miao, Qian; Chen, Yong
2012-09-01
In this paper, the symmetry group of the (2+1)-dimensional Painlevé integrable Burgers (PIB) equations is studied by means of the classical symmetry method. Ignoring the discussion of the infinite-dimensional subalgebra, we construct an optimal system of one-dimensional group invariant solutions. Furthermore, by using the conservation laws of the reduced equations, we obtain nonlocal symmetries and exact solutions of the PIB equations.
Nonlocal Symmetries and Exact Solutions for PIB Equation
Institute of Scientific and Technical Information of China (English)
辛祥鹏; 苗倩; 陈勇
2012-01-01
In this paper, the symmetry group of the is studied by means of the classical symmetry method （2＋l）-dimensionM Painlevd integrable Burgers （PIB） equations Ignoring the discussion of the infinite-dimensional subalgebra, we construct an optimal system of one-dimensional group invariant solutions. Furthermore, by using the conservation laws of the reduced equations, we obtain nonlocal symmetries and exact solutions of the PIB equations.
Symmetries and Exact Solutions of the Breaking Soliton Equation
Institute of Scientific and Technical Information of China (English)
陈美; 刘希强
2011-01-01
With the aid of the classical Lie group method and nonclassical Lie group method, we derive the classical Lie point symmetry and the nonclassical Lie point symmetry of （2＋1）-dimensional breaking soliton （BS） equation. Using the symmetries, we find six classical similarity reductions and two nonclassical similarity reductions of the BS equation. Varieties of exact solutions of the BS equation are obtained by solving the reduced equations.
Geometrical symmetries of nuclear systems: D(3h) and T(d) symmetries in light nuclei
Bijker, Roelof
2016-01-01
The role of discrete (or point-group) symmetries in alpha-cluster nuclei is discussed in the framework of the algebraic cluster model which describes the relative motion of the alpha-particles. Particular attention is paid to the discrete symmetry of the geometric arrangement of the alpha-particles, and the consequences for the structure of the corresponding rotational bands. The method is applied to study cluster states in the nuclei 12C and 16O. The observed level sequences can be understood in a simple way as a consequence of the underlying discrete symmetry that characterizes the geometrical configuration of the alpha-particles, i.e. an equilateral triangle with D(3h) symmetry for 12C, and a tetrahedron with T(d) symmetry for 16O. The structure of rotational bands provides a fingerprint of the underlying geometrical configuration of alpha-particles.
Permutation Symmetry Determines the Discrete Wigner Function
Zhu, Huangjun
2016-01-01
The Wigner function provides a useful quasiprobability representation of quantum mechanics, with applications in various branches of physics. Many nice properties of the Wigner function are intimately connected with the high symmetry of the underlying operator basis composed of phase point operators: any pair of phase point operators can be transformed to any other pair by a unitary symmetry transformation. We prove that, in the discrete scenario, this permutation symmetry is equivalent to the symmetry group being a unitary 2 design. Such a highly symmetric representation can only appear in odd prime power dimensions besides dimensions 2 and 8. It suffices to single out a unique discrete Wigner function among all possible quasiprobability representations. In the course of our study, we show that this discrete Wigner function is uniquely determined by Clifford covariance, while no Wigner function is Clifford covariant in any even prime power dimension.
Gait Symmetry in Children with Autism
Directory of Open Access Journals (Sweden)
Victoria L. Chester
2012-01-01
Full Text Available Most studies examining gait asymmetry have focused on infants and toddlers and have tended to use subjective methods of evaluating movement. No previous studies have examined gait symmetry in older children with autism using objective motion capture systems. The purpose of this paper was to quantify gait symmetry in children with autism versus age-matched controls. Fourteen children with autism (N=14 and twenty-two (N=22 age, height, and weight-matched controls participated in the study. An eight camera Vicon motion capture system and four Kistler force plates were used to compute temporal-spatial parameters and symmetry indices during walking. Group differences in these measures were tested using MANOVAs. No significant differences between the autism and control group were found for any of the temporal-spatial measures or symmetry indices. Therefore, results suggest that children with autism demonstrate typical symmetry or interlimb movement during gait. Further research is needed to examine the use of different gait inputs to the symmetry indices (e.g., joint angles and moments. A greater awareness of the movement patterns associated with autism may increase our understanding of this disorder and have important implications for treatment planning.
Symmetries, Supersymmetries, and Pairing in Nuclei
Balantekin, A B
2011-01-01
These summer school lectures cover the use of algebraic techniques in various subfields of nuclear physics. After a brief description of groups and algebras, concepts of dynamical symmetry, dynamical supersymmetry, and supersymmetric quantum mechanics are introduced. Appropriate tools such as quasiparticles, quasispin, and Bogoliubov transformations are discussed with an emphasis on group theoretical foundations of these tools. To illustrate these concepts three physics applications are worked out in some detail: i) Pairing in nuclear physics; ii) Subbarrier fusion and associated group transformations; and iii) Symmetries of neutrino mass and of a related neutrino many-body problem.
Kawamura, Yoshiharu
2015-01-01
We study the quantization of systems with local particle-ghost symmetries. The systems contain ordinary particles including gauge bosons and their counterparts obeying different statistics. The particle-ghost symmetry is a kind of fermionic symmetry, different from the space-time supersymmetry and the BRST symmetry. Subsidiary conditions on states guarantee the unitarity of systems.
Discrete flavor symmetries in D-brane models
Marchesano, Fernando; Vázquez-Mercado, Liliana
2013-01-01
We study the presence of discrete flavor symmetries in D-brane models of particle physics. By analyzing the compact extra dimensions of these models one can determine when such symmetries exist both in the context of intersecting and magnetized D-brane constructions. Our approach allows to distinguish between approximate and exact discrete symmetries, and it can be applied to compactification manifolds with continuous isometries or to manifolds that only contain discrete isometries, like Calabi-Yau three-folds. We analyze in detail the class of rigid D-branes models based on a Z_2 x Z'_2 toroidal orientifold, for which the flavor symmetry group is either the dihedral group D_4 or tensor products of it. We construct explicit Pati-Salam examples in which families transform in non-Abelian representations of the flavor symmetry group, constraining Yukawa couplings beyond the effect of massive U(1) D-brane symmetries.
Fuzzy ta/2 symmetries of straight chain conjugate polyene molecules
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
On the basis of our recent studies on the molecular fuzzy point group symmetry,we further probe into the more complicated planar one-dimensional fuzzy periodic molecules-straight chain conjugate polyene.Except for the fuzzy translation transformation,the space transformation of the fuzzy screw rotation and the glide plane will be referred to.In addition,other fuzzy point symmetry transformation lain in the space transformation is discussed.Usually there is a correlation between the fuzzy symmetry characterization caused by the transition of the point symmetry elements and by certain space symmetry transformation.For the molecular orbital,the irreducible representation component is analyzed besides the membership function of the fuzzy symmetry transformation.Also,we inquire into the relativity between some molecular property and the fuzzy symmetry characterization.
Symmetry Analysis and Exact Solutions of (2+1)-Dimensional Sawada-Kotera Equation
Institute of Scientific and Technical Information of China (English)
YU Jian-Ping; ZHI Hong-Yan; SUN Yong-Li; ZHANG Hong-Qing
2008-01-01
Based on the symbolic computation system Maple, the infinite-dimensional symmetry group of the (2+1)-dimensional Sawada Kotera equation is found by the classical Lie group method and the characterization of the group properties is given. The symmetry groups are used to perform the symmetry reduction. Moreover, with Lou's direct method that is based on Lax pairs, we obtain the symmetry transformations of the Sawada Kotera and Konopelchenko Dubrovsky equations, respectively.
Spek, Anthony L
2015-01-01
The completion of a crystal structure determination is often hampered by the presence of embedded solvent molecules or ions that are seriously disordered. Their contribution to the calculated structure factors in the least-squares refinement of a crystal structure has to be included in some way. Traditionally, an atomistic solvent disorder model is attempted. Such an approach is generally to be preferred, but it does not always lead to a satisfactory result and may even be impossible in cases where channels in the structure are filled with continuous electron density. This paper documents the SQUEEZE method as an alternative means of addressing the solvent disorder issue. It conveniently interfaces with the 2014 version of the least-squares refinement program SHELXL [Sheldrick (2015). Acta Cryst. C71. In the press] and other refinement programs that accept externally provided fixed contributions to the calculated structure factors. The PLATON SQUEEZE tool calculates the solvent contribution to the structure factors by back-Fourier transformation of the electron density found in the solvent-accessible region of a phase-optimized difference electron-density map. The actual least-squares structure refinement is delegated to, for example, SHELXL. The current versions of PLATON SQUEEZE and SHELXL now address several of the unnecessary complications with the earlier implementation of the SQUEEZE procedure that were a necessity because least-squares refinement with the now superseded SHELXL97 program did not allow for the input of fixed externally provided contributions to the structure-factor calculation. It is no longer necessary to subtract the solvent contribution temporarily from the observed intensities to be able to use SHELXL for the least-squares refinement, since that program now accepts the solvent contribution from an external file (.fab file) if the ABIN instruction is used. In addition, many twinned structures containing disordered solvents are now also
Invariants of broken discrete symmetries
Kalozoumis, P; Diakonos, F K; Schmelcher, P
2014-01-01
The parity and Bloch theorems are generalized to the case of broken global symmetry. Local inversion or translation symmetries are shown to yield invariant currents that characterize wave propagation. These currents map the wave function from an arbitrary spatial domain to any symmetry-related domain. Our approach addresses any combination of local symmetries, thus applying in particular to acoustic, optical and matter waves. Nonvanishing values of the invariant currents provide a systematic pathway to the breaking of discrete global symmetries.
SU(5) symmetry of spdfg interacting boson model
Institute of Scientific and Technical Information of China (English)
LI; Jingsheng(李京生); LIU; Yuxin(刘玉鑫); GAO; Peng(高鹏)
2003-01-01
The extended interacting boson model with s-, p-, d-, f- and g-bosons included (spdfg IBM)is investigated. The algebraic structure including the generators, the Casimir operators of the groups at the SU(5) dynamical symmetry and the branching rules of the irreducible representation reductions along the group chain are obtained. The typical energy spectrum of the symmetry is given.
Baldo, M
2016-01-01
The nuclear symmetry energy characterizes the variation of the binding energy as the neutron to proton ratio of a nuclear system is varied. This is one of the most important features of nuclear physics in general, since it is just related to the two component nature of the nuclear systems. As such it is one of the most relevant physical parameters that affect the physics of many phenomena and nuclear processes. This review paper presents a survey of the role and relevance of the nuclear symmetry energy in different fields of research and of the accuracy of its determination from the phenomenology and from the microscopic many-body theory. In recent years, a great interest was devoted not only to the Nuclear Matter symmetry energy at saturation density but also to its whole density dependence, which is an essential ingredient for our understanding of many phenomena. We analyze the nuclear symmetry energy in different realms of nuclear physics and astrophysics. In particular we consider the nuclear symmetry ene...
Energy Technology Data Exchange (ETDEWEB)
Joshipura, A.S. [Physical Research Laboratory, Navarangpura, Ahmedabad (India)
2008-01-15
The possible maximal mixing seen in the oscillations of atmospheric neutrinos has led to the postulate of {mu}-{tau} symmetry, which interchanges {nu}{sub {mu}} and {nu}{sub {tau}}. We argue that such a symmetry need not be special to neutrinos but can be extended to all fermions. The assumption that all fermion mass matrices are approximately invariant under the interchange of the second and the third generation fields is shown to be phenomenologically viable and has interesting consequences. In the quark sector, the smallness of V{sub ub} and V{sub cb} can be consequences of this approximate 2-3 symmetry. The same approximate symmetry can simultaneously lead to a large atmospheric mixing angle and can describe the leptonic mixing quite well. We identify two generic scenarios leading to this. One is based on the conventional type-I seesaw mechanism and the other follows from the type-II seesaw model. The latter requires a quasi-degenerate neutrino spectrum for obtaining large atmospheric neutrino mixing in the presence of an approximate {mu}-{tau} symmetry. (orig.)
Operational symmetries basic operations in physics
Saller, Heinrich
2017-01-01
This book describes the endeavour to relate the particle spectrum with representations of operational electroweak spacetime, in analogy to the atomic spectrum as characterizing representations of hyperbolic space. The spectrum of hyperbolic position space explains the properties of the nonrelativistic atoms; the spectrum of electroweak spacetime is hoped to explain those of the basic interactions and elementary particles. In this book, the theory of operational symmetries is developed from the numbers, from Plato’s and Kepler’s symmetries over the simple Lie groups to their applications in nonrelativistic, special relativistic and general relativistic quantum theories with the atomic spectrum for hyperbolic position and, in first attempts, the particle spectrum for electroweak spacetime. The standard model of elementary particles and interactions is characterized by a symmetry group. In general, as initiated by Weyl and stressed by Heisenberg, quantum theory can be built as a theory of operation groups an...
Wigner-Eckart theorem for induced symmetries
Energy Technology Data Exchange (ETDEWEB)
Klein, D.J. (Texas A and M University, Galveston (USA). Department of Marine Sciences); Seligman, T.H. (Universidad Nacional Autonoma de Mexico, Mexico City. Inst. de Fisica)
1982-01-01
A unified treatment is given for all group-theoretic problems arising from the evaluation of matrix elements involving operators and states of induced symmetries. To achieve this general treatment two group-theoretic theorems are proven, the first characterizing recoupling coefficients between different symmetry adaptation schemes, and the second making a double coset factorization of a group algebraic matrix basis element. A number of problems previously discussed in the literature, including the conventional Wigner-Eckart theorem and more recent double coset expansions of matrix elements, are realized as special cases in the present treatment. These results entail two new types of recoupling coefficients, namely DC coefficients and 3-symmetry symbols, so that some of their properties are indicated.
Gilmore-Perelomov symmetry based approach to photonic lattices
Vergara, Liliana Villanueva
2015-01-01
We revisit electromagnetic field propagation through tight-binding arrays of coupled photonic waveguides, with properties independent of the propagation distance, and recast it as a symmetry problem. We focus our analysis on photonic lattices with underlying symmetries given by three well-known groups, $SU(2)$, $SU(1,1)$ and Heisenberg-Weyl, to show that disperssion relations, normal states and impulse functions can be constructed following a Gilmore-Perelomov coherent state approach. Furthermore, this symmetry based approach can be followed for each an every lattice with an underlying symmetry given by a dynamical group.
History of electroweak symmetry breaking
Kibble, T W B
2015-01-01
In this talk, I recall the history of the development of the unified electroweak theory, incorporating the symmetry-breaking Higgs mechanism, as I saw it from my standpoint as a member of Abdus Salam's group at Imperial College. I start by describing the state of physics in the years after the Second World War, explain how the goal of a unified gauge theory of weak and electromagnetic interactions emerged, the obstacles encountered, in particular the Goldstone theorem, and how they were overcome, followed by a brief account of more recent history, culminating in the historic discovery of the Higgs boson in 2012.
Seeing Science through Symmetry
Gould, L. I.
Seeing Through Symmetry is a course that introduces non-science majors to the pervasive influence of symmetry in science. The concept of symmetry is usedboth as a link between subjects (such as physics, biology, mathematics, music, poetry, and art) and as a method within a subject. This is done through the development and use of interactive multimedia learning environments to stimulate learning. Computer-based labs enable the student to further explore the concept by being gently led from the arts to science. This talk is an update that includes some of the latest changes to the course. Explanations are given on methodology and how a variety of interactive multimedia tools contribute to both the lecture and lab portion of the course (created in 1991 and taught almost every semester since then, including one in Sweden).
Segmentation Using Symmetry Deviation
DEFF Research Database (Denmark)
Hollensen, Christian; Højgaard, L.; Specht, L.
2011-01-01
and evaluate the method. The method uses deformable registration on computed tomography(CT) to find anatomical symmetry deviations of Head & Neck squamous cell carcinoma and combining it with positron emission tomography (PET) images. The method allows the use anatomical and symmetrical information of CT scans...... to improve automatic delineations. Materials: PET/CT scans from 30 patients were used for this study, 20 without cancer in hypopharyngeal volume and 10 with hypharyngeal carcinoma. An head and neck atlas was created from the 20 normal patients. The atlas was created using affine and non-rigid registration...... of the CT-scans into a single atlas. Afterwards the standard deviation of anatomical symmetry for the 20 normal patients was evaluated using non-rigid registration and registered onto the atlas to create an atlas for normal anatomical symmetry deviation. The same non-rigid registration was used on the 10...
Leadership, power and symmetry
DEFF Research Database (Denmark)
Spaten, Ole Michael
2016-01-01
Research publications concerning managers who coach their own employees are barely visible despite its wide- spread use in enterprises (McCarthy & Milner, 2013; Gregory & Levy, 2011; Crabb, 2011). This article focuses on leadership, power and moments of symmetry in the coaching relationship...... session. Thereafter we executed qualitative interviews with both managers and employees. Subsequently, a Thematic Analysis resulted in several themes, including power and moments of symmetry in the coaching relationship. One main conclusion is that the most fruitful coaching was obtained when the coachee...... experienced moments of symmetry and that necessary and sufficient conditions to bring forth such moments include a strong working alliance and the coach being aware of the power at play....
Energy Technology Data Exchange (ETDEWEB)
Chanowitz, M.S.
1990-09-01
The Higgs mechanism is reviewed in its most general form, requiring the existence of a new symmetry-breaking force and associated particles, which need not however be Higgs bosons. The first lecture reviews the essential elements of the Higgs mechanism, which suffice to establish low energy theorems for the scattering of longitudinally polarized W and Z gauge bosons. An upper bound on the scale of the symmetry-breaking physics then follows from the low energy theorems and partial wave unitarity. The second lecture reviews particular models, with and without Higgs bosons, paying special attention to how the general features discussed in lecture 1 are realized in each model. The third lecture focuses on the experimental signals of strong WW scattering that can be observed at the SSC above 1 TeV in the WW subenergy, which will allow direct measurement of the strength of the symmetry-breaking force. 52 refs., 10 figs.
Trautmann, Wolfgang; Russotto, Paolo
2016-01-01
The nuclear equation-of-state is a topic of highest current interest in nuclear structure and reactions as well as in astrophysics. In particular, the equation-of-state of asymmetric matter and the symmetry energy representing the difference between the energy densities of neutron matter and of symmetric nuclear matter are not sufficiently well constrained at present. The density dependence of the symmetry energy is conventionally expressed in the form of the slope parameter L describing the derivative with respect to density of the symmetry energy at saturation. Results deduced from nuclear structure and heavy-ion reaction data are distributed around a mean value L=60 MeV. Recent studies have more thoroughly investigated the density range that a particular observable is predominantly sensitive to. Two thirds of the saturation density is a value typical for the information contained in nuclear-structure data. Higher values exceeding saturation have been shown to be probed with meson production and collective ...
Gravitation and Duality Symmetry
D'Andrade, V C; Pereira, J G
2005-01-01
By generalizing the Hodge dual operator to the case of soldered bundles, and working in the context of the teleparallel equivalent of general relativity, an analysis of the duality symmetry in gravitation is performed. Although the basic conclusion is that, at least in the general case, gravitation does not present duality symmetry, there is a particular theory in which this symmetry is present. This theory is a self dual (or anti-self dual) teleparallel gravity in which, owing to the fact that it does not contribute to the gravitational interaction of fermions, the purely tensor part of torsion is assumed to vanish. The corresponding fermionic gravitational interaction is found to be chiral. Since duality is intimately related to renormalizability, this theory will probably be much more amenable to renormalization than teleparallel gravity or general relativity. Although obtained in the context of teleparallel gravity, these results must also be true for general relativity.
Discrete symmetries in the three-Higgs-doublet model
Ivanov, I P
2012-01-01
N-Higgs-doublet models (NHDM) are among the most popular examples of electroweak symmetry breaking mechanisms beyond the Standard Model. Discrete symmetries imposed on the NHDM scalar potential play a pivotal role in shaping the phenomenology of the model, and various symmetry groups have been studied so far. However, in spite of all efforts, the classification of finite Higgs-family symmetry groups realizable in NHDM for any N>2 is still missing. Here, we solve this problem for the three-Higgs-doublet model. Using recently found realizable abelian groups and applying Burnside's theorem and other group-theoretic tools, we find the full list of finite symmetry groups of Higgs-family transformations which are realizable in the scalar sector of 3HDM.
Neutrino mass, mixing and discrete symmetries
Smirnov, Alexei Y.
2013-07-01
Status of the discrete symmetry approach to explanation of the lepton masses and mixing is summarized in view of recent experimental results, in particular, establishing relatively large 1-3 mixing. The lepton mixing can originate from breaking of discrete flavor symmetry Gf to different residual symmetries Gl and Gv in the charged lepton and neutrino sectors. In this framework the symmetry group condition has been derived which allows to get relations between the lepton mixing elements immediately without explicit model building. The condition has been applied to different residual neutrino symmetries Gv. For generic (mass independent) Gv = Z2 the condition leads to two relations between the mixing parameters and fixes one column of the mixing matrix. In the case of Gv = Z2 × Z2 the condition fixes the mixing matrix completely. The non-generic (mass spectrum dependent) Gv lead to relations which include mixing angles, neutrino masses and Majorana phases. The symmetries Gl, Gv, Gf are identified which lead to the experimentally observed values of the mixing angles and allow to predict the CP phase.
Symmetry, structure, and spacetime
Rickles, Dean
2007-01-01
In this book Rickles considers several interpretative difficulties raised by gauge-type symmetries (those that correspond to no change in physical state). The ubiquity of such symmetries in modern physics renders them an urgent topic in philosophy of physics. Rickles focuses on spacetime physics, and in particular classical and quantum general relativity. Here the problems posed are at their most pathological, involving the apparent disappearance of spacetime! Rickles argues that both traditional ontological positions should be replaced by a structuralist account according to which relational
Weakly broken galileon symmetry
Energy Technology Data Exchange (ETDEWEB)
Pirtskhalava, David [Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa (Italy); Santoni, Luca; Trincherini, Enrico [Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa (Italy); INFN, Sezione di Pisa, Piazza dei Cavalieri 7, 56126 Pisa (Italy); Vernizzi, Filippo [Institut de Physique Théorique, Université Paris Saclay, CEA, CNRS, Gif-sur-Yvette cédex, F-91191 (France)
2015-09-01
Effective theories of a scalar ϕ invariant under the internal galileon symmetryϕ→ϕ+b{sub μ}x{sup μ} have been extensively studied due to their special theoretical and phenomenological properties. In this paper, we introduce the notion of weakly broken galileon invariance, which characterizes the unique class of couplings of such theories to gravity that maximally retain their defining symmetry. The curved-space remnant of the galileon’s quantum properties allows to construct (quasi) de Sitter backgrounds largely insensitive to loop corrections. We exploit this fact to build novel cosmological models with interesting phenomenology, relevant for both inflation and late-time acceleration of the universe.
Liu, Keh-Fei
2016-01-01
The relevance of chiral symmetry in baryons is highlighted in three examples in the nucleon spectroscopy and structure. The first one is the importance of chiral dynamics in understanding the Roper resonance. The second one is the role of chiral symmetry in the lattice calculation of $\\pi N \\sigma$ term and strangeness. The third one is the role of chiral $U(1)$ anomaly in the anomalous Ward identity in evaluating the quark spin and the quark orbital angular momentum. Finally, the chiral effective theory for baryons is discussed.
Directory of Open Access Journals (Sweden)
Reza korrang beheshti
2014-06-01
Full Text Available Although there is not a fully developed theory of evil in Plato, some various remarks are interspersed throughout his dialogues which provided the main materials for subsequent Platonists to elaborate a systematic doctrine of evil. Proclus is the most distinguished philosopher of the later Neoplatonism whose view became authoritative within the School and thus is most representative of the Neoplatonic doctrine of evil. By a critical assessment of the antecedent theories of evil, Proclus attempts to give a monistic interpretation of Platonic remarks on the problem of evil. According to his explanation, the higher degrees and principles of Being are only and purely good and are not the causes of evils but the good things for all things alone. Evils, however, exist necessarily but only among particular beings in a relative, parasitic, accidental way and dependent upon the good. The parasitic accidental existence of evil does not have a real efficient cause. It arises due to an asymmetry between the activities of the several faculties or powers of a complex particular being. Moreover, the existence of evil is so mixed with and dependent upon the good that despite its opposition to the good, contributes, in its own manner, to the fulfillment of goodness of the whole Universe, being thus reconcilable with Divine Providence and Efficiency.
Weak Lie symmetry and extended Lie algebra
Energy Technology Data Exchange (ETDEWEB)
Goenner, Hubert [Institute for Theoretical Physics, Friedrich-Hund-Platz 1, University of Goettingen, D-37077 Gottingen (Germany)
2013-04-15
The concept of weak Lie motion (weak Lie symmetry) is introduced. Applications given exhibit a reduction of the usual symmetry, e.g., in the case of the rotation group. In this context, a particular generalization of Lie algebras is found ('extended Lie algebras') which turns out to be an involutive distribution or a simple example for a tangent Lie algebroid. Riemannian and Lorentz metrics can be introduced on such an algebroid through an extended Cartan-Killing form. Transformation groups from non-relativistic mechanics and quantum mechanics lead to such tangent Lie algebroids and to Lorentz geometries constructed on them (1-dimensional gravitational fields).
Caputo, Christine A; Guo, Jing-Dong; Nagase, Shigeru; Fettinger, James C; Power, Philip P
2012-04-25
The heavier group 13 element alkene analogue, digallene Ar(iPr(4))GaGaAr(iPr(4)) (1) [Ar(iPr(4)) = C(6)H(3)-2,6-(C(6)H(3)-2,6-(i)Pr(2))(2)], has been shown to react readily in [n + 2] (n = 6, 4, 2 + 2) cycloaddition reactions with norbornadiene and quadricyclane, 1,3,5,7-cyclooctatetraene, 1,3-cyclopentadiene, and 1,3,5-cycloheptatriene to afford the heavier element deltacyclane species Ar(iPr(4))Ga(C(7)H(8))GaAr(iPr(4)) (2), pseudoinverse sandwiches Ar(iPr(4))Ga(C(8)H(8))GaAr(iPr(4)) (3, 3(iso)), and polycyclic compounds Ar(iPr(4))Ga(C(5)H(6))GaAr(iPr(4)) (4) and Ar(iPr(4))Ga(C(7)H(8))GaAr(iPr(4)) (5, 5(iso)), respectively, under ambient conditions. These reactions are facile and may be contrasted with other all-carbon versions, which require transition-metal catalysis or forcing conditions (temperature, pressure), or with the reactions of the corresponding heavier group 14 species Ar(iPr(4))EEAr(iPr(4)) (E = Ge, Sn), which give very different product structures. We discuss several mechanistic possibilities, including radical- and non-radical-mediated cyclization pathways. These mechanisms are consistent with the improved energetic accessibility of the LUMO of the heavier group 13 element multiple bond in comparison with that of a simple alkene or alkyne. We show that the calculated frontier molecular orbitals (FMOs) of Ar(iPr(4))GaGaAr(iPr(4)) are of π-π symmetry, allowing this molecule to engage in a wider range of reactions than permitted by the usual π-π* FMOs of C-C π bonds or the π-n(+) FMOs of heavier group 14 alkyne analogues.
Lie symmetries and invariants of constrained Hamiltonian systems
Institute of Scientific and Technical Information of China (English)
Liu Rong-Wan; Chen Li-Qun
2004-01-01
According to the theory of the invariance of ordinary differential equations under the infinitesimal transformations of group, the relations between Lie symmetries and invariants of the mechanical system with a singular Lagrangian are investigated in phase space. New dynamical equations of the system are given in canonical form and the determining equations of Lie symmetry transformations are derived. The proposition about the Lie symmetries and invariants are presented. An example is given to illustrate the application of the result in this paper.
Noether-Lie Symmetry of Generalized Classical Mechanical Systems
Institute of Scientific and Technical Information of China (English)
JIA Wen-Zhi; ZHANG Xiao-Ni; WANG Shun-Jin; FANG Jian-Hui; WANG Peng; DING Ning
2008-01-01
In this paper, the Noether-Lie symmetry and conserved quantities of generalized classical mechanical system are studied. The definition and the criterion of the Noether Lie symmetry for the system under the general infinitesimal transformations of groups are given. The Noether conserved quantity and the Hojman conserved quantity deduced from the Noether-Lie symmetry are obtained. An example is given to illustrate the application of the results.
Symmetry characterization of eigenstates in opal-based photonic crystals
Lopez-Tejeira, F.; Ochiai, T; Sakoda, K; Sanchez-Dehesa, J.
2001-01-01
The complete symmetry characterization of eigenstates in bare opal systems is obtained by means of group theory. This symmetry assignment has allowed us to identify several bands that cannot couple with an incident external plane wave. Our prediction is supported by layer-KKR calculations, which are also performed: the coupling coefficients between bulk modes and externally excited field tend to zero when symmetry properties mismatch.
Directory of Open Access Journals (Sweden)
Maher Kamel Nafeeh Al-Nassery م.د. ماهر كامل نافع الناصري
2015-06-01
Full Text Available Find addresses marked: (Platonic ideal applications in modern European painting -almadrsh abstract model provide the nature of the effect of thought on the Platonic ideal orientations school abstract aesthetic that made the beauty of a goal. The contained four chapters: the first chapter interested in the methodological framework for representing the search: Find which dealt with the problem of identifying the impact of Platonic philosophy in the school abstract. The search was confined to the limits of the study of philosophy and its impact on the school and abstract pictorial analysis models for the drawings of the year (1900-1950 m. The second chapter contained two sections, taking the first section: (Platonic philosophy by eating the views of philosophical idealism and attainable beauty ideal of absolute, while Me second section (b Schools of Modern Art through a review of artistic movements beginner Baromantekah and Impressionism through symbolism and Alouhoshih and Cubism and Expressionism and future Dadaism and Surrealism ending with stylized promised that references poignant. The third chapter Me Platonic ideal applications in drawing global online research procedures, which included: the research community and appointed, and research methodology, research and analysis of samples amounting to (5 of the plate. Contained in Chapter IV, on the search results, and conclusions, as well as recommendations and suggestions, the researchers have come to a number of findings and conclusions, including: I worked at 1- abstract (Mondrian to unforeseen forces through its focus on geometric shape as a form is open, and her cognitive effects of gaining character totally not partially. Figure 2 The abstract carries prescription beauty essence, what has the laws of repetition and symmetry, harmony, and Find College (sample No. 4 by stripping the shape neighborhood divisions based systems engineering, which serves as the essence and origin of the samples
Development of Symmetry Concepts for Aperiodic Crystals
Directory of Open Access Journals (Sweden)
Ted Janssen
2014-03-01
Full Text Available An overview is given of the use of symmetry considerations for aperiodic crystals. Superspace groups were introduced in the seventies for the description of incommensurate modulated phases with one modulation vector. Later, these groups were also used for quasi-periodic crystals of arbitrary rank. Further extensions use time reversal and time translation operations on magnetic and electrodynamic systems. An alternative description of magnetic structures to that with symmetry groups, the Shubnikov groups, is using representations of space groups. The same can be done for aperiodic crystals. A discussion of the relation between the two approaches is given. Representations of space groups and superspace groups play a role in the study of physical properties. These, and generalizations of them, are discussed for aperiodic crystals. They are used, in particular, for the characterization of phase transitions between aperiodic crystal phases.
Dieperink, AEL; van Neck, D; Suzuki, T; Otsuka, T; Ichimura, M
2005-01-01
The role of isospin asymmetry in nuclei and neutron stars is discussed, with an emphasis on the density dependence of the nuclear symmetry energy. Results obtained with the self-consistent Green function method are presented and compared with various other theoretical predictions. Implications for t
Gray, P L
2003-01-01
"The subatomic pion particle breaks the charge symmetry rule that governs both fusion and decay. In experiments performed at the Indiana University Cyclotron Laboratory, physicists forced heavy hydrogen (1 proton + 1 neutron) to fuse into helium in a controlled, measurable environment" (1 paragraph).
Symmetries in fundamental physics
Sundermeyer, Kurt
2014-01-01
Over the course of the last century it has become clear that both elementary particle physics and relativity theories are based on the notion of symmetries. These symmetries become manifest in that the "laws of nature" are invariant under spacetime transformations and/or gauge transformations. The consequences of these symmetries were analyzed as early as in 1918 by Emmy Noether on the level of action functionals. Her work did not receive due recognition for nearly half a century, but can today be understood as a recurring theme in classical mechanics, electrodynamics and special relativity, Yang-Mills type quantum field theories, and in general relativity. As a matter of fact, as shown in this monograph, many aspects of physics can be derived solely from symmetry considerations. This substantiates the statement of E.P.Wigner "... if we knew all the laws of nature, or the ultimate Law of nature, the invariance properties of these laws would not furnish us new information." Thanks to Wigner we now also underst...
Symmetries in fundamental physics
Sundermeyer, Kurt
2014-01-01
Over the course of the last century it has become clear that both elementary particle physics and relativity theories are based on the notion of symmetries. These symmetries become manifest in that the "laws of nature" are invariant under spacetime transformations and/or gauge transformations. The consequences of these symmetries were analyzed as early as in 1918 by Emmy Noether on the level of action functionals. Her work did not receive due recognition for nearly half a century, but can today be understood as a recurring theme in classical mechanics, electrodynamics and special relativity, Yang-Mills type quantum field theories, and in general relativity. As a matter of fact, as shown in this monograph, many aspects of physics can be derived solely from symmetry considerations. This substantiates the statement of E.P. Wigner "... if we knew all the laws of nature, or the ultimate Law of nature, the invariance properties of these laws would not furnish us new information." Thanks to Wigner we now also unders...
Crumpecker, Cheryl
2003-01-01
Describes an art lesson used with children in the third grade to help them learn about symmetry, as well as encouraging them to draw larger than usual. Explains that students learn about the belief called "Horror Vacui" of the Northwest American Indian tribes and create their interpretation of this belief. (CMK)
Pels, D.L.
1996-01-01
While symmetry and impartiality have become ruling principles in S&TS, defining its core ideal of a 'value-free relativism', their philosophical anchorage has attracted much less discussion than the issue or:how far their jurisdiction can be extended or generalized. This paper seeks to argue that sy
Applications of chiral symmetry
Pisarski, R D
1995-01-01
I discuss several topics in the applications of chiral symmetry at nonzero temperature, including: where the rho goes, disoriented chiral condensates, and the phase diagram for QCD with 2+1 flavors. (Based upon talks presented at the "Workshop on Finite Temperature QCD", Wuhan, P.R.C., April, 1994.)
Einmahl, John; Gan, Zhuojiong
2016-01-01
Omnibus tests for central symmetry of a bivariate probability distribution are proposed. The test statistics compare empirical measures of opposite regions. Under rather weak conditions, we establish the asymptotic distribution of the test statistics under the null hypothesis; it follows that they a
Symmetries of hadrons after unbreaking the chiral symmetry
Glozman, L Ya; Schröck, M
2012-01-01
We study hadron correlators upon artificial restoration of the spontaneously broken chiral symmetry. In a dynamical lattice simulation we remove the lowest lying eigenmodes of the Dirac operator from the valence quark propagators and study evolution of the hadron masses obtained. All mesons and baryons in our study, except for a pion, survive unbreaking the chiral symmetry and their exponential decay signals become essentially better. From the analysis of the observed spectroscopic patterns we conclude that confinement still persists while the chiral symmetry is restored. All hadrons fall into different chiral multiplets. The broken U(1)_A symmetry does not get restored upon unbreaking the chiral symmetry. We also observe signals of some higher symmetry that includes chiral symmetry as a subgroup. Finally, from comparison of the \\Delta - N splitting before and after unbreaking of the chiral symmetry we conclude that both the color-magnetic and the flavor-spin quark-quark interactions are of equal importance.
Quasi Regular Polyhedra and Their Duals with Coxeter Symmetries Represented by Quaternions II
Koca, Mehmet; Shidhani, Saleh Al-
2010-01-01
In this paper we construct the quasi regular polyhedra and their duals which are the generalizations of the Archimedean and Catalan solids respectively. This work is an extension of two previous papers of ours which were based on the Archimedean and Catalan solids obtained as the orbits of the Coxeter groups . When these groups act on an arbitrary vector in 3D Euclidean space they generate the orbits corresponding to the quasi regular polyhedra. Special choices of the vectors lead to the platonic and Archimedean solids. In general, the faces of the quasi regular polyhedra consist of the equilateral triangles, squares, regular pentagons as well as rectangles, isogonal hexagons, isogonal octagons, and isogonal decagons depending on the choice of the Coxeter groups of interest. We follow the quaternionic representation of the group elements of the Coxeter groups which necessarily leads to the quaternionic representation of the vertices. We note the fact that the molecule can best be represented by a truncated ic...
Gauge and space-time symmetry unification
Besprosvany, J
2000-01-01
Unification ideas suggest an integral treatment of fermion and boson spin and gauge-group degrees of freedom. Hence, a generalized quantum field equation, based on Dirac's, is proposed and investigated which contains gauge and flavor symmetries, determines vector gauge field and fermion solution representations, and fixes their mode of interaction. The simplest extension of the theory with a 6-dimensional Clifford algebra predicts an SU(2)_L X U(1) symmetry, which is associated with the isospin and the hypercharge, their vector carriers, two-flavor charged and chargeless leptons, and scalar particles. A mass term produces breaking of the symmetry to an electromagnetic U(1), and a Weinberg's angle theta_W with sin^2(theta_W)=.25 . A more realistic 8-d extension gives coupling constants of the respective groups g=1/sqrt 2~.707 and g'=1/sqrt 6~.408, with the same theta_W.
On Symmetries in Optimal Control
van der Schaft, A. J.
1986-01-01
We discuss the use of symmetries in solving optimal control problems. In particular a procedure for obtaining symmetries is given which can be performed before the actual calculation of the optimal control and optimal Hamiltonian.
On Symmetries in Optimal Control
Schaft, A.J. van der
1986-01-01
We discuss the use of symmetries in solving optimal control problems. In particular a procedure for obtaining symmetries is given which can be performed before the actual calculation of the optimal control and optimal Hamiltonian.
A relativistic symmetry in nuclei
Energy Technology Data Exchange (ETDEWEB)
Ginocchio, J N [MS B283, Theoretical Division, Los Alamos National Laboratory Los Alamos, New Mexico 87545 (Mexico)
2007-11-15
We review some of the empirical and theoretical evidence supporting pseudospin symmetry in nuclei as a relativistic symmetry. We review the case that the eigenfunctions of realistic relativistic nuclear mean fields approximately conserve pseudospin symmetry in nuclei. We discuss the implications of pseudospin symmetry for magnetic dipole transitions and Gamow-Teller transitions between states in pseudospin doublets. We explore a more fundamental rationale for pseudospin symmetry in terms of quantum chromodynamics (QCD), the basic theory of the strong interactions. We show that pseudospin symmetry in nuclei implies spin symmetry for an anti-nucleon in a nuclear environment. We also discuss the future and what role pseudospin symmetry may be expected to play in an effective field theory of nucleons.
Abelian symmetries in multi-Higgs-doublet models
Ivanov, Igor P; Vdovin, Evgeny
2012-01-01
Classifying symmetry groups which can be implemented in the scalar sector of a model with $N$ Higgs doublets is a difficult and an unsolved task for $N>2$. Here, we make the first step towards this goal by classifying the Abelian symmetry groups. We describe a strategy that identifies all Abelian groups which can be realized as symmetry groups of the NHDM scalar potential. We give examples of the use of this strategy in 3HDM and 4HDM and prove several statements for arbitrary $N$.
Lattice-Symmetry-Driven Phase Competition in Vanadium Dioxide
Energy Technology Data Exchange (ETDEWEB)
Tselev, Alexander [ORNL; Luk' yanchuk, Prof. Igor A. [University of Picardie Jules Verne, Amiens, France; Ivanov, Ilia N [ORNL; Budai, John D [ORNL; Tischler, Jonathan Zachary [ORNL; Strelcov, Evgheni [Southern Illinois University; Kolmakov, Andrei [Southern Illinois University; Kalinin, Sergei V [ORNL
2011-01-01
We performed group-theoretical analysis of the symmetry relationships between lattice structures of R, M1, M2, and T phases of vanadium dioxide in the frameworks of the general Ginzburg-Landau phase transition theory. The analysis leads to a conclusion that the competition between the lower-symmetry phases M1, M2, and T in the metal-insulator transition is pure symmetry driven, since all the three phases correspond to different directions of the same multi-component structural order parameter. Therefore, the lower-symmetry phases can be stabilized in respect to each other by small perturbations such as doping or stress.
Invariants of broken discrete symmetries
Kalozoumis, P.; Morfonios, C.; Diakonos, F. K.; Schmelcher, P.
2014-01-01
The parity and Bloch theorems are generalized to the case of broken global symmetry. Local inversion or translation symmetries are shown to yield invariant currents that characterize wave propagation. These currents map the wave function from an arbitrary spatial domain to any symmetry-related domain. Our approach addresses any combination of local symmetries, thus applying in particular to acoustic, optical and matter waves. Nonvanishing values of the invariant currents provide a systematic ...
Vladan Nikolić; Ljiljana Radović; Biserka Marković
2015-01-01
The idea of construction of twin buildings is as old as architecture itself, and yet there is hardly any study emphasizing their specificity. Most frequently there are two objects or elements in an architectural composition of “twins” in which there may be various symmetry relations, mostly bilateral symmetries. The classification of “twins” symmetry in this paper is based on the existence of bilateral symmetry, in terms of the perception of an observer. The classification includes both, 2D a...
SO(10) models with flavour symmetries: classification and examples
Ivanov, I. P.; Lavoura, L.
2016-10-01
Renormalizable SO(10) grand unified theory (GUT) models equipped with flavour symmetries are a popular framework for addressing the flavour puzzle. Usually, the flavour symmetry group has been an ad hoc choice, and no general arguments limiting this choice were known. In this paper, we establish the full list of flavour symmetry groups which may be enforced, without producing any further accidental symmetry, on the Yukawa-coupling matrices of an SO(10) GUT with arbitrary numbers of scalar multiplets in the {{10}}, \\bar{{{126}}}, and {{120}} representations of SO(10). For each of the possible discrete non-Abelian symmetry groups, we present examples of minimal models which do not run into obvious contradiction with the phenomenological fermion masses and mixings.
Dynamical Symmetries in Classical Mechanics
Boozer, A. D.
2012-01-01
We show how symmetries of a classical dynamical system can be described in terms of operators that act on the state space for the system. We illustrate our results by considering a number of possible symmetries that a classical dynamical system might have, and for each symmetry we give examples of dynamical systems that do and do not possess that…
Scattering matrices with block symmetries
Życzkowski, Karol
1997-01-01
Scattering matrices with block symmetry, which corresponds to scattering process on cavities with geometrical symmetry, are analyzed. The distribution of transmission coefficient is computed for different number of channels in the case of a system with or without the time reversal invariance. An interpolating formula for the case of gradual time reversal symmetry breaking is proposed.
Emergence of Symmetries from Entanglement
CERN. Geneva
2016-01-01
Maximal Entanglement appears to be a key ingredient for the emergence of symmetries. We first illustrate this phenomenon using two examples: the emergence of conformal symmetry in condensed matter systems and the relation of tensor networks to holography. We further present a Principle of Maximal Entanglement that seems to dictate to a large extend the structure of gauge symmetry.
Dimensional reduction and dynamical symmetry breaking
Energy Technology Data Exchange (ETDEWEB)
Forgacs, P.; Zoupanos, G.
1984-11-22
We present a model in which the electroweak gauge group is broken according to a dynamical scenario based on the chiral symmetry breaking of high colour representations. The dynamical scenario requires also the existence of elementary Higgs fields, which in the present scheme come from the dimensional reduction of a pure gauge theory.
Dimensional reduction and dynamical symmetry breaking
Energy Technology Data Exchange (ETDEWEB)
Forgacs, P.; Zoupanos, G. (European Organization for Nuclear Research, Geneva (Switzerland))
1984-11-22
We present a model in which the electroweak gauge group is broken according to a dynamical scenario based on the chiral symmetry breaking of high colour representations. The dynamical scenario also requires the existence of elementary Higgs fields, which in the present scheme come from the dimensional reduction of a pure gauge theory.
Symmetry and reduction in implicit generalized Hamiltonian systems
Blankenstein, G.; Schaft, van der A.J.
2001-01-01
In this paper we study the notion of symmetry for implicit generalized Hamiltonian systems, which are Hamiltonian systems with respect to a generalized Dirac structure. We investigate the reduction of these systems admitting a symmetry Lie group with corresponding quantities. Main features in this a
Symmetry and Reduction in Implicit Generalized Hamiltonian Systems
Blankenstein, G.; Schaft, A.J. van der
2001-01-01
In this paper we study the notion of symmetry for implicit generalized Hamiltonian systems, which are Hamiltonian systems with respect to a generalized Dirac structure. We investigate the reduction of these systems admitting a symmetry Lie group with corresponding conserved quantities. Main features
Comments on the spontaneous symmetry breaking in supersymmetric theories
Energy Technology Data Exchange (ETDEWEB)
Girardi, G.; Sorba, P.; Stora, R. (Grenoble-1 Univ., 74 - Annecy (France). Lab. de Physique des Particules)
1984-08-30
The role of the complex extension of the symmetry group in supersymmetric theories is revisited. We prove, in particular, that if symmetry breaking occurs at an extremum of the superpotential, then supersymmetry will be preserved if and only if the complex stabilizer of the vacuum is the complexified of its maximal compact part.
Noncommutative geometry, symmetries and quantum structure of space-time
Energy Technology Data Exchange (ETDEWEB)
Govindarajan, T R [Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai 600113 (India); Gupta, Kumar S [Theory Division, Saha Institute of Nuclear Physics, 1/AF Bidhannagar, Kolkata 700064 (India); Harikumar, E [School of Physics, University of Hyderabad, Hyderabad 500046 (India); Meljanac, S, E-mail: trg@imsc.res.in, E-mail: kumars.gupta@saha.ac.in, E-mail: harisp@uohyd.ernet.in, E-mail: meljanac@irb.hr [Rudjer Botkovic Institute, Bijenicka c.54, HR-10002 Zagreb (Croatia)
2011-07-08
We discuss how space-time noncommutativity affects the symmetry groups and particle statistics. Assuming that statistics is superselected under a symmetry transformation, we argue that the corresponding flip operator must be twisted. It is argued that the twisted statistics naturally leads to a deformed oscillator algebra for scalar fields in such a background.
Leadership, power and symmetry
DEFF Research Database (Denmark)
Spaten, Ole Michael
2016-01-01
regarding managers coaching their employees and it is asked; what contributes to coaching of high quality when one reflects on the power aspect as being immanent? Fourteen middle managers coached five of their employees, and all members of each party wrote down cues and experiences immediately after each......Research publications concerning managers who coach their own employees are barely visible despite its wide- spread use in enterprises (McCarthy & Milner, 2013; Gregory & Levy, 2011; Crabb, 2011). This article focuses on leadership, power and moments of symmetry in the coaching relationship...... session. Thereafter we executed qualitative interviews with both managers and employees. Subsequently, a Thematic Analysis resulted in several themes, including power and moments of symmetry in the coaching relationship. One main conclusion is that the most fruitful coaching was obtained when the coachee...
Asymmetry, Symmetry and Beauty
Directory of Open Access Journals (Sweden)
Abbe R. Kopra
2010-07-01
Full Text Available Asymmetry and symmetry coexist in natural and human processes. The vital role of symmetry in art has been well demonstrated. This article highlights the complementary role of asymmetry. Further we show that the interaction of asymmetric action (recursion and symmetric opposition (sinusoidal waves are instrumental in generating creative features (relatively low entropy, temporal complexity, novelty (less recurrence in the data than in randomized copies and complex frequency composition. These features define Bios, a pattern found in musical compositions and in poetry, except for recurrence instead of novelty. Bios is a common pattern in many natural and human processes (quantum processes, the expansion of the universe, gravitational waves, cosmic microwave background radiation, DNA, physiological processes, animal and human populations, and economic time series. The reduction in entropy is significant, as it reveals creativity and contradicts the standard claim of unavoidable decay towards disorder. Artistic creations capture fundamental features of the world.
Symmetry in bonding and spectra an introduction
Douglas, Bodie E
1985-01-01
Many courses dealing with the material in this text are called ""Applications of Group Theory."" Emphasizing the central role and primary importance of symmetry in the applications, Symmetry in Bonding and Spectra enables students to handle applications, particularly applications to chemical bonding and spectroscopy. It contains the essential background in vectors and matrices for the applications, along with concise reviews of simple molecular orbital theory, ligand field theory, and treatments of molecular shapes, as well as some quantum mechanics. Solved examples in the text illustra
1985-08-01
way to choose among them. Spirals can occur in natural figures, e.g. a spiralled tail or a coil of rope or vine tendril, and in line drawings. Since...generated and removes it and all regions similar to it from the list of regions. The end result is a pruned list of distinct optimal regions. 4.7...that, at least to a first approximation, the potential symmetry regions pruned by the locality restriction are not perceptually salient. For example
Momeni, Davood
2014-01-01
The symmetry issue for Galileons has been studied. In particular we address scaling (conformal) and Noether symmetrized Galileons. We have been proven a series of theorems about the form of Noether conserved charge (current) for irregular (not quadratic) dynamical systems. Special attentions have been made on Galileons. We have been proven that for Galileons always is possible to find a way to "symmetrized" Galileo's field .
MOSTAFAZADEH, Ali
2013-01-01
PHYSICAL REVIEW A 87, 012103 (2013) Invisibility and PT symmetry Ali Mostafazadeh* Department of Mathematics, Koc¸ University, Sarıyer 34450, Istanbul, Turkey (Received 9 July 2012; published 3 January 2013) For a general complex scattering potential defined on a real line, we show that the equations governing invisibility of the potential are invariant under the combined action of parity and time-reversal (PT ) transformation. We determine the PT -symmetric as well as no...
Energy Technology Data Exchange (ETDEWEB)
Herrero, O F, E-mail: o.f.herrero@hotmail.co [Conservatorio Superior de Musica ' Eduardo Martinez Torner' Corrada del Obispo s/n 33003 - Oviedo - Asturias (Spain)
2010-06-01
Music and Physics are very close because of the symmetry that appears in music. A periodic wave is what music really is, and there is a field of Physics devoted to waves researching. The different musical scales are the base of all kind of music. This article tries to show how this musical scales are made, how the consonance is the base of many of them and how symmetric they are.
Noether symmetries of vacuum classes of pp-waves and the wave equation
Jamal, Sameerah; Shabbir, Ghulam
2016-06-01
The Noether symmetry algebras admitted by wave equations on plane-fronted gravitational waves with parallel rays are determined. We apply the classification of different metric functions to determine generators for the wave equation, and also adopt Noether's theorem to derive conserved forms. For the possible cases considered, there exist symmetry groups with dimensions two, three, five, six and eight. These symmetry groups contain the homothetic symmetries of the spacetime.
Abelian symmetries in multi-Higgs-doublet models
Ivanov, Igor P; Vdovin, Evgeny
2011-01-01
N-Higgs-doublet models (NHDM) are a popular framework to construct electroweak symmetry breaking mechanisms beyond the Standard model. Usually, one builds an NHDM scalar sector which is invariant under a certain symmetry group. Although several such groups have been used, no general analysis of symmetries possible in the NHDM scalar sector exists. Here, we describe a strategy that identifies all abelian groups which are realizable as symmetry groups of the NHDM Higgs potential. We consider both the groups of Higgs-family transformations only and the groups which also contain generalized CP transformations. We illustrate this strategy with the examples of 3HDM and 4HDM and prove several statements for arbitrary N.
Gardner, Adrian M.; Tuttle, William D.; Groner, Peter; Wright, Timothy G.
2017-03-01
For the first time, a molecular symmetry group (MSG) analysis has been undertaken in the investigation of the electronic spectroscopy of p-xylene (p-dimethylbenzene). Torsional and vibration-torsional (vibtor) levels in the S1 state and ground state of the cation of p-xylene are investigated using resonance-enhanced multiphoton ionization (REMPI) and zero-kinetic-energy (ZEKE) spectroscopy. In the present work, we concentrate on the 0-350 cm-1 region, where there are a number of torsional and vibtor bands and we discuss the assignment of this region. In Paper II [W. D. Tuttle et al., J. Chem. Phys. 146, 124309 (2017)], we examine the 350-600 cm-1 region where vibtor levels are observed as part of a Fermi resonance. The similarity of much of the observed spectral activity to that in the related substituted benzenes, toluene and para-fluorotoluene, is striking, despite the different symmetries. The discussion necessitates a consideration of the MSG of p-xylene, which has been designated G72, but we shall also designate [{3,3}]D2h and we include the symmetry operations, character table, and direct product table for this. We also discuss the symmetries of the internal rotor (torsional) levels and the selection rules for the particular electronic transition of p-xylene investigated here.
Symmetries in proteins: A knot theory approach
Chen, Shi-Jie; Dill, Ken A.
1996-04-01
Whereas the symmetries of small molecules are described by the methods of group theory, there is no corresponding way to describe the complex symmetries in proteins. We develop a quantitative method to define and classify symmetries in compact polymers, based on the mathematical theory of graphs and knots. We represent different chain folds by their ``polymer graphs,'' equivalent to contact maps. We transform those graphs into mathematical knots to give a parsing of different possible chain folds into conformational taxonomies. We use Alexander-Conway knot polynomials to characterize the knots. We find that different protein structures with the same tertiary fold, e.g., a βαβ motif with different lengths of α helix and β sheet, can be described in terms of the different powers of the propagation matrices of the knot polynomial. This identifies a fundamental type of topological length invariance in proteins, ``elongatable'' symmetries. For example, ``helix,'' ``sheet,'' ``helix-turn-helix,'' and other secondary, supersecondary, and tertiary structures define structures of any chain length. Possibly the nine superfolds identified by Thornton et al. have elongatable symmetries.
Symmetry of many-electron systems
Kaplan, I G
2013-01-01
Symmetry of Many-Electron Systems discusses the group-theoretical methods applied to physical and chemical problems. Group theory allows an individual to analyze qualitatively the elements of a certain system in scope. The text evaluates the characteristics of the Schrodinger equations. It is proved that some groups of continuous transformation from the Lie groups are useful in identifying conditions and in developing wavefunctions. A section of the book is devoted to the utilization of group-theoretical methods in quantal calculations on many-electron systems. The focus is on the use of group
Invariants of Broken Discrete Symmetries
Kalozoumis, P. A.; Morfonios, C.; Diakonos, F. K.; Schmelcher, P.
2014-08-01
The parity and Bloch theorems are generalized to the case of broken global symmetry. Local inversion or translation symmetries in one dimension are shown to yield invariant currents that characterize wave propagation. These currents map the wave function from an arbitrary spatial domain to any symmetry-related domain. Our approach addresses any combination of local symmetries, thus applying, in particular, to acoustic, optical, and matter waves. Nonvanishing values of the invariant currents provide a systematic pathway to the breaking of discrete global symmetries.
Directory of Open Access Journals (Sweden)
Vladan Nikolić
2015-02-01
Full Text Available The idea of construction of twin buildings is as old as architecture itself, and yet there is hardly any study emphasizing their specificity. Most frequently there are two objects or elements in an architectural composition of “twins” in which there may be various symmetry relations, mostly bilateral symmetries. The classification of “twins” symmetry in this paper is based on the existence of bilateral symmetry, in terms of the perception of an observer. The classification includes both, 2D and 3D perception analyses. We start analyzing a pair of twin buildings with projection of the architectural composition elements in 2D picture plane (plane of the composition and we distinguish four 2D keyframe cases based on the relation between the bilateral symmetry of the twin composition and the bilateral symmetry of each element. In 3D perception for each 2D keyframe case there are two sub-variants, with and without a symmetry plane parallel to the picture plane. The bilateral symmetry is dominant if the corresponding symmetry plane is orthogonal to the picture plane. The essence of the complete classification is relation between the bilateral (dominant symmetry of the architectural composition and the bilateral symmetry of each element of that composition.
Symmetry classification of time-fractional diffusion equation
Naeem, I.; Khan, M. D.
2017-01-01
In this article, a new approach is proposed to construct the symmetry groups for a class of fractional differential equations which are expressed in the modified Riemann-Liouville fractional derivative. We perform a complete group classification of a nonlinear fractional diffusion equation which arises in fractals, acoustics, control theory, signal processing and many other applications. Introducing the suitable transformations, the fractional derivatives are converted to integer order derivatives and in consequence the nonlinear fractional diffusion equation transforms to a partial differential equation (PDE). Then the Lie symmetries are computed for resulting PDE and using inverse transformations, we derive the symmetries for fractional diffusion equation. All cases are discussed in detail and results for symmetry properties are compared for different values of α. This study provides a new way of computing symmetries for a class of fractional differential equations.
Continuous symmetry of C60 fullerene and its derivatives.
Sheka, E F; Razbirin, B S; Nelson, D K
2011-04-21
Conventionally, the I(h) symmetry of fullerene C(60) is accepted, which is supported by numerous calculations. However, this conclusion results from the consideration of the molecule electron system, of its odd electrons in particular, in a closed-shell approximation without taking the electron spin into account. Passing to the open-shell approximation has led to both the energy and the symmetry lowering up to C(i). Seemingly contradicting to a high-symmetry pattern of experimental recording, particularly concerning the molecule electronic spectra, the finding is considered in this Article from the continuous symmetry viewpoint. Exploiting continuous symmetry measure and continuous symmetry level approaches, it was shown that formal C(i) symmetry of the molecule is by 99.99% I(h). A similar continuous symmetry analysis of the fullerene monoderivatives gives a reasonable explanation of a large variety of their optical spectra patterns within the framework of the same C(1) formal symmetry exhibiting a strong stability of the C(60) skeleton. TOC color pictures present chemical portrait of C(60) in terms of atomic chemical susceptibility (Sheka, E. Fullerenes: Nanochemistry, Nanomagnetism, Nanomedicine, Nanophotonics; CRC Press: Taylor and Francis Group, Boca Raton, 2011).
Necessary Condition for Emergent Symmetry from the Conformal Bootstrap
Nakayama, Yu; Ohtsuki, Tomoki
2016-09-01
We use the conformal bootstrap program to derive the necessary conditions for emergent symmetry enhancement from discrete symmetry (e.g., Zn ) to continuous symmetry [e.g., U (1 )] under the renormalization group flow. In three dimensions, in order for Z2 symmetry to be enhanced to U (1 ) symmetry, the conformal bootstrap program predicts that the scaling dimension of the order parameter field at the infrared conformal fixed point must satisfy Δ1>1.08 . We also obtain the similar necessary conditions for Z3 symmetry with Δ1>0.580 and Z4 symmetry with Δ1>0.504 from the simultaneous conformal bootstrap analysis of multiple four-point functions. As applications, we show that our necessary conditions impose severe constraints on the nature of the chiral phase transition in QCD, the deconfinement criticality in Néel valence bond solid transitions, and anisotropic deformations in critical O (n ) models. We prove that some fixed points proposed in the literature are unstable under the perturbation that cannot be forbidden by the discrete symmetry. In these situations, the second-order phase transition with enhanced symmetry cannot happen.
Electroweak symmetry breaking via QCD.
Kubo, Jisuke; Lim, Kher Sham; Lindner, Manfred
2014-08-29
We propose a new mechanism to generate the electroweak scale within the framework of QCD, which is extended to include conformally invariant scalar degrees of freedom belonging to a larger irreducible representation of SU(3)c. The electroweak symmetry breaking is triggered dynamically via the Higgs portal by the condensation of the colored scalar field around 1 TeV. The mass of the colored boson is restricted to be 350 GeV≲mS≲3 TeV, with the upper bound obtained from perturbative renormalization group evolution. This implies that the colored boson can be produced at the LHC. If the colored boson is electrically charged, the branching fraction of the Higgs boson decaying into two photons can slightly increase, and moreover, it can be produced at future linear colliders. Our idea of nonperturbative electroweak scale generation can serve as a new starting point for more realistic model building in solving the hierarchy problem.
Renormalizable theories with symmetry breaking
Becchi, Carlo M
2016-01-01
The description of symmetry breaking proposed by K. Symanzik within the framework of renormalizable theories is generalized from the geometrical point of view. For an arbitrary compact Lie group, a soft breaking of arbitrary covariance, and an arbitrary field multiplet, the expected integrated Ward identities are shown to hold to all orders of renormalized perturbation theory provided the Lagrangian is suitably chosen. The corresponding local Ward identity which provides the Lagrangian version of current algebra through the coupling to an external, classical, Yang-Mills field, is then proved to hold up to the classical Adler-Bardeen anomaly whose general form is written down. The BPHZ renormalization scheme is used throughout in such a way that the algebraic structure analyzed in the present context may serve as an introduction to the study of fully quantized gauge theories.
Platone interprete di se stesso. «Menone» 98a alla luce di «Fedro» 249b-c
Directory of Open Access Journals (Sweden)
Lavinia Maggi
2016-01-01
Full Text Available La definizione di ἐπιστήμη come ὀρθὴ δόξα legata αἰτίας λογισμῷ, che compare in Menone 98a, presenta notevoli difficoltà interpretative non solo per quanto riguarda l’identificazione dell’αἰτία, ma anche per la possibilità o meno di scorgere sullo sfondo di tale enunciazione la teoria delle Idee (nella versione dei cosiddetti “dialoghi della maturità”. La questione può essere affrontata sia considerando il controverso passo all’interno del contesto più ampio del dialogo (dove compare per la prima volta la teoria dell’ἀνάμνησις, che alla teoria delle Idee è strettamente legata, ma anche in relazione a passi di altri dialoghi platonici, in particolare Fedro 249b-c: qui, dove l’epistemologia platonica si sviluppa secondo la teoria delle Idee, la volontà di Platone di alludere direttamente a Menone 98a sembra offrire una chiave interpretativa anche per quella precedente formulazione. La necessità di leggere ogni dialogo secondo le sue specificità (periodo di composizione, argomento principale, tipologia dei personaggi coinvolti non esclude infatti che, almeno in alcuni casi, Platone stabilisca dei collegamenti che consentano una continuità di lettura nel percorso di sviluppo del suo pensiero.
Renner, R
2007-01-01
Given a quantum system consisting of many parts, we show that symmetry of the system's state, i.e., invariance under swappings of the subsystems, implies that almost all of its parts are virtually identical and independent of each other. This result generalises de Finetti's classical representation theorem for infinitely exchangeable sequences of random variables as well as its quantum-mechanical analogue. It has applications in various areas of physics as well as information theory and cryptography. For example, in experimental physics, one typically collects data by running a certain experiment many times, assuming that the individual runs are mutually independent. Our result can be used to justify this assumption.
Greene, Brian R
1997-01-01
Mirror symmetry has undergone dramatic progress during the last five years. Tremendous insight has been gained on a number of key issues. This volume surveys these results. Some of the contributions in this work have appeared elsewhere, while others were written specifically for this collection. The areas covered are organized into 4 sections, and each presents papers by both physicists and mathematicians. This volume collects the most important developments that have taken place in mathematical physics since 1991. It is an essential reference tool for both mathematics and physics libraries and for students of physics and mathematics.
Symmetry and physical properties of crystals
Malgrange, Cécile; Schlenker, Michel
2014-01-01
Crystals are everywhere, from natural crystals (minerals) through the semiconductors and magnetic materials in electronic devices and computers or piezoelectric resonators at the heart of our quartz watches to electro-optical devices. Understanding them in depth is essential both for pure research and for their applications. This book provides a clear, thorough presentation of their symmetry, both at the microscopic space-group level and the macroscopic point-group level. The implications of the symmetry of crystals for their physical properties are then presented, together with their mathematical description in terms of tensors. The conditions on the symmetry of a crystal for a given property to exist then become clear, as does the symmetry of the property. The geometrical representation of tensor quantities or properties is presented, and its use in determining important relationships emphasized. An original feature of this book is that most chapters include exercises with complete solutions. This all...
Hill, R; Davis, P
2000-12-01
Romantic jealousy has long been of interest to psychodynamically oriented clinicians. More recently empirical investigations have emerged into the causes and treatments of romantic jealousy. What has not kept pace with this interest is a wider research agenda into non-romantic forms of jealousy. While work has appeared in relation to specific groups or topics, such as sibling rivalry, no attempt has been made to draw together the material on non-romantic jealousy. In this paper the theoretical and empirical material on non-romantic jealousy is reviewed in order to answer two fundamental questions. Firstly, is non-romantic jealousy necessarily pathological? Secondly, to what extent is it helpful to subsume all forms of non-romantic jealousy under one term? It is suggested that while non-romantic jealousy is not always pathological, the term non-romantic jealousy may be a useful differentiating term, not least in highlighting an important area for future research.
Bootstrap Dynamical Symmetry Breaking
Directory of Open Access Journals (Sweden)
Wei-Shu Hou
2013-01-01
Full Text Available Despite the emergence of a 125 GeV Higgs-like particle at the LHC, we explore the possibility of dynamical electroweak symmetry breaking by strong Yukawa coupling of very heavy new chiral quarks Q . Taking the 125 GeV object to be a dilaton with suppressed couplings, we note that the Goldstone bosons G exist as longitudinal modes V L of the weak bosons and would couple to Q with Yukawa coupling λ Q . With m Q ≳ 700 GeV from LHC, the strong λ Q ≳ 4 could lead to deeply bound Q Q ¯ states. We postulate that the leading “collapsed state,” the color-singlet (heavy isotriplet, pseudoscalar Q Q ¯ meson π 1 , is G itself, and a gap equation without Higgs is constructed. Dynamical symmetry breaking is affected via strong λ Q , generating m Q while self-consistently justifying treating G as massless in the loop, hence, “bootstrap,” Solving such a gap equation, we find that m Q should be several TeV, or λ Q ≳ 4 π , and would become much heavier if there is a light Higgs boson. For such heavy chiral quarks, we find analogy with the π − N system, by which we conjecture the possible annihilation phenomena of Q Q ¯ → n V L with high multiplicity, the search of which might be aided by Yukawa-bound Q Q ¯ resonances.
Directory of Open Access Journals (Sweden)
Angel Garrido
2011-01-01
Full Text Available In this paper, we analyze a few interrelated concepts about graphs, such as their degree, entropy, or their symmetry/asymmetry levels. These concepts prove useful in the study of different types of Systems, and particularly, in the analysis of Complex Networks. A System can be defined as any set of components functioning together as a whole. A systemic point of view allows us to isolate a part of the world, and so, we can focus on those aspects that interact more closely than others. Network Science analyzes the interconnections among diverse networks from different domains: physics, engineering, biology, semantics, and so on. Current developments in the quantitative analysis of Complex Networks, based on graph theory, have been rapidly translated to studies of brain network organization. The brain's systems have complex network features—such as the small-world topology, highly connected hubs and modularity. These networks are not random. The topology of many different networks shows striking similarities, such as the scale-free structure, with the degree distribution following a Power Law. How can very different systems have the same underlying topological features? Modeling and characterizing these networks, looking for their governing laws, are the current lines of research. So, we will dedicate this Special Issue paper to show measures of symmetry in Complex Networks, and highlight their close relation with measures of information and entropy.
The symmetry of single-molecule conduction.
Solomon, Gemma C; Gagliardi, Alessio; Pecchia, Alessandro; Frauenheim, Thomas; Di Carlo, Aldo; Reimers, Jeffrey R; Hush, Noel S
2006-11-14
We introduce the conductance point group which defines the symmetry of single-molecule conduction within the nonequilibrium Green's function formalism. It is shown, either rigorously or to within a very good approximation, to correspond to a molecular-conductance point group defined purely in terms of the properties of the conducting molecule. This enables single-molecule conductivity to be described in terms of key qualitative chemical descriptors that are independent of the nature of the molecule-conductor interfaces. We apply this to demonstrate how symmetry controls the conduction through 1,4-benzenedithiol chemisorbed to gold electrodes as an example system, listing also the molecular-conductance point groups for a range of molecules commonly used in molecular electronics research.
Wilczek, Frank
2004-01-01
Powerful symmetry principles have guided physicists in their quest for nature's fundamental laws. The successful gauge theory of electroweak interactions postulates a more extensive symmetry for its equations than are manifest in the world (8 pages) Powerful symmetry principles have guided physicists in their quest for nature's fundamental laws. The successful gauge theory of electroweak interactions postulates a more extensive symmetry for its equations than are manifest in the world. The discrepancy is ascribed to a pervasive symmetry-breaking field, which fills all space uniformly, rendering the Universe a sort of exotic superconductor. So far, the evidence for these bold ideas is indirect. But soon the theory will undergo a critical test depending on whether the quanta of this symmetry-breaking field, the so-called Higgs particles, are produced at the Large Hadron Collider (due to begin operation in 2007).
Particle model with generalized Poincaré symmetry
Smith, A.
2017-08-01
Using the techniques of nonlinear coset realization with a generalized Poincaré group, we construct a relativistic particle model, invariant under the generalized symmetries, providing a dynamical realization of the B5 algebra.
Energy Technology Data Exchange (ETDEWEB)
Strocchi, F. [Scuola Normale Superiore, Classe di Scienze, Pisa (Italy)
2008-07-01
This new edition of Prof. Strocchi's well received primer on rigorous aspects of symmetry breaking presents a more detailed and thorough discussion of the mechanism of symmetry breaking in classical field theory in relation with the Noether theorem. Moreover, the link between symmetry breaking without massless Goldstone bosons in Coulomb systems and in gauge theories is made more explicit in terms of the delocalized Coulomb dynamics. Furthermore, the chapter on the Higgs mechanism has been significantly expanded with a non-perturbative treatment of the Higgs phenomenon, at the basis of the standard model of particle physics, in the local and in the Coulomb gauges. Last but not least, a subject index has been added and a number of misprints have been corrected. From the reviews of the first edition: The notion of spontaneous symmetry breaking has proven extremely valuable, the problem is that most derivations are perturbative and heuristic. Yet mathematically precise versions do exist, but are not widely known. It is precisely the aim of his book to correct this unbalance. - It is remarkable to see how much material can actually be presented in a rigorous way (incidentally, many of the results presented are due to Strocchi himself), yet this is largely ignored, the original heuristic derivations being, as a rule, more popular. - At each step he strongly emphasizes the physical meaning and motivation of the various notions introduced, a book that fills a conspicuous gap in the literature, and does it rather well. It could also be a good basis for a graduate course in mathematical physics. It can be recommended to physicists as well and, of course, for physics/mathematics libraries. J.-P. Antoine, Physicalia 28/2, 2006 Strocchi's main emphasis is on the fact that the loss of symmetric behaviour requires both the non-symmetric ground states and the infinite extension of the system. It is written in a pleasant style at a level suitable for graduate students in
Spontaneous symmetry breaking and masses numerical results in DFR noncommutative space-time
Neves, M J
2015-01-01
With the elements of the Doplicher, Fredenhagen and Roberts (DFR) noncommutative formalism, we have constructed the standard electroweak model. To accomplish this task we have begun with the WM-product basis group of symmetry. We have introduced the spontaneous symmetry breaking and the hypercharge in DFR framework. The electroweak symmetry breaking was analyzed and the masses of the new bosons were computed.
Understanding topological symmetry: a heuristic approach to its determination.
Contreras, M L; Alvarez, J; Guajardo, D; Rozas, R
2008-03-01
An algorithm based on heuristic rules for topological symmetry perception of organic structures having heteroatoms, multiple bonds, and any kind of cycle, and configuration, is presented. This algorithm identifies topological symmetry planes and sets of equivalent atoms in the structure, named symmetry atom groups (SAGs). This approach avoids both the need to explore the entire graph automorphism groups, and to encompass cycle determination, resulting in a very effective computer processing. Applications to several structures, some of them highly symmetrical such as dendrimers, are presented.
Symmetries in heavy nuclei and the proton-neutron interaction
Energy Technology Data Exchange (ETDEWEB)
Casten, R.F.
1986-01-01
The Interacting Boson Approximation (IBA) nuclear structure model can be expressed in terms of the U(6) group, and thereby leads to three dynamical symmetries (or group chains) corresponding to different nuclear coupling schemes and geometrical shapes. The status of the empirical evidence for these three symmetries is reviewed, along with brief comments on the possible existence of supersymmetries in nuclei. The relationships between these symmetries, the nuclear phase transitional regions linking them, and the residual proton-neutron interaction are discussed in terms of a particularly simple scheme for parameterizing the effects of that interaction. 34 refs., 15 figs.
Fermion mass generation and electroweak symmetry breaking from colour forces
Energy Technology Data Exchange (ETDEWEB)
Zoupanos, G. (European Organization for Nuclear Research, Geneva (Switzerland))
1983-09-29
The colour gauge group is extended to SU(3) x SU(3) and is subsequently broken to diagonal SU(3)sub(c). Under the diagonal SU(3)sub(c) the fundamental fermionic constituents of the larger strong group become ordinary quarks plus new quarks with exotic quantum numbers. Chiral symmetry breaking in the exotic quark sector may occur at much larger mass scales than ordinary chiral symmetry breaking, and could produce dynamical breaking of electroweak gauge symmetry and radiative masses for the light fermions.
SYMMETRIES AND CONSERVED QUANTITIES FOR SYSTEMS OF GENERALIZED CLASSICAL MECHANICS
Institute of Scientific and Technical Information of China (English)
Zhang Yi; Shang Mei; Mei Feng-xiang
2000-01-01
In this paper, the symmetries and the conserved quantities for systemsof generalized classical mechanics are studied. First, the generalizedNoether's theorem and the generalized Noether's inverse theorem of thesystems are given, which are based upon the invariant properties of thecanonical action with respect to the action of the infinitesimaltransformation of r-parameter finite group of transformation; second,the Lie symmetries and conserved quantities of the systems are studiedin accordance with the Lie's theory of the invariance of differentialequations under the transformation of infinitesimal groups; and finally,the inner connection between the two kinds of symmetries of systems isdiscussed.
Directory of Open Access Journals (Sweden)
Stan Schein
2016-08-01
Full Text Available The Goldberg construction of symmetric cages involves pasting a patch cut out of a regular tiling onto the faces of a Platonic host polyhedron, resulting in a cage with the same symmetry as the host. For example, cutting equilateral triangular patches from a 6.6.6 tiling of hexagons and pasting them onto the full triangular faces of an icosahedron produces icosahedral fullerene cages. Here we show that pasting cutouts from a 6.6.6 tiling onto the full hexagonal and triangular faces of an Archimedean host polyhedron, the truncated tetrahedron, produces two series of tetrahedral (Td fullerene cages. Cages in the first series have 28n2 vertices (n ≥ 1. Cages in the second (leapfrog series have 3 × 28n2. We can transform all of the cages of the first series and the smallest cage of the second series into geometrically convex equilateral polyhedra. With tetrahedral (Td symmetry, these new polyhedra constitute a new class of “convex equilateral polyhedra with polyhedral symmetry”. We also show that none of the other Archimedean polyhedra, six with octahedral symmetry and six with icosahedral, can host full-face cutouts from regular tilings to produce cages with the host’s polyhedral symmetry.
Exact Dynamical and Partial Symmetries
Leviatan, A
2010-01-01
We discuss a hierarchy of broken symmetries with special emphasis on partial dynamical symmetries (PDS). The latter correspond to a situation in which a non-invariant Hamiltonian accommodates a subset of solvable eigenstates with good symmetry, while other eigenstates are mixed. We present an algorithm for constructing Hamiltonians with this property and demonstrate the relevance of the PDS notion to nuclear spectroscopy, to quantum phase transitions and to mixed systems with coexisting regularity and chaos.
Exact dynamical and partial symmetries
Energy Technology Data Exchange (ETDEWEB)
Leviatan, A, E-mail: ami@phys.huji.ac.il [Racah Institute of Physics, The Hebrew University, Jerusalem 91904 (Israel)
2011-03-01
We discuss a hierarchy of broken symmetries with special emphasis on partial dynamical symmetries (PDS). The latter correspond to a situation in which a non-invariant Hamiltonian accommodates a subset of solvable eigenstates with good symmetry, while other eigenstates are mixed. We present an algorithm for constructing Hamiltonians with this property and demonstrate the relevance of the PDS notion to nuclear spectroscopy, to quantum phase transitions and to mixed systems with coexisting regularity and chaos.
Physical Theories with Average Symmetry
Alamino, Roberto C.
2013-01-01
This Letter probes the existence of physical laws invariant only in average when subjected to some transformation. The concept of a symmetry transformation is broadened to include corruption by random noise and average symmetry is introduced by considering functions which are invariant only in average under these transformations. It is then shown that actions with average symmetry obey a modified version of Noether's Theorem with dissipative currents. The relation of this with possible violat...
Symmetry enrichment in three-dimensional topological phases
Ning, Shang-Qiang; Liu, Zheng-Xin; Ye, Peng
2016-12-01
While two-dimensional symmetry-enriched topological phases (SETs ) have been studied intensively and systematically, three-dimensional ones are still open issues. We propose an algorithmic approach of imposing global symmetry Gs on gauge theories (denoted by GT) with gauge group Gg. The resulting symmetric gauge theories are dubbed "symmetry-enriched gauge theories" (SEG), which may be served as low-energy effective theories of three-dimensional symmetric topological quantum spin liquids. We focus on SEGs with gauge group Gg=ZN1×ZN2×⋯ and onsite unitary symmetry group Gs=ZK1×ZK2×⋯ or Gs=U (1 ) ×ZK 1×⋯ . Each SEG(Gg,Gs) is described in the path-integral formalism associated with certain symmetry assignment. From the path-integral expression, we propose how to physically diagnose the ground-state properties (i.e., SET orders) of SEGs in experiments of charge-loop braidings (patterns of symmetry fractionalization) and the mixed multiloop braidings among deconfined loop excitations and confined symmetry fluxes. From these symmetry-enriched properties, one can obtain the map from SEGs to SETs . By giving full dynamics to background gauge fields, SEGs may be eventually promoted to a set of new gauge theories (denoted by GT*). Based on their gauge groups, GT*s may be further regrouped into different classes, each of which is labeled by a gauge group Gg*. Finally, a web of gauge theories involving GT,SEG,SET, and GT* is achieved. We demonstrate the above symmetry-enrichment physics and the web of gauge theories through many concrete examples.
Physical Theories with Average Symmetry
Alamino, Roberto C
2013-01-01
This Letter probes the existence of physical laws invariant only in average when subjected to some transformation. The concept of a symmetry transformation is broadened to include corruption by random noise and average symmetry is introduced by considering functions which are invariant only in average under these transformations. It is then shown that actions with average symmetry obey a modified version of Noether's Theorem with dissipative currents. The relation of this with possible violations of physical symmetries, as for instance Lorentz invariance in some quantum gravity theories, is briefly commented.
The conservation of orbital symmetry
Woodward, R B
2013-01-01
The Conservation of Orbital Symmetry examines the principle of conservation of orbital symmetry and its use. The central content of the principle was that reactions occur readily when there is congruence between orbital symmetry characteristics of reactants and products, and only with difficulty when that congruence does not obtain-or to put it more succinctly, orbital symmetry is conserved in concerted reaction. This principle is expected to endure, whatever the language in which it may be couched, or whatever greater precision may be developed in its application and extension. The book ope
Karp, Dagan; Riggins, Paul; Whitcher, Ursula
2011-01-01
We exhaustively analyze the toric symmetries of CP^3 and its toric blowups. Our motivation is to study toric symmetry as a computational technique in Gromov-Witten theory and Donaldson-Thomas theory. We identify all nontrivial toric symmetries. The induced nontrivial isomorphisms lift and provide new symmetries at the level of Gromov-Witten Theory and Donaldson-Thomas Theory. The polytopes of the toric varieties in question include the permutohedron, the cyclohedron, the associahedron, and in fact all graph associahedra, among others.
Leptogenesis and residual CP symmetry
Energy Technology Data Exchange (ETDEWEB)
Chen, Peng; Ding, Gui-Jun [Department of Modern Physics, University of Science and Technology of China,Hefei, Anhui 230026 (China); King, Stephen F. [Physics and Astronomy, University of Southampton,Southampton, SO17 1BJ (United Kingdom)
2016-03-31
We discuss flavour dependent leptogenesis in the framework of lepton flavour models based on discrete flavour and CP symmetries applied to the type-I seesaw model. Working in the flavour basis, we analyse the case of two general residual CP symmetries in the neutrino sector, which corresponds to all possible semi-direct models based on a preserved Z{sub 2} in the neutrino sector, together with a CP symmetry, which constrains the PMNS matrix up to a single free parameter which may be fixed by the reactor angle. We systematically study and classify this case for all possible residual CP symmetries, and show that the R-matrix is tightly constrained up to a single free parameter, with only certain forms being consistent with successful leptogenesis, leading to possible connections between leptogenesis and PMNS parameters. The formalism is completely general in the sense that the two residual CP symmetries could result from any high energy discrete flavour theory which respects any CP symmetry. As a simple example, we apply the formalism to a high energy S{sub 4} flavour symmetry with a generalized CP symmetry, broken to two residual CP symmetries in the neutrino sector, recovering familiar results for PMNS predictions, together with new results for flavour dependent leptogenesis.
Institute of Scientific and Technical Information of China (English)
Metin Orbay; Telhat Ozdogan
2003-01-01
In this paper, the symmetry properties of linear combination coefficients for molecular orbitals of diatomicmolecules, using Slater type orbitals, are presented with the help of the symmetry operations in group theory. In order totest the presented symmetry properties, the linear combination coefficients of molecular orbitalsfor the ground electronicstate of pilot molecules F2 and CO are calculated using constructed computer programs for Hartree-Fock-Roothaanequation. It is seen that the obtained computing results satisfy the presented symmetry properties.
Symmetry Breaking on Density in Escaping Ants: Experiment and Alarm Pheromone Model
Geng Li; Di Huan; Bertrand Roehner; Yijuan Xu; Ling Zeng; Zengru Di; Zhangang Han
2014-01-01
International audience; The symmetry breaking observed in nature is fascinating. This symmetry breaking is observed in both human crowds and ant colonies. In such cases, when escaping from a closed space with two symmetrically located exits, one exit is used more often than the other. Group size and density have been reported as having no significant impact on symmetry breaking, and the alignment rule has been used to model symmetry breaking. Density usually plays important roles in collectiv...
Nonlocal symmetry generators and explicit solutions of some partial differential equations
Energy Technology Data Exchange (ETDEWEB)
Qin Maochang [School of Science, Chongqing Technology and Business University, Chongqing 400067 (China)
2007-04-27
The nonlocal symmetry of a partial differential equation is studied in this paper. The partial differential equation written as a conservation law can be transformed into an equivalent system by introducing a suitable potential. The nonlocal symmetry group generators of original partial differential equations can be obtained through their equivalent system. Further, new explicit solutions can be constructed from the newly obtained symmetry generators. The Burgers equation is chosen as an example; many new valuable explicit solutions and nonlocal symmetry generators are presented.
Nonclassical Symmetry Analysis of Heated Two-Dimensional Flow Problems
Naeem, Imran; Naz, Rehana; Khan, Muhammad Danish
2015-12-01
This article analyses the nonclassical symmetries and group invariant solution of boundary layer equations for two-dimensional heated flows. First, we derive the nonclassical symmetry determining equations with the aid of the computer package SADE. We solve these equations directly to obtain nonclassical symmetries. We follow standard procedure of computing nonclassical symmetries and consider two different scenarios, ξ1≠0 and ξ1=0, ξ2≠0. Several nonclassical symmetries are reported for both scenarios. Furthermore, numerous group invariant solutions for nonclassical symmetries are derived. The similarity variables associated with each nonclassical symmetry are computed. The similarity variables reduce the system of partial differential equations (PDEs) to a system of ordinary differential equations (ODEs) in terms of similarity variables. The reduced system of ODEs are solved to obtain group invariant solution for governing boundary layer equations for two-dimensional heated flow problems. We successfully formulate a physical problem of heat transfer analysis for fluid flow over a linearly stretching porous plat and, with suitable boundary conditions, we solve this problem.
Symmetry reduction related with nonlocal symmetry for Gardner equation
Ren, Bo
2017-01-01
Based on the truncated Painlevé method or the Möbious (conformal) invariant form, the nonlocal symmetry for the (1+1)-dimensional Gardner equation is derived. The nonlocal symmetry can be localized to the Lie point symmetry by introducing one new dependent variable. Thanks to the localization procedure, the finite symmetry transformations are obtained by solving the initial value problem of the prolonged systems. Furthermore, by using the symmetry reduction method to the enlarged systems, many explicit interaction solutions among different types of solutions such as solitary waves, rational solutions, Painlevé II solutions are given. Especially, some special concrete soliton-cnoidal interaction solutions are analyzed both in analytical and graphical ways.
Bosonization and Mirror Symmetry
Kachru, Shamit; Torroba, Gonzalo; Wang, Huajia
2016-01-01
We study bosonization in 2+1 dimensions using mirror symmetry, a duality that relates pairs of supersymmetric theories. Upon breaking supersymmetry in a controlled way, we dynamically obtain the bosonization duality that equates the theory of a free Dirac fermion to QED3 with a single scalar boson. This duality may be used to demonstrate the bosonization duality relating an $O(2)$-symmetric Wilson-Fisher fixed point to QED3 with a single Dirac fermion, Peskin-Dasgupta-Halperin duality, and the recently conjectured duality relating the theory of a free Dirac fermion to fermionic QED3 with a single flavor. Chern-Simons and BF couplings for both dynamical and background gauge fields play a central role in our approach. In the course of our study, we describe a chiral mirror pair that may be viewed as the minimal supersymmetric generalization of the two bosonization dualities.
Greiner, Walter
1989-01-01
"Quantum Dynamics" is a major survey of quantum theory based on Walter Greiner's long-running and highly successful courses at the University of Frankfurt. The key to understanding in quantum theory is to reinforce lecture attendance and textual study by working through plenty of representative and detailed examples. Firm belief in this principle led Greiner to develop his unique course and to transform it into a remarkable and comprehensive text. The text features a large number of examples and exercises involving many of the most advanced topics in quantum theory. These examples give practical and precise demonstrations of how to use the often subtle mathematics behind quantum theory. The text is divided into five volumes: Quantum Mechanics I - An Introduction, Quantum Mechanics II - Symmetries, Relativistic Quantum Mechanics, Quantum Electrodynamics, Gauge Theory of Weak Interactions. These five volumes take the reader from the fundamental postulates of quantum mechanics up to the latest research in partic...
Bosonization and mirror symmetry
Kachru, Shamit; Mulligan, Michael; Torroba, Gonzalo; Wang, Huajia
2016-10-01
We study bosonization in 2 +1 dimensions using mirror symmetry, a duality that relates pairs of supersymmetric theories. Upon breaking supersymmetry in a controlled way, we dynamically obtain the bosonization duality that equates the theory of a free Dirac fermion to QED3 with a single scalar boson. This duality may be used to demonstrate the bosonization duality relating an O (2 )-symmetric Wilson-Fisher fixed point to QED3 with a single Dirac fermion, Peskin-Dasgupta-Halperin duality, and the recently conjectured duality relating the theory of a free Dirac fermion to fermionic QED3 with a single flavor. Chern-Simons and BF couplings for both dynamical and background gauge fields play a central role in our approach. In the course of our study, we describe a "chiral" mirror pair that may be viewed as the minimal supersymmetric generalization of the two bosonization dualities.
Is space-time symmetry a suitable generalization of parity-time symmetry?
Energy Technology Data Exchange (ETDEWEB)
Amore, Paolo, E-mail: paolo.amore@gmail.com [Facultad de Ciencias, CUICBAS, Universidad de Colima, Bernal Díaz del Castillo 340, Colima, Colima (Mexico); Fernández, Francisco M., E-mail: fernande@quimica.unlp.edu.ar [INIFTA (UNLP, CCT La Plata-CONICET), División Química Teórica, Diag. 113 y 64 (S/N), Sucursal 4, Casilla de Correo 16, 1900 La Plata (Argentina); Garcia, Javier [INIFTA (UNLP, CCT La Plata-CONICET), División Química Teórica, Diag. 113 y 64 (S/N), Sucursal 4, Casilla de Correo 16, 1900 La Plata (Argentina)
2014-11-15
We discuss space-time symmetric Hamiltonian operators of the form H=H{sub 0}+igH{sup ′}, where H{sub 0} is Hermitian and g real. H{sub 0} is invariant under the unitary operations of a point group G while H{sup ′} is invariant under transformation by elements of a subgroup G{sup ′} of G. If G exhibits irreducible representations of dimension greater than unity, then it is possible that H has complex eigenvalues for sufficiently small nonzero values of g. In the particular case that H is parity-time symmetric then it appears to exhibit real eigenvalues for all 0
Flavor Symmetry and Vacuum Aligned Mass Textures
Kaneko, S; Shingai, T; Tanimoto, M; Yoshioka, K; Kaneko, Satoru; Sawanaka, Hideyuki; Shingai, Takaya; Tanimoto, Morimitsu; Yoshioka, Koichi
2007-01-01
The mass matrix forms of quarks and leptons are discussed in theory with permutation flavor symmetry. The structure of scalar potential is analyzed in case that electroweak doublet Higgs fields have non-trivial flavor symmetry charges. We find that realistic forms of mass matrices are obtained dynamically in the vacuum of the theory, where some of Higgs bosons have vanishing expectation values which lead to vanishing elements in quark and lepton mass matrices. Mass textures are realized in the true vacuum and their positions are controlled by flavor symmetry. An interesting point is that, due to the flavor group structure, the up and down quark mass matrices are automatically made different in the vacuum, which lead to non-vanishing generation mixing. It is also discussed that flavor symmetry is needed to be broken in order not to have too light scalars. The lower bounds of Higgs masses are derived from the experimental data of flavor-changing rare processes such as the neutral K meson mixing.
On systems having Poincaré and Galileo symmetry
Energy Technology Data Exchange (ETDEWEB)
Holland, Peter, E-mail: peter.holland@gtc.ox.ac.uk
2014-12-15
Using the wave equation in d≥1 space dimensions it is illustrated how dynamical equations may be simultaneously Poincaré and Galileo covariant with respect to different sets of independent variables. This provides a method to obtain dynamics-dependent representations of the kinematical symmetries. When the field is a displacement function both symmetries have a physical interpretation. For d=1 the Lorentz structure is utilized to reveal hitherto unnoticed features of the non-relativistic Chaplygin gas including a relativistic structure with a limiting case that exhibits the Carroll group, and field-dependent symmetries and associated Noether charges. The Lorentz transformations of the potentials naturally associated with the Chaplygin system are given. These results prompt the search for further symmetries and it is shown that the Chaplygin equations support a nonlinear superposition principle. A known spacetime mixing symmetry is shown to decompose into label-time and superposition symmetries. It is shown that a quantum mechanical system in a stationary state behaves as a Chaplygin gas. The extension to d>1 is used to illustrate how the physical significance of the dual symmetries is contingent on the context by showing that Maxwell’s equations exhibit an exact Galileo covariant formulation where Lorentz and gauge transformations are represented by field-dependent symmetries. A natural conceptual and formal framework is provided by the Lagrangian and Eulerian pictures of continuum mechanics.
Flavor Symmetry and Topology Change in Nuclear Symmetry Energy for Compact Stars
Lee, Hyun Kyu; Rho, Mannque
2013-03-01
The nuclear symmetry energy figures crucially in the structure of asymmetric nuclei and, more importantly, in the equation of state (EoS) of compact stars. At present it is almost totally unknown, both experimentally and theoretically, in the density regime appropriate for the interior of neutron stars. Basing on a strong-coupled structure of dense baryonic matter encoded in the skyrmion crystal approach with a topology change and resorting to the notion of generalized hidden local symmetry in hadronic interactions, we address a variety of hitherto unexplored issues of nuclear interactions associated with the symmetry energy, i.e., kaon condensation and hyperons, possible topology change in dense matter, nuclear tensor forces, conformal symmetry, chiral symmetry, etc., in the EoS of dense compact-star matter. One of the surprising results coming from HLS structure that is distinct from what is given by standard phenomenological approaches is that at high density, baryonic matter is driven by renormalization group flow to the "dilaton-limit fixed point" constrained by "mended symmetries". We further propose how to formulate kaon condensation and hyperons in compact-star matter in a framework anchored on a single effective Lagrangian by treating hyperons as the Callan-Klebanov kaon-skyrmion bound states simulated on crystal lattice. This formulation suggests that hyperons can figure in the stellar matter — if at all — when or after kaons condense, in contrast to the standard phenomenological approaches where the hyperons appear as the first strangeness degree of freedom in matter, thereby suppressing or delaying kaon condensation. In our simplified description of the stellar structure in terms of symmetry energies, which is compatible with that of the 1.97 solar mass star, kaon condensation plays a role of "doorway state" to strange quark matter.
Topological methods for variational problems with symmetries
Bartsch, Thomas
1993-01-01
Symmetry has a strong impact on the number and shape of solutions to variational problems. This has been observed, for instance, in the search for periodic solutions of Hamiltonian systems or of the nonlinear wave equation; when one is interested in elliptic equations on symmetric domains or in the corresponding semiflows; and when one is looking for "special" solutions of these problems. This book is concerned with Lusternik-Schnirelmann theory and Morse-Conley theory for group invariant functionals. These topological methods are developed in detail with new calculations of the equivariant Lusternik-Schnirelmann category and versions of the Borsuk-Ulam theorem for very general classes of symmetry groups. The Morse-Conley theory is applied to bifurcation problems, in particular to the bifurcation of steady states and hetero-clinic orbits of O(3)-symmetric flows; and to the existence of periodic solutions nearequilibria of symmetric Hamiltonian systems. Some familiarity with the usualminimax theory and basic a...
Symmetry of the polarizability tensors for molecules with D 5h and I h symmetry
Ramaniah, Lavanya M.; Nair, Selvakumar V.; Rustagi, Kailash C.
1993-02-01
We present the spatial symmetry relations between the components of the linear and nonlinear electric dipolar polarizability tensors for the symmetry groups of C 60 and C 70 molecules viz., I h and D 5h. We show that the first hyperpolarizability β of C 7 0 vanishes although the molecule is not inversion symmetric. The second hyperpolarizability γ for C 60 has the same structure as that for an isotropic system. Based on these results, optical harmonic generation measurements to study the inter-molecular bonding in C 60 and C 70 crystals are suggested.
Group theory and its applications
Thapa, Ram Kumar
2019-01-01
Every molecule possesses symmetry and hence has symmetry operations and symmetry elements. From symmetry properties of a system we can deduce its significant physical results. Consequently it is essential to operations of a system forms a group. Group theory is an abstract mathematical tool that underlies the study of symmetry and invariance. By using the concepts of symmetry and group theory, it is possible to obtain the members of complete set of known basis functions of the various irreducible representations of the group. I practice this is achieved by applying the projection operators to linear combinations of atomic orbital (LCAO) when the valence electrons are tightly bound to the ions, to orthogonalized plane waves (OPW) when valence electrons are nearly free and to the other given functions that are judged to the particular system under consideration. In solid state physics the group theory is indispensable in the context of finding the energy bands of electrons in solids. Group theory can be applied...
Symmetry Breaking by Nonstationay Optimisation
Prestwich, S.; Hnich, B.; Rossi, R.; Tarim, S.A.
2008-01-01
We describe a new partial symmetry breaking method that can be used to break arbitrary variable/value symmetries in combination with depth first search, static value ordering and dynamic variable ordering. The main novelty of the method is a new dominance detection technique based on local search in
Lie Symmetries of Ishimori Equation
Institute of Scientific and Technical Information of China (English)
SONG Xu-Xia
2013-01-01
The Ishimori equation is one of the most important (2+1)-dimensional integrable models,which is an integrable generalization of (1+1)-dimensional classical continuous Heisenberg ferromagnetic spin equations.Based on importance of Lie symmetries in analysis of differential equations,in this paper,we derive Lie symmetries for the Ishimori equation by Hirota's direct method.
Hole localization and symmetry breaking
Broer, R; Nieuwpoort, W.C.
1999-01-01
A brief overview is presented of some theoretical work on the symmetry breaking of electronic wavefunctions that followed the early work on Bagus and Schaefer who observed that a considerable lower SCF energy could be obtained for an ionized state of the O2 molecule with a 1s hole if the symmetry re
Symmetry Breaking by Nonstationay Optimisation
Prestwich, S.; Hnich, B.; Rossi, R.; Tarim, S.A.
2008-01-01
We describe a new partial symmetry breaking method that can be used to break arbitrary variable/value symmetries in combination with depth first search, static value ordering and dynamic variable ordering. The main novelty of the method is a new dominance detection technique based on local search in
From scale invariance to Lorentz symmetry
Sibiryakov, Sergey
2014-01-01
It is shown that a unitary translationally invariant field theory in (1+1) dimensions satisfying isotropic scale invariance, standard assumptions about the spectrum of states and operators and the requirement that signals propagate with finite velocity possesses an infinite dimensional symmetry given by one or a product of several copies of conformal algebra. In particular, this implies presence of one or several Lorentz groups acting on the operator algebra of the theory.
Asymptotic Symmetries from finite boxes
Andrade, Tomas
2015-01-01
It is natural to regulate an infinite-sized system by imposing a boundary condition at finite distance, placing the system in a "box." This breaks symmetries, though the breaking is small when the box is large. One should thus be able to obtain the asymptotic symmetries of the infinite system by studying regulated systems. We provide concrete examples in the context of Einstein-Hilbert gravity (with negative or zero cosmological constant) by showing in 4 or more dimensions how the Anti-de Sitter and Poincar\\'e asymptotic symmetries can be extracted from gravity in a spherical box with Dirichlet boundary conditions. In 2+1 dimensions we obtain the full double-Virasoro algebra of asymptotic symmetries for AdS$_3$ and, correspondingly, the full Bondi-Metzner-Sachs (BMS) algebra for asymptotically flat space. In higher dimensions, a related approach may continue to be useful for constructing a good asymptotically flat phase space with BMS asymptotic symmetries.
UV completion without symmetry restoration
Endlich, Solomon; Penco, Riccardo
2013-01-01
We show that it is not possible to UV-complete certain low-energy effective theories with spontaneously broken space-time symmetries by embedding them into linear sigma models, that is, by adding "radial" modes and restoring the broken symmetries. When such a UV completion is not possible, one can still raise the cutoff up to arbitrarily higher energies by adding fields that transform non-linearly under the broken symmetries, that is, new Goldstone bosons. However, this (partial) UV completion does not necessarily restore any of the broken symmetries. We illustrate this point by considering a concrete example in which a combination of space-time and internal symmetries is broken down to a diagonal subgroup. Along the way, we clarify a recently proposed interpretation of inverse Higgs constraints as gauge-fixing conditions.
Shape analysis with subspace symmetries
Berner, Alexander
2011-04-01
We address the problem of partial symmetry detection, i.e., the identification of building blocks a complex shape is composed of. Previous techniques identify parts that relate to each other by simple rigid mappings, similarity transforms, or, more recently, intrinsic isometries. Our approach generalizes the notion of partial symmetries to more general deformations. We introduce subspace symmetries whereby we characterize similarity by requiring the set of symmetric parts to form a low dimensional shape space. We present an algorithm to discover subspace symmetries based on detecting linearly correlated correspondences among graphs of invariant features. We evaluate our technique on various data sets. We show that for models with pronounced surface features, subspace symmetries can be found fully automatically. For complicated cases, a small amount of user input is used to resolve ambiguities. Our technique computes dense correspondences that can subsequently be used in various applications, such as model repair and denoising. © 2010 The Author(s).
A symmetry classification for a class of (2+1)-nonlinear wave equation
Nadjafikhah, Mehdi; Mahdipour-Shirayeh, Ali
2009-01-01
In this paper, a symmetry classification of a $(2+1)$-nonlinear wave equation $u_{tt}-f(u)(u_{xx}+u_{yy})=0$ where $f(u)$ is a smooth function on $u$, using Lie group method, is given. The basic infinitesimal method for calculating symmetry groups is presented, and used to determine the general symmetry group of this $(2+1)$-nonlinear wave equation.
[Plato psychiatrist, Foucault platonic].
Mathov, Nicolás
2016-05-01
This work explores the links between the concepts of "soul", "law" and "word" in Plato's work, in order to highlight the importance and the centrality of the philosophical-therapeutic dimension in the Greek philosopher's thought. In that way, this work pretends to show that "contemporary" problems usually discussed within "Human Sciences" in general, and Psychiatry in particular, should confront their knowledge with Plato's work, mainly due to the profound influence his ideas have had in our Greco-Christian culture. In that sense, and with that objective, this work also explores Michel Foucault's lucid and controversial interpretation of Plato.
Hawkins, David
1985-01-01
Some questions about the relevance of the philosophy of mathematics to mathematics teaching and to early mathematics learning are discussed. Books by Lakatos, Davis and Hersh, and Kitcher are referred to extensively, with comments on a variety of instructional practices. (MNS)
DEFF Research Database (Denmark)
Tortzen, Gorm
2007-01-01
Den korte dialog 'Kleitofon' hører til den gruppe i Corpus Platonicum, der ofte anses for at være uægte. Indledningen problematiserer dette, der gives en ny ovesættelse, og der føjes en række oplysende noter til teksten. Udgivelsesdato: April...
Socrates: Platonic Political Ideal
Directory of Open Access Journals (Sweden)
Christopher P. Long
2012-01-01
Full Text Available El ensayo articula diferencias y sugiere similitudes entre las prácticas del diálogo político de Sócrates y aquellas de la escritura política de Platón. Propone, además, que tanto el diálogo socrático como la escritura platónica se orientan eróticamente hacia ideales capaces de transformar las vidas de los individuos y sus relaciones. Demuestra que en el Protágoras las prácticas del diálogo socrático se ocupan menos de Protágoras que del joven Hipócrates. En el Fedón, este ideal de Sócrates se amplía de tal manera que la misma escritura platónica aparece como capaz de hacer con los lectores lo que el diálogo de Sócrates hacía con sus interlocutores. Sócrates es el ideal político platónico. El resultado es una visión del poder de transformación política tanto del diálogo socrático como de la escritura platónica.
Platonic Relationships among Resistors
Allen, Bradley; Liu, Tongtian
2015-01-01
Calculating the effective resistance of an electrical network is a common problem in introductory physics courses. Such calculations are typically restricted to two-dimensional networks, though even such networks can become increasingly complex, leading to several studies on their properties. Furthermore, several authors have used advanced…
Directory of Open Access Journals (Sweden)
Maria Chiara Pievatolo
2015-01-01
Full Text Available Nei colloqui precedenti si erano toccate molte opinioni filosofiche sbagliate, e allora Socrate dice: “Sarebbe ben comprensibile se uno, a motivo dell’irritazione per tante cose sbagliate, per il resto della sua vita prendesse in odio ogni discorso sull’essere e lo...
Mei Symmetry and Lie Symmetry of the Rotational Relativistic Variable Mass System
Institute of Scientific and Technical Information of China (English)
FANGJian-Hui
2003-01-01
The Mei symmetry and the Lie symmetry of a rotational relativistic variable mass system are studied. The definitions and criteria of the Mei symmetry and the Lie symmetry of the rotational relativistic variable mass system are given. The relation between the Mei symmetry and the Lie symmetry is found. The conserved quantities which the Mei symmetry and the Lie symmetry lead to are obtained. An example is given to illustrate the application of the result.
Replica symmetry breaking for anisotropic magnets with quenched disorder
Kogan, E.; Kaveh, M.
2017-01-01
We study critical behaviour of a magnet with cubic anisotropy and quenched scalar disorder which is taken into account by replica method. We derive to first order in ε approximation the renormalization group equations taking into account possible replica symmetry breaking. We study the stability of the replica symmetric fixed points with respect to perturbations without (in general case) replica symmetry. However, we find that if a fixed point is stable with respect to replica symmetric deviations, it is also stable with respect to deviations without replica symmetry.
Symmetry and structure of SrTiO3 nanotubes
Evarestov, Robert
2011-06-01
The full study of perovskite type nanotubes with square morphology is given for the first time. The line symmetry group L = ZP (a product of one axial point group P and one infinite cyclic group Z of generalized translations) of single-walled (SW) and double-walled (DW) SrTiO3 nanotubes (NT) is considered. The nanotube is defined by the square lattice translation vector L = l1a + l2b and chiral vector R = n1a + n2b, (l1, l2, n1 and n2 are integers). The nanotube of the chirality (n1,n2) is obtained by folding the (001) slabs of two- layers (with the layer group P4mm) and of three layers (with the layer group P4/mmm) in a way that the chiral vector R becomes circumference of the nanotube. Due to the orthogonality relation (RL) = 0, l1/l2 = -n2/n1 i.e. SW nanotubes with square morphology are commensurate for any rolling vector R(n1,n2). For SW (n,0) NTs the line symmetry groups belong to family 11 (T^Dnh) and are n/mmm or for even and odd n, respectively. For SW (n,n) NTs the line symmetry groups (2n)n/mcm belong to family 13 (T2n1 Dnh). The line symmetry group of a double-wall nanotube is found as intersection L2 = Z2P2 = (L ∩ L') of the symmetry groups L and L' of its single-wall constituents as earlier considered for DW CNTs. The symmetry group of DWNT (n,0)@M(n,0) belongs to the same family 11 (T^Dnh) as its SW constituents. The symmetry group of DWNT (n,n)@M(n,n) depends on the parity of M. For DW NTs with odd M, the line symmetry groups are the same as for their SW constituents and belong to family 13 (T2n1 Dnh). For even M, the rotations about screw axis of order 2n are changed by rotations around pure rotation axis of order n so that DW NT line symmetry groups belong to family 11 (T^Dnh). Commensurate STO DWNTs (n1,0)@(n2,0) and (n1, n1)@(n2, n2) belong to family 11 (T^Dnh) with n equal to the greatest common divisor of n1 and n2.
Haghshenas, R; Langari, A; Rezakhani, A T
2014-11-12
We study different phases of the one-dimensional bond-alternating spin-1/2 Heisenberg model by using the symmetry fractionalization mechanism. We employ the infinite matrix-product state representation of the ground state (through the infinite-size density matrix renormalization group algorithm) to obtain inequivalent projective representations and commutation relations of the (unbroken) symmetry groups of the model, which are used to identify the different phases. We find that the model exhibits trivial as well as symmetry-protected topological phases. The symmetry-protected topological phases are Haldane phases on even/odd bonds, which are protected by the time-reversal (acting on the spin as σ → -σ), parity (permutation of the chain about a specific bond), and dihedral (π-rotations about a pair of orthogonal axes) symmetries. Additionally, we investigate the phases of the most general two-body bond-alternating spin-1/2 model, which respects the time-reversal, parity, and dihedral symmetries, and obtain its corresponding twelve different types of the symmetry-protected topological phases.
Directory of Open Access Journals (Sweden)
José Lourenço Pereira da Silva
2011-03-01
Full Text Available The platonic ontology as known through the Phaedo and Republic is centered on the hypothesis of the intelligible Forms, that is, the platonic Socrates' belief that there are ontologically independent entities such as "the beautiful itself", "the good itself", "the equal itself" etc., of which all empirical things participate thereby receiving the properties they exhibit. Clearly, the main philosophical influences on this doctrine are pre-Socratic philosophy, the sophistic and Socrates' thought. The aim of this paper is to present which ideas or philosophical questions led Plato to postulate the Forms.
A ontologia platônica, como conhecida a partir do Fédon e da República, está centrada na hipótese das Formas inteligíveis, ou seja, a crença defendida pelo Sócrates platônico na existência de entidades ontologicamente independentes, “o belo em si”, “o bem em si”, “o igual em si”, etc., das quais as coisas empíricas participam recebendo por isso as propriedades que exibem. Notoriamente, as principais influências filosóficas dessa doutrina são a filosofia pré-socrática, a sofística e o pensamento de Sócrates. O objetivo deste artigo é mostrar que ideias ou questões filosóficas levaram Platão a postular as Formas.
Gravitation and Gauge Symmetries
Stewart, J
2002-01-01
The purpose of this book (I quote verbatim from the back cover) is to 'shed light upon the intrinsic structure of gravity and the principle of gauge invariance, which may lead to a consistent unified field theory', a very laudable aim. The content divides fairly clearly into four sections (and origins). After a brief introduction, chapters 2-6 review the 'Structure of gravity as a theory based on spacetime gauge symmetries'. This is fairly straightforward material, apparently based on a one-semester graduate course taught at the University of Belgrade for about two decades, and, by implication, this is a reasonably accurate description of its level and assumed knowledge. There follow two chapters of new material entitled 'Gravity in flat spacetime' and 'Nonlinear effects in gravity'. The final three chapters, entitled 'Supersymmetry and supergravity', 'Kaluza-Klein theory' and 'String theory' have been used for the basis of a one-semester graduate course on the unification of fundamental interactions. The boo...
Symmetries in nuclear structure
Allaart, K; Dieperink, A
1983-01-01
The 1982 summer school on nuclear physics, organized by the Nuclear Physics Division of the Netherlands' Physical Society, was the fifth in a series that started in 1963. The number of students attending has always been about one hundred, coming from about thirty countries. The theme of this year's school was symmetry in nuclear physics. This book covers the material presented by the enthusi astic speakers, who were invited to lecture on this subject. We think they have succeeded in presenting us with clear and thorough introductory talks at graduate or higher level. The time schedule of the school and the location allowed the participants to make many informal contacts during many social activities, ranging from billiards to surf board sailing. We hope and expect that the combination of a relaxed atmosphere during part of the time and hard work during most of the time, has furthered the interest in, and understanding of, nuclear physics. The organization of the summer school was made possible by substantia...
Structural and Symmetry Analysis of Discrete Dynamical Systems
Kornyak, Vladimir V
2010-01-01
To study discrete dynamical systems of different types --- deterministic, statistical and quantum --- we develope various approaches. We introduce the concept of a system of discrete relations on an abstract simplicial complex and develope algorithms for analysis of compatibility and construction of canonical decompositions of such systems. To illustrate these techniques we describe their application to some cellular automata. Much attention is paid to study symmetries of the systems. In the case of deterministic systems we reveale some important relations between symmetries and dynamics. We demonstrate that moving soliton-like structures arise inevitably in deterministic dynamical system whose symmetry group splits the set of states into finite number of group orbits. We develope algorithms and programs exploiting discrete symmetries to study microcanonical ensembles and search phase transitions in mesoscopic lattice models. We propose an approach to quantization of discrete systems based on introduction of ...
O'Hanlon actions by Noether symmetry
Darabi, F.
2015-01-01
By using the conformal symmetry between Brans-Dicke action with $\\omega=-\\frac{3}{2}$ and O'Hanlon action, we seek the O'Hanlon actions in Einstein frame respecting the Noether symmetry. Since the Noether symmetry is preserved under conformal transformations, the existence of Noether symmetry in the Brans-Dicke action asserts the Noether symmetry in O'Hanlon action in Einstein frame. Therefore, the potentials respecting Noether symmetry in Brans-Dicke action give the corresponding potentials ...
Quasidynamical symmetries in the backbending of chromium isotopes
Herrera, Raúl A.; Johnson, Calvin W.
2017-02-01
Background: Symmetries are a powerful way to characterize nuclear wave functions. A true dynamical symmetry, where the Hamiltonian is block-diagonal in subspaces defined by the group, is rare. More likely is a quasidynamical symmetry: states with different quantum numbers (i.e., angular momentum) nonetheless sharing similar group-theoretical decompositions. Purpose: We use group-theoretical decomposition to investigate backbending, an abrupt change in the moment of inertia along the yrast line, in 48,49,50Cr: prior mean-field calculations of these nuclides suggest a change from strongly prolate to more spherical configurations as one crosses the backbending and increases in angular momentum. Methods: We decompose configuration-interaction shell-model wave functions using the SU(2) groups L (total orbital angular momentum) and S (total spin), and the groups SU(3) and SU(4). We do not need a special basis but only matrix elements of Casimir operators, applied with a modified Lanczos algorithm. Results: We find quasidynamical symmetries, albeit often of a different character above and below the backbending, for each group. While the strongest evolution was in SU(3), the decompositions did not suggest a decrease in deformation. We point out with a simple example that mean-field and SU(3) configurations may give very different pictures of deformation. Conclusions: Persistent quasidynamical symmetries for several groups allow us to identify the members of a band and to characterize how they evolve with increasing angular momentum, especially before and after backbending.
Spectral theorem and partial symmetries
Energy Technology Data Exchange (ETDEWEB)
Gozdz, A. [University of Maria Curie-Sklodowska, Department of Mathematical Physics, Institute of Physics (Poland); Gozdz, M. [University of Maria Curie-Sklodowska, Department of Complex Systems and Neurodynamics, Institute of Informatics (Poland)
2012-10-15
A novel method of the decompositon of a quantum system's Hamiltonian is presented. In this approach the criterion of the decomposition is determined by the symmetries possessed by the sub-Hamiltonians. This procedure is rather generic and independent of the actual global symmetry, or the lack of it, of the full Hamilton operator. A detailed investigation of the time evolution of the various sub-Hamiltonians, therefore the change in time of the symmetry of the physical object, is presented for the case of a vibrator-plus-rotor model. Analytical results are illustrated by direct numerical calculations.
Astroparticle tests of Lorentz symmetry
Energy Technology Data Exchange (ETDEWEB)
Diaz, Jorge [Karlsruhe Institute of Technology, Karlsruhe (Germany)
2016-07-01
Lorentz symmetry is a cornerstone of modern physics. As the spacetime symmetry of special relativity, Lorentz invariance is a basic component of the standard model of particle physics and general relativity, which to date constitute our most successful descriptions of nature. Deviations from exact symmetry would radically change our view of the universe and current experiments allow us to test the validity of this assumption. In this talk, I describe effects of Lorentz violation in cosmic rays and gamma rays that can be studied in current observatories.
Symmetry protected single photon subradiance
Cai, Han; Svidzinsky, Anatoly A; Zhu, Shi-Yao; Scully, Marlan O
2016-01-01
We study the protection of subradiant states by the symmetry of the atomic distributions in the Dicke limit, in which collective Lamb shift cannot be neglected. We find that anti-symmetric states are subradiant states for distribution with reflection symmetry. These states can be prepared by anti-symmetric optical modes and converted to superradiant states by properly tailored 2\\pipulses. Continuous symmetry can also be used to achieve subradiance. This study is relevant to the problem of robust quantum memory with long storage time and fast readout.
The flavour problem and family symmetry beyond the Standard Model
Dziewit, Bartosz; Richter, Monika; Zając, Sebastian; Zrałek, Marek
2016-01-01
In the frame of two Higgs doublet model we try to explain the lepton masses and mixing matrix elements assuming that neutrinos are Dirac particles. Discrete family symmetry groups, which are subgroups of U(3) up to the 1025 order are considered. Like in the one Higgs Standard Model, we found that discrete family symmetries do not give satisfactory answer for this basic questions in the flavour problem.
Application of Symmetry Methods to Low-Dimensional Heisenberg Magnets
Directory of Open Access Journals (Sweden)
Irene G. Bostrem
2010-04-01
Full Text Available An account of symmetry is very fruitful in studies of quantum spin systems. In the present paper we demonstrate how to use the spin SU(2 and the point symmetries in optimization of the theoretical condensed matter tools: the exact diagonalization, the renormalization group approach, the cluster perturbation theory. We apply the methods for study of Bose-Einstein condensation in dimerized antiferromagnets, for investigations of magnetization processes and magnetocaloric effect in quantum ferrimagnetic chain.
Crystallographic interpretation of Galois symmetries for magnetic pentagonal ring
Milewski, J.; Lulek, T.; Łabuz, M.
2017-03-01
Galois symmetry of exact Bethe Ansatz eigenstates for the magnetic pentagonal ring within the XXX model are investigated by a comparison with crystallographic constructions of space groups. It follows that the arithmetic symmetry of Bethe parameters for the interior of the Brillouin zone admits crystallographic interpretation, in terms of the periodic square Z2 ×Z2 , that is the two-dimensional crystal lattice with Born-Karman period two in both directions.