International Nuclear Information System (INIS)
Webb, G M; Zank, G P
2007-01-01
We explore the role of the Lagrangian map for Lie symmetries in magnetohydrodynamics (MHD) and gas dynamics. By converting the Eulerian Lie point symmetries of the Galilei group to Lagrange label space, in which the Eulerian position coordinate x is regarded as a function of the Lagrange fluid labels x 0 and time t, one finds that there is an infinite class of symmetries in Lagrange label space that map onto each Eulerian Lie point symmetry of the Galilei group. The allowed transformation of the Lagrangian fluid labels x 0 corresponds to a fluid relabelling symmetry, including the case where there is no change in the fluid labels. We also consider a class of three, well-known, scaling symmetries for a gas with a constant adiabatic index γ. These symmetries map onto a modified form of the fluid relabelling symmetry determining equations, with non-zero source terms. We determine under which conditions these symmetries are variational or divergence symmetries of the action, and determine the corresponding Lagrangian and Eulerian conservation laws by use of Noether's theorem. These conservation laws depend on the initial entropy, density and magnetic field of the fluid. We derive the conservation law corresponding to the projective symmetry in gas dynamics, for the case γ = (n + 2)/n, where n is the number of Cartesian space coordinates, and the corresponding result for two-dimensional (2D) MHD, for the case γ = 2. Lie algebraic structures in Lagrange label space corresponding to the symmetries are investigated. The Lie algebraic symmetry relations between the fluid relabelling symmetries in Lagrange label space, and their commutators with a linear combination of the three symmetries with a constant adiabatic index are delineated
Dorodnitsyn, Vladimir A.; Kozlov, Roman; Meleshko, Sergey V.; Winternitz, Pavel
2018-05-01
A recent article was devoted to an analysis of the symmetry properties of a class of first-order delay ordinary differential systems (DODSs). Here we concentrate on linear DODSs, which have infinite-dimensional Lie point symmetry groups due to the linear superposition principle. Their symmetry algebra always contains a two-dimensional subalgebra realized by linearly connected vector fields. We identify all classes of linear first-order DODSs that have additional symmetries, not due to linearity alone, and we present representatives of each class. These additional symmetries are then used to construct exact analytical particular solutions using symmetry reduction.
Structure of Lie point and variational symmetry algebras for a class of odes
Ndogmo, J. C.
2018-04-01
It is known for scalar ordinary differential equations, and for systems of ordinary differential equations of order not higher than the third, that their Lie point symmetry algebras is of maximal dimension if and only if they can be reduced by a point transformation to the trivial equation y(n)=0. For arbitrary systems of ordinary differential equations of order n ≥ 3 reducible by point transformations to the trivial equation, we determine the complete structure of their Lie point symmetry algebras as well as that for their variational, and their divergence symmetry algebras. As a corollary, we obtain the maximal dimension of the Lie point symmetry algebra for any system of linear or nonlinear ordinary differential equations.
On Lie point symmetry of classical Wess-Zumino-Witten model
International Nuclear Information System (INIS)
Maharana, Karmadeva
2001-06-01
We perform the group analysis of Witten's equations of motion for a particle moving in the presence of a magnetic monopole, and also when constrained to move on the surface of a sphere, which is the classical example of Wess-Zumino-Witten model. We also consider variations of this model. Our analysis gives the generators of the corresponding Lie point symmetries. The Lie symmetry corresponding to Kepler's third law is obtained in two related examples. (author)
Lie Point Symmetries and Exact Solutions of the Coupled Volterra System
International Nuclear Information System (INIS)
Ping, Liu; Sen-Yue, Lou
2010-01-01
The coupled Volterra system, an integrable discrete form of a coupled Korteweg–de Vries (KdV) system applied widely in fluids, Bose–Einstein condensation and atmospheric dynamics, is studied with the help of the Lie point symmetries. Two types of delayed differential reduction systems are derived from the coupled Volterra system by means of the symmetry reduction approach and symbolic computation. Cnoidal wave and solitary wave solutions for a delayed differential reduction system and the coupled Volterra system are proposed, respectively. (general)
Lie symmetries and superintegrability
International Nuclear Information System (INIS)
Nucci, M C; Post, S
2012-01-01
We show that a known superintegrable system in two-dimensional real Euclidean space (Post and Winternitz 2011 J. Phys. A: Math. Theor. 44 162001) can be transformed into a linear third-order equation: consequently we construct many autonomous integrals—polynomials up to order 18—for the same system. The reduction method and the connection between Lie symmetries and Jacobi last multiplier are used.
Lie symmetries in differential equations
International Nuclear Information System (INIS)
Pleitez, V.
1979-01-01
A study of ordinary and Partial Differential equations using the symmetries of Lie groups is made. Following such a study, an application to the Helmholtz, Line-Gordon, Korleweg-de Vries, Burguer, Benjamin-Bona-Mahony and wave equations is carried out [pt
Classical Lie Point Symmetry Analysis of a Steady Nonlinear One-Dimensional Fin Problem
Directory of Open Access Journals (Sweden)
R. J. Moitsheki
2012-01-01
Full Text Available We consider the one-dimensional steady fin problem with the Dirichlet boundary condition at one end and the Neumann boundary condition at the other. Both the thermal conductivity and the heat transfer coefficient are given as arbitrary functions of temperature. We perform preliminary group classification to determine forms of the arbitrary functions appearing in the considered equation for which the principal Lie algebra is extended. Some invariant solutions are constructed. The effects of thermogeometric fin parameter and the exponent on temperature are studied. Also, the fin efficiency is analyzed.
Comparison of IBM-2 calculations with X(5) critical point symmetry for low lying states in 128-140Nd
International Nuclear Information System (INIS)
Uluer, I.; Olgun, D.; Inan, S.; Tuerkan, N.
2006-01-01
The X(5) would take place when moving continuously from the pure U(5) symmetry to the SU(3) symmetry and it implies a definite relations among the level energies and among the E2 transition strengths. It was recently shown that a signature of phase transition is observed in the chain of Sm, Mo and Nd isotopes, where 1 52Sm, 1 04Mo and 1 50Nd display the predicted features of the X(5) symmetry and mark therefore the critical point. However, more detailed studies and experiments are needed to get ideas about this signature. Without entering into detail we have firstly compared the results obtained in our previous study of 1 28- 1 40Nd with that of the limits in X(5) symmetry and then given a clear description about the validity of the Hamiltonian parameters used in the study. At the end, we have concluded that some of Nd isotopes display X(5) symmetry features
Lie and Noether symmetries of systems of complex ordinary ...
Indian Academy of Sciences (India)
2014-07-02
Jul 2, 2014 ... Abstract. The Lie and Noether point symmetry analyses of a kth-order system of m complex ordi- nary differential equations (ODEs) with m dependent variables are performed. The decomposition of complex symmetries of the given system of complex ODEs yields Lie- and Noether-like opera- tors.
Lie symmetries for systems of evolution equations
Paliathanasis, Andronikos; Tsamparlis, Michael
2018-01-01
The Lie symmetries for a class of systems of evolution equations are studied. The evolution equations are defined in a bimetric space with two Riemannian metrics corresponding to the space of the independent and dependent variables of the differential equations. The exact relation of the Lie symmetries with the collineations of the bimetric space is determined.
Automorphic Lie algebras with dihedral symmetry
International Nuclear Information System (INIS)
Knibbeler, V; Lombardo, S; A Sanders, J
2014-01-01
The concept of automorphic Lie algebras arises in the context of reduction groups introduced in the early 1980s in the field of integrable systems. automorphic Lie algebras are obtained by imposing a discrete group symmetry on a current algebra of Krichever–Novikov type. Past work shows remarkable uniformity between algebras associated to different reduction groups. For example, if the base Lie algebra is sl 2 (C) and the poles of the automorphic Lie algebra are restricted to an exceptional orbit of the symmetry group, changing the reduction group does not affect the Lie algebra structure. In this research we fix the reduction group to be the dihedral group and vary the orbit of poles as well as the group action on the base Lie algebra. We find a uniform description of automorphic Lie algebras with dihedral symmetry, valid for poles at exceptional and generic orbits. (paper)
International Nuclear Information System (INIS)
Ma Hongcai
2005-01-01
Using the (2+1)-dimensional Broer-Kaup equation as an simple example, a new direct method is developed to find symmetry groups and symmetry algebras and then exact solutions of nonlinear mathematical physical equations.
Lie-algebra approach to symmetry breaking
International Nuclear Information System (INIS)
Anderson, J.T.
1981-01-01
A formal Lie-algebra approach to symmetry breaking is studied in an attempt to reduce the arbitrariness of Lagrangian (Hamiltonian) models which include several free parameters and/or ad hoc symmetry groups. From Lie algebra it is shown that the unbroken Lagrangian vacuum symmetry can be identified from a linear function of integers which are Cartan matrix elements. In broken symmetry if the breaking operators form an algebra then the breaking symmetry (or symmetries) can be identified from linear functions of integers characteristic of the breaking symmetries. The results are applied to the Dirac Hamiltonian of a sum of flavored fermions and colored bosons in the absence of dynamical symmetry breaking. In the partially reduced quadratic Hamiltonian the breaking-operator functions are shown to consist of terms of order g 2 , g, and g 0 in the color coupling constants and identified with strong (boson-boson), medium strong (boson-fermion), and fine-structure (fermion-fermion) interactions. The breaking operators include a boson helicity operator in addition to the familiar fermion helicity and ''spin-orbit'' terms. Within the broken vacuum defined by the conventional formalism, the field divergence yields a gauge which is a linear function of Cartan matrix integers and which specifies the vacuum symmetry. We find that the vacuum symmetry is chiral SU(3) x SU(3) and the axial-vector-current divergence gives a PCAC -like function of the Cartan matrix integers which reduces to PCAC for SU(2) x SU(2) breaking. For the mass spectra of the nonets J/sup P/ = 0 - ,1/2 + ,1 - the integer runs through the sequence 3,0,-1,-2, which indicates that the breaking subgroups are the simple Lie groups. Exact axial-vector-current conservation indicates a breaking sum rule which generates octet enhancement. Finally, the second-order breaking terms are obtained from the second-order spin tensor sum of the completely reduced quartic Hamiltonian
DEFF Research Database (Denmark)
Webb, Garry; Sørensen, Mads Peter; Brio, Moysey
2004-01-01
the electromagnetic momentum and energy conservation laws, corresponding to the space and time translation invariance symmetries. The symmetries are used to obtain classical similarity solutions of the equations. The traveling wave similarity solutions for the case of a cubic Kerr nonlinearity, are shown to reduce...... the properties of Maxwell's equations in nonlinear optics, without resorting to the commonly used nonlinear Schr\\"odinger (NLS) equation approximation in which a high frequency carrier wave is modulated on long length and time scales due to nonlinear sideband wave interactions. This is important in femto......-second pulse propagation in which the NLS approximation is expected to break down. The canonical Hamiltonian description of the equations involves the solution of a polynomial equation for the electric field $E$, in terms of the the canonical variables, with possible multiple real roots for $E$. In order...
Integrable systems and lie symmetries in classical mechanics
International Nuclear Information System (INIS)
Sen, T.
1986-01-01
The interrelationship between integrability and symmetries in classical mechanics is studied. Two-dimensional time- and velocity-independent potentials form the domain of the study. It is shown that, contrary to folklore, existence of a single finite symmetry does not ensure integrability. A method due to Darboux is used to construct potentials that admit a time-independent invariant. All potentials admitting invariants linear or quadratic in the momentum coordinates are constructed. These are the only integrable potentials which can be expressed as arbitrary functions of certain arguments. A complete construction of potentials admitting higher-order invariants does not seem possible. However, the necessary general forms for potentials that admit a particular invariant of arbitrary order are found. These invariants must be spherically symmetric in the leading terms. Two kinds of symmetries are studied: point Lie symmetries of the Newtonian equations of motion for conservative potentials, and point Noether symmetries of the action functionals obtained from the standard Lagrangians associated with these potentials. All conservative potentials which admit these symmetries are constructed. The class of potentials admitting Noether symmetries is shown to be a subclass of those admitting Lie symmetries
Noether and Lie symmetries for charged perfect fluids
International Nuclear Information System (INIS)
Kweyama, M C; Govinder, K S; Maharaj, S D
2011-01-01
We study the underlying nonlinear partial differential equation that governs the behaviour of spherically symmetric charged fluids in general relativity. We investigate the conditions for the equation to admit a first integral or be reduced to quadratures using symmetry methods for differential equations. A general Noether first integral is found. We also undertake a comprehensive group analysis of the underlying equation using Lie point symmetries. The existence of a Lie symmetry is subject to solving an integro-differential equation in general; we investigate the conditions under which it can be reduced to quadratures. Earlier results for uncharged fluids and particular first integrals for charged matter are regained as special cases of our treatment.
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
Higher order Lie-Baecklund symmetries of evolution equations
International Nuclear Information System (INIS)
Roy Chowdhury, A.; Roy Chowdhury, K.; Paul, S.
1983-10-01
We have considered in detail the analysis of higher order Lie-Baecklund symmetries for some representative nonlinear evolution equations. Until now all such symmetry analyses have been restricted only to the first order of the infinitesimal parameter. But the existence of Baecklund transformation (which can be shown to be an overall sum of higher order Lie-Baecklund symmetries) makes it necessary to search for such higher order Lie-Baecklund symmetries directly without taking recourse to the Baecklund transformation or inverse scattering technique. (author)
International Nuclear Information System (INIS)
Zhi Hongyan
2009-01-01
In this paper, based on the symbolic computing system Maple, the direct method for Lie symmetry groups presented by Sen-Yue Lou [J. Phys. A: Math. Gen. 38 (2005) L129] is extended from the continuous differential equations to the differential-difference equations. With the extended method, we study the well-known differential-difference KP equation, KZ equation and (2+1)-dimensional ANNV system, and both the Lie point symmetry groups and the non-Lie symmetry groups are obtained.
Lie Symmetry Analysis of the Inhomogeneous Toda Lattice Equation via Semi-Discrete Exterior Calculus
International Nuclear Information System (INIS)
Liu Jiang; Wang Deng-Shan; Yin Yan-Bin
2017-01-01
In this work, the Lie point symmetries of the inhomogeneous Toda lattice equation are obtained by semi-discrete exterior calculus, which is a semi-discrete version of Harrison and Estabrook’s geometric approach. A four-dimensional Lie algebra and its one-, two- and three-dimensional subalgebras are given. Two similarity reductions of the inhomogeneous Toda lattice equation are obtained by using the symmetry vectors. (paper)
A note on the Lie symmetries of complex partial differential
Indian Academy of Sciences (India)
Folklore suggests that the split Lie-like operators of a complex partial differential equation are symmetries of the split system of real partial differential equations. However, this is not the case generally. We illustrate this by using the complex heat equation, wave equation with dissipation, the nonlinear Burgers equation and ...
Lie algebra symmetries and quantum phase transitions in nuclei
Indian Academy of Sciences (India)
2014-04-05
Apr 5, 2014 ... 743–755. Lie algebra symmetries and quantum phase transitions in nuclei .... Applications of this CS to QPT in sdgIBM model will be briefly ..... as a linear combination of ˆC2, ˆC3 and ˆC4 of SUsdg(5) and similarly also for the.
Directory of Open Access Journals (Sweden)
W. Sinkala
2012-01-01
Full Text Available We use Lie symmetry analysis to solve a boundary value problem that arises in chemical engineering, namely, mass transfer during the contact of a solid slab with an overhead flowing fluid. This problem was earlier tackled using Adomian decomposition method (Fatoorehchi and Abolghasemi 2011, leading to the Adomian series form of solution. It turns out that the application of Lie group analysis yields an elegant form of the solution. After introducing the governing mathematical model and some preliminaries of Lie symmetry analysis, we compute the Lie point symmetries admitted by the governing equation and use these to construct the desired solution as an invariant solution.
Lie-isotopic generalization of the Poincare symmetry: Classical formulation
International Nuclear Information System (INIS)
Santilli, R.M.
1991-03-01
This paper is devoted to the origin and methodology of the several phenomenological predictions of deviations from Einstein's Special Relativity and related Lorentz symmetry in the behaviour of the lifetime of unstable hadrons at different speeds, that exist in the literature since the early '60's. After reviewing the background phenomenological literature, we outline the Lie-isotopic symmetry of the emerging deformations of the Minkowski metric introduced in a preceding paper, and extend the results to the construction of the full Poincare-isotopic symmetry. The local isomorphism of the Poincare-isotopic symmetry with the conventional symmetry is proved for all possible topology-preserving deformations of the Minkowski metric. In this way we establish that the phenomenological predictions of deviations recalled earlier must be specifically referred to Einstein's Special Relativity, but they cannot be referred to the Lorentz (or to the Poincare) symmetry which remains exact. Particular attention is devoted to the proof of the compatibility of the exact validity of the Special Relativity for the center-of-mass trajectory of a hadron in a particle accelerator, with conceivable deviations from the same relativity in the interior structural problem. For completeness, the analysis is complemented with a few remarks on the gravitational profile. First, we review the pioneering Lie-isotopic generalization of Einstein's Gravitation worked out by Gasperini, which possesses precisely a locally Lorentz-isotopic structure. We then restrict this theory to the interior gravitational problem in order to achieve compatibility with the particle setting. The paper concludes with a review of the need to finally conduct direct experimental measures of the lifetime of unstable hadrons at different speeds, in order to finally resolve whether Einsteins's Special and General Relativities are locally valid in the interior of hadrons, or structurally more general relativities must be worked
Lie symmetry analysis and conservation laws for the time fractional fourth-order evolution equation
Directory of Open Access Journals (Sweden)
Wang Li
2017-06-01
Full Text Available In this paper, we study Lie symmetry analysis and conservation laws for the time fractional nonlinear fourth-order evolution equation. Using the method of Lie point symmetry, we provide the associated vector fields, and derive the similarity reductions of the equation, respectively. The method can be applied wisely and efficiently to get the reduced fractional ordinary differential equations based on the similarity reductions. Finally, by using the nonlinear self-adjointness method and Riemann-Liouville time-fractional derivative operator as well as Euler-Lagrange operator, the conservation laws of the equation are obtained.
Lie Symmetry Analysis of the Inhomogeneous Toda Lattice Equation via Semi-Discrete Exterior Calculus
Liu, Jiang; Wang, Deng-Shan; Yin, Yan-Bin
2017-06-01
In this work, the Lie point symmetries of the inhomogeneous Toda lattice equation are obtained by semi-discrete exterior calculus, which is a semi-discrete version of Harrison and Estabrook’s geometric approach. A four-dimensional Lie algebra and its one-, two- and three-dimensional subalgebras are given. Two similarity reductions of the inhomogeneous Toda lattice equation are obtained by using the symmetry vectors. Supported by National Natural Science Foundation of China under Grant Nos. 11375030, 11472315, and Department of Science and Technology of Henan Province under Grant No. 162300410223 and Beijing Finance Funds of Natural Science Program for Excellent Talents under Grant No. 2014000026833ZK19
Does a point lie inside a polygon
International Nuclear Information System (INIS)
Milgram, M.S.
1988-01-01
A superficially simple problem in computational geometry is that of determining whether a query point P lies in the interior of a polygon if it lies in the polygon's plane. Answering this question is often required when tracking particles in a Monte Carlo program; it is asked frequently and an efficient algorithm is crucial. Littlefield has recently rediscovered Shimrat's algorithm, while in separate works, Wooff, Preparata and Shamos and Mehlhorn, as well as Yamaguchi, give other algorithms. A practical algorithm answering this question when the polygon's plane is skewed in space is not immediately evident from most of these methods. Additionally, all but one fails when two sides extend to infinity (open polygons). In this paper the author review the above methods and present a new, efficient algorithm, valid for all convex polygons, open or closed, and topologically connected in n-dimensional space (n ≥ 2)
International Nuclear Information System (INIS)
Chowdhury, A.R.; Mukherjee, R.
1984-01-01
The authors have made an exhaustive analysis for an equation introduced by Sabatier (1981) which in the special case reduces to the Harry-Dym equation. First they have deduced the Lie point symmetries and the corresponding ordinary differential equation, through the similarity forms. Next the extended Lie-Backlund type generators are deduced. In the second part the cnoidal wave like solutions are considered. From the Fourier spectrum analysis it is shown that a cnoidal wave breaks into several ordinary solitary waves. (Auth.)
Radiative symmetry breaking from interacting UV fixed points
DEFF Research Database (Denmark)
Abel, Steven; Sannino, Francesco
2017-01-01
It is shown that the addition of positive mass-squared terms to asymptotically safe gauge-Yukawa theories with perturbative UV fixed points leads to calculable radiative symmetry breaking in the IR. This phenomenon, and the multiplicative running of the operators that lies behind it, is akin...
Lie and conditional symmetries of the three-component diffusive Lotka–Volterra system
International Nuclear Information System (INIS)
Cherniha, Roman; Davydovych, Vasyl’
2013-01-01
Lie and Q-conditional symmetries of the classical three-component diffusive Lotka–Volterra system in the case of one space variable are studied. The group-classification problems for finding Lie symmetries and Q-conditional symmetries of the first type are completely solved. Notably, non-Lie symmetries (Q-conditional symmetry operators) for a multi-component nonlinear reaction–diffusion system are constructed for the first time. The results are compared with those derived for the two-component diffusive Lotka–Volterra system. The conditional symmetry obtained for the non-Lie reduction of the three-component system used for modeling competition between three species in population dynamics is applied and the relevant exact solutions are found. Particularly, the exact solution describing different scenarios of competition between three species is constructed. (paper)
Directory of Open Access Journals (Sweden)
Emrullah Yaşar
Full Text Available In this paper Lie symmetry analysis of the seventh-order time fractional Sawada–Kotera–Ito (FSKI equation with Riemann–Liouville derivative is performed. Using the Lie point symmetries of FSKI equation, it is shown that it can be transformed into a nonlinear ordinary differential equation of fractional order with a new dependent variable. In the reduced equation the derivative is in Erdelyi–Kober sense. Furthermore, adapting the Ibragimov’s nonlocal conservation method to time fractional partial differential equations, we obtain conservation laws of the underlying equation. In addition, we construct some exact travelling wave solutions for the FSKI equation using the sub-equation method. Keywords: Fractional Sawada–Kotera–Ito equation, Lie symmetry, Riemann–Liouville fractional derivative, Conservation laws, Exact solutions
Lie symmetries of a generalized Kuznetsov-Zabolotskaya-Khoklov equation
Gungor, F.; Ozemir, C.
2014-01-01
We consider a class of generalized Kuznetsov--Zabolotskaya--Khokhlov (gKZK) equations and determine its equivalence group, which is then used to give a complete symmetry classification of this class. The infinite-dimensional symmetry is used to reduce such equations to (1+1)-dimensional PDEs. Special attention is paid to group-theoretical properties of a class of generalized dispersionless KP (gdKP) or Zabolotskaya--Khokhlov equations as a subclass of gKZK equations. The conditions are determ...
The Exceptional Lie symmetry groups hierarchy and the expected number of Higgs bosons
International Nuclear Information System (INIS)
El Naschie, M.S.
2008-01-01
New insights into the structure of various exceptional Lie symmetry groups hierarchies are utilized to shed light on various problems pertinent to the standard model of high energy physics and the Higgs
Deconfined Quantum Critical Points: Symmetries and Dualities
Directory of Open Access Journals (Sweden)
Chong Wang
2017-09-01
Full Text Available The deconfined quantum critical point (QCP, separating the Néel and valence bond solid phases in a 2D antiferromagnet, was proposed as an example of (2+1D criticality fundamentally different from standard Landau-Ginzburg-Wilson-Fisher criticality. In this work, we present multiple equivalent descriptions of deconfined QCPs, and use these to address the possibility of enlarged emergent symmetries in the low-energy limit. The easy-plane deconfined QCP, besides its previously discussed self-duality, is dual to N_{f}=2 fermionic quantum electrodynamics, which has its own self-duality and hence may have an O(4×Z_{2}^{T} symmetry. We propose several dualities for the deconfined QCP with SU(2 spin symmetry which together make natural the emergence of a previously suggested SO(5 symmetry rotating the Néel and valence bond solid orders. These emergent symmetries are implemented anomalously. The associated infrared theories can also be viewed as surface descriptions of (3+1D topological paramagnets, giving further insight into the dualities. We describe a number of numerical tests of these dualities. We also discuss the possibility of “pseudocritical” behavior for deconfined critical points, and the meaning of the dualities and emergent symmetries in such a scenario.
Lie symmetries for charged particles in the presence of a general electromagnetic field
International Nuclear Information System (INIS)
Medeiros Ritter, Oswaldo de.
1991-10-01
We discuss the Lie method and apply it to differential equations obtaining their symmetries. We also discuss methods of how to obtain first integrals from these symmetries. We apply these methods to some interesting physical problems, all of them involving charged particles in electromagnetic fields. (author). 77 refs
Lie symmetries for the electric charge-magnetic monopole interaction problem
International Nuclear Information System (INIS)
Moreira, I.C.; Ritter, O.M.; Santos, F.C.
1985-01-01
The symmetries of the equation of motion for an electric charge interacting with a magnetic monopole are analyzed. Two methods, starting from the knowledge of the Lie symmetries, are discussed and employed in this case. This procedure is also compared with the hamiltonians methods. (ltonians methods. (Author) [pt
Lie symmetry analysis and soliton solutions of time-fractional K(m, n ...
Indian Academy of Sciences (India)
2016-12-03
Dec 3, 2016 ... Abstract. In this note, method of Lie symmetries is applied to investigate symmetry properties of time- fractional K (m, n) equation with the Riemann–Liouville derivatives. Reduction of time-fractional K (m, n) equation is done by virtue of the Erdélyi–Kober fractional derivative which depends on a parameter α.
On geometric approach to Lie symmetries of differential-difference equations
International Nuclear Information System (INIS)
Li Hongjing; Wang Dengshan; Wang Shikun; Wu Ke; Zhao Weizhong
2008-01-01
Based upon Cartan's geometric formulation of differential equations, Harrison and Estabrook proposed a geometric approach for the symmetries of differential equations. In this Letter, we extend Harrison and Estabrook's approach to analyze the symmetries of differential-difference equations. The discrete exterior differential technique is applied in our approach. The Lie symmetry of (2+1)-dimensional Toda equation is investigated by means of our approach
Hierarchy of kissing numbers for exceptional Lie symmetry groups in high energy physics
International Nuclear Information System (INIS)
El Naschie, M.S.
2008-01-01
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 8 E 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
Block (or Hamiltonian) Lie Symmetry of Dispersionless D-Type Drinfeld–Sokolov Hierarchy
International Nuclear Information System (INIS)
Li Chuan-Zhong; He Jing-Song; Su Yu-Cai
2014-01-01
In this paper, the dispersionless D-type Drinfeld–Sokolov hierarchy, i.e. a reduction of the dispersionless two-component BKP hierarchy, is studied. The additional symmetry flows of this hierarchy are presented. These flows form an infinite-dimensional Lie algebra of Block type as well as a Lie algebra of Hamiltonian type
Boyko, Vyacheslav M; Popovych, Roman O; Shapoval, Nataliya M
2013-01-01
Lie symmetries of systems of second-order linear ordinary differential equations with constant coefficients are exhaustively described over both the complex and real fields. The exact lower and upper bounds for the dimensions of the maximal Lie invariance algebras possessed by such systems are obtained using an effective algebraic approach.
Lie-Mei symmetry and conserved quantities of the Rosenberg problem
International Nuclear Information System (INIS)
Liu Xiao-Wei; Li Yuan-Cheng
2011-01-01
The Rosenberg problem is a typical but not too complicated problem of nonholonomic mechanical systems. The Lie—Mei symmetry and the conserved quantities of the Rosenberg problem are studied. For the Rosenberg problem, the Lie and the Mei symmetries for the equation are obtained, the conserved quantities are deduced from them and then the definition and the criterion for the Lie—Mei symmetry of the Rosenberg problem are derived. Finally, the Hojman conserved quantity and the Mei conserved quantity are deduced from the Lie—Mei symmetry. (general)
Lie-Mei symmetry and conserved quantities of the Rosenberg problem
Liu, Xiao-Wei; Li, Yuan-Cheng
2011-07-01
The Rosenberg problem is a typical but not too complicated problem of nonholonomic mechanical systems. The Lie—Mei symmetry and the conserved quantities of the Rosenberg problem are studied. For the Rosenberg problem, the Lie and the Mei symmetries for the equation are obtained, the conserved quantities are deduced from them and then the definition and the criterion for the Lie—Mei symmetry of the Rosenberg problem are derived. Finally, the Hojman conserved quantity and the Mei conserved quantity are deduced from the Lie—Mei symmetry.
The geometry of lie algebras and broken SO(6) symmetries
International Nuclear Information System (INIS)
Lawrence, T.R.
2001-10-01
Non-linear realisations of the groups SU(2), SO(1,4) and SO(2,4) are analysed, described by the coset spaces SU(2)/U(1), SO(1,4)/SO(1,3) and SO(2,4)/SO(1,3) x SO(1,1). The Lie algebras of certain special unitary and special orthogonal groups are studied and their projection operators are determined in order to facilitate the above analyses, in particular that of SO(2,4)/SO(l,3) x SO(1,1). The analysis consists of determining the transformation properties of the Goldstone bosons, constructing the most general possible Lagrangian for the realisations and finding the metric of the coset space. (author)
Lie Symmetry of the Diffusive Lotka–Volterra System with Time-Dependent Coefficients
Directory of Open Access Journals (Sweden)
Vasyl’ Davydovych
2018-02-01
Full Text Available Lie symmetry classification of the diffusive Lotka–Volterra system with time-dependent coefficients in the case of a single space variable is studied. A set of such symmetries in an explicit form is constructed. A nontrivial ansatz reducing the Lotka–Volterra system with correctly-specified coefficients to the system of ordinary differential equations (ODEs and an example of the exact solution with a biological interpretation are found.
Wheeler-DeWitt equation and Lie symmetries in Bianchi scalar-field cosmology
Energy Technology Data Exchange (ETDEWEB)
Paliathanasis, A. [Universidad Austral de Chile, Instituto de Ciencias Fisicas y Matematicas, Valdivia (Chile); Karpathopoulos, L. [University of Athens, Faculty of Physics, Department of Astronomy-Astrophysics-Mechanics, Athens (Greece); Wojnar, A. [Institute for Theoretical Physics, Wroclaw (Poland); Universita' di Napoli Federico II, Complesso Universitario di Monte S. Angelo, Dipartimento di Fisica ' ' E. Pancini' ' , Naples (Italy); Complesso Universitario di Monte S. Angelo, Naples (Italy); Istituto Nazionale di Fisica Nucleare (INFN) Sez. di Napoli, Naples (Italy); Capozziello, S. [Universita' di Napoli Federico II, Complesso Universitario di Monte S. Angelo, Dipartimento di Fisica ' ' E. Pancini' ' , Naples (Italy); Complesso Universitario di Monte S. Angelo, Naples (Italy); Gran Sasso Science Institute (INFN), L' Aquila (Italy); Istituto Nazionale di Fisica Nucleare (INFN) Sez. di Napoli, Naples (Italy)
2016-04-15
Lie symmetries are discussed for the Wheeler-De Witt equation in Bianchi Class A cosmologies. In particular, we consider general relativity, minimally coupled scalar-field gravity and hybrid gravity as paradigmatic examples of the approach. Several invariant solutions are determined and classified according to the form of the scalar-field potential. The approach gives rise to a suitable method to select classical solutions and it is based on the first principle of the existence of symmetries. (orig.)
International Nuclear Information System (INIS)
Zhang Mei-Ling; Wang Xiao-Xiao; Xie Yin-Li; Jia Li-Qun; Sun Xian-Ting
2011-01-01
Lie symmetry and the generalized Hojman conserved quantity of Nielsen equations for a variable mass holonomic system of relative motion are studied. The determining equation of Lie symmetry of Nielsen equations for a variable mass holonomic system of relative motion under the infinitesimal transformations of groups is given. The expression of generalized Hojman conserved quantity deduced directly from Lie symmetry for a variable mass holonomic system of relative motion is obtained. An example is given to illustrate the application of the results. (general)
Application of the Lie Symmetry Analysis for second-order fractional differential equations
Directory of Open Access Journals (Sweden)
Mousa Ilie
2017-12-01
Full Text Available Obtaining analytical or numerical solution of fractional differential equations is one of the troublesome and challenging issue among mathematicians and engineers, specifically in recent years. The purpose of this paper Lie Symmetry method is developed to solve second-order fractional differential equations, based on conformable fractional derivative. Some numerical examples are presented to illustrate the proposed approach.
Hilbert schemes of points and infinite dimensional Lie algebras
Qin, Zhenbo
2018-01-01
Hilbert schemes, which parametrize subschemes in algebraic varieties, have been extensively studied in algebraic geometry for the last 50 years. The most interesting class of Hilbert schemes are schemes X^{[n]} of collections of n points (zero-dimensional subschemes) in a smooth algebraic surface X. Schemes X^{[n]} turn out to be closely related to many areas of mathematics, such as algebraic combinatorics, integrable systems, representation theory, and mathematical physics, among others. This book surveys recent developments of the theory of Hilbert schemes of points on complex surfaces and its interplay with infinite dimensional Lie algebras. It starts with the basics of Hilbert schemes of points and presents in detail an example of Hilbert schemes of points on the projective plane. Then the author turns to the study of cohomology of X^{[n]}, including the construction of the action of infinite dimensional Lie algebras on this cohomology, the ring structure of cohomology, equivariant cohomology of X^{[n]} a...
The quantum poisson-Lie T-duality and mirror symmetry
International Nuclear Information System (INIS)
Parkhomenko, S.E.
1999-01-01
Poisson-Lie T-duality in quantum N=2 superconformal Wess-Zumino-Novikov-Witten models is considered. The Poisson-Lie T-duality transformation rules of the super-Kac-Moody algebra currents are found from the conjecture that, as in the classical case, the quantum Poisson-Lie T-duality transformation is given by an automorphism which interchanges the isotropic subalgebras of the underlying Manin triple in one of the chirality sectors of the model. It is shown that quantum Poisson-Lie T-duality acts on the N=2 super-Virasoro algebra generators of the quantum models as a mirror symmetry acts: in one of the chirality sectors it is a trivial transformation while in another chirality sector it changes the sign of the U(1) current and interchanges the spin-3/2 currents. A generalization of Poisson-Lie T-duality for the quantum Kazama-Suzuki models is proposed. It is shown that quantum Poisson-Lie T-duality acts in these models as a mirror symmetry also
Energy Technology Data Exchange (ETDEWEB)
Medeiros Ritter, Oswaldo de
1991-10-01
We discuss the Lie method and apply it to differential equations obtaining their symmetries. We also discuss methods of how to obtain first integrals from these symmetries. We apply these methods to some interesting physical problems, all of them involving charged particles in electromagnetic fields. (author). 77 refs.
Some exact solutions for a unidimensional fokker-planck equation by using lie symmetries
Directory of Open Access Journals (Sweden)
Hugo Hernán Ortíz-Álvarez
2015-01-01
Full Text Available The Fokker Planck equation appears in the study of diffusion phenomena, stochastics processes and quantum and classical mechanics. A particular case fromthis equation, ut − uxx − xux − u=0, is examined by the Lie group method approach. From the invariant condition it was possible to obtain the infinitesimal generators or vectors associated to this equation, identifying the corresponding symmetry groups. Exact solution were found for each one of this generators and new solution were constructed by using symmetry properties.
Inc, Mustafa; Yusuf, Abdullahi; Aliyu, Aliyu Isa; Baleanu, Dumitru
2018-04-01
This paper studies the symmetry analysis, explicit solutions, convergence analysis, and conservation laws (Cls) for two different space-time fractional nonlinear evolution equations with Riemann-Liouville (RL) derivative. The governing equations are reduced to nonlinear ordinary differential equation (ODE) of fractional order using their Lie point symmetries. In the reduced equations, the derivative is in Erdelyi-Kober (EK) sense, power series technique is applied to derive an explicit solutions for the reduced fractional ODEs. The convergence of the obtained power series solutions is also presented. Moreover, the new conservation theorem and the generalization of the Noether operators are developed to construct the nonlocal Cls for the equations . Some interesting figures for the obtained explicit solutions are presented.
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…
Paliathanasis, Andronikos; Vakili, Babak
2016-01-01
We apply as selection rule to determine the unknown functions of a cosmological model the existence of Lie point symmetries for the Wheeler-DeWitt equation of quantum gravity. Our cosmological setting consists of a flat Friedmann-Robertson-Walker metric having the scale factor a( t), a scalar field with potential function V(φ ) minimally coupled to gravity and a vector field of its kinetic energy is coupled with the scalar field by a coupling function f(φ ). Then, the Lie symmetries of this dynamical system are investigated by utilizing the behavior of the corresponding minisuperspace under the infinitesimal generator of the desired symmetries. It is shown that by applying the Lie symmetry condition the form of the coupling function and also the scalar field potential function may be explicitly determined so that we are able to solve the Wheeler-DeWitt equation. Finally, we show how we can use the Lie symmetries in order to construct conservation laws and exact solutions for the field equations.
Symmetry breaking in fluid dynamics: Lie group reducible motions for real fluids
International Nuclear Information System (INIS)
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
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.
Ray, S. Saha
2018-04-01
In this paper, the symmetry analysis and similarity reduction of the (2+1)-dimensional Bogoyavlensky-Konopelchenko (B-K) equation are investigated by means of the geometric approach of an invariance group, which is equivalent to the classical Lie symmetry method. Using the extended Harrison and Estabrook’s differential forms approach, the infinitesimal generators for (2+1)-dimensional B-K equation are obtained. Firstly, the vector field associated with the Lie group of transformation is derived. Then the symmetry reduction and the corresponding explicit exact solution of (2+1)-dimensional B-K equation is obtained.
On the Lie symmetry group for classical fields in noncommutative space
Energy Technology Data Exchange (ETDEWEB)
Pereira, Ricardo Martinho Lima Santiago [Universidade Federal da Bahia (UFBA), BA (Brazil); Instituto Federal da Bahia (IFBA), BA (Brazil); Ressureicao, Caio G. da [Universidade Federal da Bahia (UFBA), BA (Brazil). Inst. de Fisica; Vianna, Jose David M. [Universidade Federal da Bahia (UFBA), BA (Brazil); Universidade de Brasilia (UnB), DF (Brazil)
2011-07-01
Full text: An alternative way to include effects of noncommutative geometries in field theory is based on the concept of noncommutativity among degrees of freedom of the studied system. In this context it is reasonable to consider that, in the multiparticle noncommutative quantum mechanics (NCQM), the noncommutativity among degrees of freedom to discrete system with N particles is also verified. Further, an analysis of the classical limit of the single particle NCQM leads to a deformed Newtonian mechanics where the Newton's second law is modified in order to include the noncommutative parameter {theta}{sub {iota}j} and, for a one-dimensional discrete system with N particles, the dynamical evolution of each particle is given by this modified Newton's second law. Hence, applying the continuous limit to this multiparticle classical system it is possible to obtain a noncommutative extension of two -dimensional field theory in a noncommutative space. In the present communication we consider a noncommutative extension of the scalar field obtained from this approach and we analyze the Lie symmetries in order to compare the Lie group of this field with the usual scalar field in the commutative space. (author)
The open superstring 6-point amplitude with manifest symmetries
International Nuclear Information System (INIS)
Barreiro, Luiz Antonio; Medina, Ricardo; Stieberger, Stephan
2011-01-01
Full text: The general tree level amplitude for massless bosons states of open superstrings has been known for a long time ago. It is clear how to obtain this general formula using vertex operators in the Ramond-Neveu-Schwarz formalism. From the beginning of the eighties the explicit expression for this formula has been known in the case of 3 and 4-point amplitudes. In that decade an attempt (with partial success) was done, by Kitazawa, to obtain the corresponding 5-point amplitude. Only in 2002 a complete and correct expression for this amplitude was obtained. Its low energy expansion was compared to the corresponding one from the low energy effective Lagrangian of the open superstring, finding a perfect match. A few years later, in 2005, it was realized that the 5-point formula could be written in a very much compact form, as a sum of two terms: each of them consisting of a momentum factor and a kinematic expression. This constituted a generalization of the 4-point amplitude case, which had been known to be cast in only one momentum factor multiplied by one kinematic expression. For this simplification to happen, known symmetries of the (tree level) scattering amplitudes were implemented in a manifest form. These symmetries are (on-shell) gauge symmetry, cyclic symmetry and twisting symmetry (or world sheet parity). In the recent years it has been realized that the N-point amplitude can be written as a sum of (N - 3)! terms (where N > 3). This result not only agrees with the 3, 4 and 5-point results, but also with the 6-point result which had been obtained by 2005, written as a sum of six terms. The expression that up to now has been obtained for the 6-point amplitude is quite complicated and, besides knowing that it consists of six terms, is not very illuminating. In this work we report on the recent result of writing the 6-point amplitude with gauge, cyclic and twisting symmetries manifest. Not only because of the manifest symmetries this result is important
Lie symmetry analysis and soliton solutions of time-fractional K(m, n ...
Indian Academy of Sciences (India)
2016-12-03
Dec 3, 2016 ... Factional differential equations are increasingly used to model problems in physics, such as fluid mechan- ics, biology, viscoelasticity, engineering etc. [1–4]. In .... According to the Lie theory, applying the prolongation. Pr.
Baleanu, Dumitru; Inc, Mustafa; Yusuf, Abdullahi; Aliyu, Aliyu Isa
2018-06-01
In this work, we investigate the Lie symmetry analysis, exact solutions and conservation laws (Cls) to the time fractional Caudrey-Dodd-Gibbon-Sawada-Kotera (CDGDK) equation with Riemann-Liouville (RL) derivative. The time fractional CDGDK is reduced to nonlinear ordinary differential equation (ODE) of fractional order. New exact traveling wave solutions for the time fractional CDGDK are obtained by fractional sub-equation method. In the reduced equation, the derivative is in Erdelyi-Kober (EK) sense. Ibragimov's nonlocal conservation method is applied to construct Cls for time fractional CDGDK.
Lie Symmetries and Solitons in Nonlinear Systems with Spatially Inhomogeneous Nonlinearities
International Nuclear Information System (INIS)
Belmonte-Beitia, Juan; Perez-Garcia, Victor M.; Vekslerchik, Vadym; Torres, Pedro J.
2007-01-01
Using Lie group theory and canonical transformations, we construct explicit solutions of nonlinear Schroedinger equations with spatially inhomogeneous nonlinearities. We present the general theory, use it to show that localized nonlinearities can support bound states with an arbitrary number solitons, and discuss other applications of interest to the field of nonlinear matter waves
Fixed points of IA-endomorphisms of a free metabelian Lie algebra
Indian Academy of Sciences (India)
Let be a free metabelian Lie algebra of finite rank at least 2. We show the existence of non-trivial fixed points of an -endomorphism of and give an algorithm detecting them. In particular, we prove that the fixed point subalgebra Fix of an -endomorphism of is not finitely generated.
A non-Lie algebraic framework and its possible merits for symmetry descriptions
International Nuclear Information System (INIS)
Ktorides, C.N.
1975-01-01
A nonassociative algebraic construction is introduced which bears a relation to a Lie algebra L paralleling the relation between an associative enveloping algebra and L. The key ingredient of this algebraic construction is the presence of two parameters which relate it to the enveloping algebra of L. The analog of the Poincare--Birkhoff--Witt theorem is proved for the new algebra. Possibilities of physical relevance are also considered. It is noted that, if fully developed, the mathematical framework suggested by this new algebra should be non-Lie. Subsequently, a certain scheme resulting from specific considerations connected with this (non-Lie) algebraic structure is found to bear striking resemblance to a recent phenomenological theory proposed for explaining CP violation by the K 0 system. Some relevant speculations are also made in view of certain recent trends of thought in elementary particle physics. Finally, in an appendix, a Gell-Mann--Okubo-like mass formula for the new algebra is derived for an SU (3) octet
International Nuclear Information System (INIS)
Halpern, L.
1981-01-01
Invariant varieties of suitable semisimple groups of transformations can serve as models of the space-time of the universe. The metric is expressible in terms of the basis vectors of the group. The symmetry of the group is broken by introducing a gauge formalism in the space of the basis vectors with the adjoint group as gauge group. The gauge potentials are expressible in terms of the basis vectors for the case of the De Sitter group. The resulting gauge theory is equivalent to De Sitter covariant general relativity. Group covariant generalizations of gravitational theory are discussed. (Auth.)
Metallic magnets without inversion symmetry and antiferromagnetic quantum critical points
Energy Technology Data Exchange (ETDEWEB)
Fischer, I.A.
2006-07-01
This thesis focusses on two classes of systems that exhibit non-Fermi liquid behaviour in experiments: we investigated aspects of chiral ferromagnets and of antiferromagnetic metals close to a quantum critical point. In chiral ferromagnets, the absence of inversion symmetry makes spin-orbit coupling possible, which leads to a helical modulation of the ferromagnetically ordered state. We studied the motion of electrons in the magnetically ordered state of a metal without inversion symmetry by calculating their generic band-structure. We found that spin-orbit coupling, although weak, has a profound effect on the shape of the Fermi surface: On a large portion of the Fermi surface the electron motion parallel to the helix practically stops. Signatures of this effect can be expected to show up in measurements of the anomalous Hall effect. Recent neutron scattering experiments uncovered the existence of a peculiar kind of partial order in a region of the phase diagram adjacent to the ordered state of the chiral ferromagnet MnSi. Starting from the premise that this partially ordered state is a thermodynamically distinct phase, we investigated an extended Ginzburg-Landau theory for chiral ferromagnets. In a certain parameter regime of the Ginzburg-Landau theory we identified crystalline phases that are reminiscent of the so-called blue phases in liquid crystals. Many antiferromagnetic heavy-fermion systems can be tuned into a regime where they exhibit non-Fermi liquid exponents in the temperature dependence of thermodynamic quantities such as the specific heat capacity; this behaviour could be due to a quantum critical point. If the quantum critical behaviour is field-induced, the external field does not only suppress antiferromagnetism but also induces spin precession and thereby influences the dynamics of the order parameter. We investigated the quantum critical behavior of clean antiferromagnetic metals subject to a static, spatially uniform external magnetic field. We
The Emergence of Dirac points in Photonic Crystals with Mirror Symmetry
He, Wen-Yu; Chan, C. T.
2015-01-01
We show that Dirac points can emerge in photonic crystals possessing mirror symmetry when band gap closes. The mechanism of generating Dirac points is discussed in a two-dimensional photonic square lattice, in which four Dirac points split out naturally after the touching of two bands with different parity. The emergence of such nodal points, characterized by vortex structure in momentum space, is attributed to the unavoidable band crossing protected by mirror symmetry. The Dirac nodes can be unbuckled through breaking the mirror symmetry and a photonic analog of Chern insulator can be achieved through time reversal symmetry breaking. Breaking time reversal symmetry can lead to unidirectional helical edge states and breaking mirror symmetry can reduce the band gap to amplify the finite size effect, providing ways to engineer helical edge states. PMID:25640993
Discrete Symmetries Analysis and Exact Solutions of the Inviscid Burgers Equation
Directory of Open Access Journals (Sweden)
Hongwei Yang
2012-01-01
Full Text Available We discuss the Lie point symmetries and discrete symmetries of the inviscid Burgers equation. By employing the Lie group method of infinitesimal transformations, symmetry reductions and similarity solutions of the governing equation are given. Based on discrete symmetries analysis, two groups of discrete symmetries are obtained, which lead to new exact solutions of the inviscid Burgers equation.
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…
International Nuclear Information System (INIS)
Haas, Fernando
2016-01-01
A didactic and systematic derivation of Noether point symmetries and conserved currents is put forward in special relativistic field theories, without a priori assumptions about the transformation laws. Given the Lagrangian density, the invariance condition develops as a set of partial differential equations determining the symmetry transformation. The solution is provided in the case of real scalar, complex scalar, free electromagnetic, and charged electromagnetic fields. Besides the usual conservation laws, a less popular symmetry is analyzed: the symmetry associated with the linear superposition of solutions, whenever applicable. The role of gauge invariance is emphasized. The case of the charged scalar particle under external electromagnetic fields is considered, and the accompanying Noether point symmetries determined. Noether point symmetries for a dynamical system in extended gravity cosmology are also deduced. (paper)
Haas, Fernando
2016-11-01
A didactic and systematic derivation of Noether point symmetries and conserved currents is put forward in special relativistic field theories, without a priori assumptions about the transformation laws. Given the Lagrangian density, the invariance condition develops as a set of partial differential equations determining the symmetry transformation. The solution is provided in the case of real scalar, complex scalar, free electromagnetic, and charged electromagnetic fields. Besides the usual conservation laws, a less popular symmetry is analyzed: the symmetry associated with the linear superposition of solutions, whenever applicable. The role of gauge invariance is emphasized. The case of the charged scalar particle under external electromagnetic fields is considered, and the accompanying Noether point symmetries determined. Noether point symmetries for a dynamical system in extended gravity cosmology are also deduced.
Measure of departure from marginal point-symmetry for two-way contingency tables
Directory of Open Access Journals (Sweden)
Kouji Yamamoto
2013-05-01
Full Text Available For two-way contingency tables, Tomizawa (1985 considered the point-symmetry and marginal point-symmetry models, and Tomizawa, Yamamoto and Tahata (2007 proposed a measure to represent the degree of departure from point-symmetry. The present paper proposes a measure to represent the degree of departure from marginal pointsymmetry for two-way tables. The proposed measure is expressed by using Cressie-Read power-divergence or Patil-Taillie diversity index. This measure would be useful for comparing the degrees of departure from marginal point-symmetry in several tables. The relationship between the degree of departure from marginal point-symmetry and the measure is shown when it is reasonable to assume underlying bivariate normal distribution. Examples are shown.
International Nuclear Information System (INIS)
Leone, Raphaël; Haas, Fernando
2017-01-01
This article brings to light the fact that linearity is by itself a meaningful symmetry in the senses of Lie and Noether. First, the role played by that ‘linearity symmetry’ in the quadrature of linear second-order differential equations is revisited through the use of adapted variables and the identification of a conserved quantity as Lie invariant. Second, the celebrated Caldirola–Kanai Lagrangian—from which the differential equation is deducible—is shown to be naturally generated by a Jacobi last multiplier inherited from the linearity symmetry. Then, the latter is recognised to be also a Noether one. Finally, the study is extended to higher-order linear differential equations, derivable or not from an action principle. Incidentally, this work can serve as an introduction to the central question of continuous symmetries in physics and mathematics. It has the advantage of being approachable to undergraduate students since the linearity symmetry is by its very nature sufficiently simple to be treatable without any use of Lie generators. (paper)
Directory of Open Access Journals (Sweden)
Roman Cherniha
2018-04-01
Full Text Available This review is devoted to search for Lie and Q-conditional (nonclassical symmetries and exact solutions of a class of reaction-diffusion-convection equations with exponential nonlinearities. A complete Lie symmetry classification of the class is derived via two different algorithms in order to show that the result depends essentially on the type of equivalence transformations used for the classification. Moreover, a complete description of Q-conditional symmetries for PDEs from the class in question is also presented. It is shown that all the well-known results for reaction-diffusion equations with exponential nonlinearities follow as particular cases from the results derived for this class of reaction-diffusion-convection equations. The symmetries obtained for constructing exact solutions of the relevant equations are successfully applied. The exact solutions are compared with those found by means of different techniques. Finally, an application of the exact solutions for solving boundary-value problems arising in population dynamics is presented.
Xiao, R. C.; Cheung, C. H.; Gong, P. L.; Lu, W. J.; Si, J. G.; Sun, Y. P.
2018-06-01
k paths exactly with symmetry allow to find triply degenerate points (TDPs) in band structures. The paths that host the type-II Dirac points in PtSe2 family materials also have the spatial symmetry. However, due to Kramers degeneracy (the systems have both inversion symmetry and time reversal symmetry), the crossing points in them are Dirac ones. In this work, based on symmetry analysis, first-principles calculations, and method, we predict that PtSe2 family materials should undergo topological transitions if the inversion symmetry is broken, i.e. the Dirac fermions in PtSe2 family materials split into TDPs in PtSeTe family materials (PtSSe, PtSeTe, and PdSeTe) with orderly arranged S/Se (Se/Te). It is different from the case in high-energy physics that breaking inversion symmetry I leads to the splitting of Dirac fermion into Weyl fermions. We also address a possible method to achieve the orderly arranged in PtSeTe family materials in experiments. Our study provides a real example that Dirac points transform into TDPs, and is helpful to investigate the topological transition between Dirac fermions and TDP fermions.
Fourier-space TEM reconstructions with symmetry adapted functions for all rotational point groups.
Trapani, Stefano; Navaza, Jorge
2013-05-01
A general-purpose and simple expression for the coefficients of symmetry adapted functions referred to conveniently oriented symmetry axes is given for all rotational point groups. The expression involves the computation of reduced Wigner-matrix elements corresponding to an angle specific to each group and has the computational advantage of leading to Fourier-space TEM (transmission electron microscopy) reconstruction procedures involving only real valued unknowns. Using this expression, a protocol for ab initio view and center assignment and reconstruction so far used for icosahedral particles has been tested with experimental data in other point groups. Copyright © 2013 Elsevier Inc. All rights reserved.
International Nuclear Information System (INIS)
El Naschie, M.S.
2008-01-01
The short note gives a derivation for a new E12 exceptional Lie group corresponding to affine KAC-Moody algebra. We derive the dimension of the group by intersectionally embedding the intrinsic dimension of E8 namely D(E8) = 57 into the 12 spacetime dimensions of F theory and finding that Dim E12 = D(E8) (DF) + 1 = (57)(12) + 1 = 685
International Nuclear Information System (INIS)
Barik, N.; Dash, B.K.
1986-01-01
Under the assumption that baryons are an assembly of independent quarks, confined in a first approximation by an effective potential U(r) = 1/2(1+γ 0 )(ar 2 +V 0 ) which presumably represents the nonperturbative gluon interactions, the mass spectrum of the low-lying ground-state baryons has been calculated by considering perturbatively the contributions of the residual quark-pion coupling arising out of the requirement of chiral symmetry and that of the quark-gluon coupling due to one-gluon exchange over and above the necessary center-of-mass correction. The physical masses of the baryons so obtained agree quite well with the corresponding experimental value. The strong coupling constant α/sub c/ = 0.58 required here to describe the QCD mass splittings is quite consistent with the idea of treating one-gluon-exchange effects in lowest-order perturbation theory
Klink, William H.; Schweiger, Wolfgang
2018-03-01
This book covers relativistic quantum theory from the point of view of a particle theory, based on the irreducible representations of the Poincaré group, the group that expresses the symmetry of Einstein relativity. There are several ways of formulating such a theory; this book develops what is called relativistic point form quantum mechanics, which, unlike quantum field theory, deals with a fixed number of particles in a relativistically invariant way. A chapter is devoted to applications of point form quantum mechanics to nuclear physics.
Fingerprints of bosonic symmetry protected topological state in a quantum point contact
Zhang, Rui-Xing; Liu, Chao-Xing
2016-01-01
In this work, we study the transport through a quantum point contact for bosonic helical liquid that exists at the edge of a bilayer graphene under a strong magnetic field. We identify "smoking gun" transport signatures to distinguish bosonic symmetry protected topological (BSPT) state from fermionic two-channel quantum spin Hall (QSH) state in this system. In particular, a novel charge insulator/spin conductor phase is found for BSPT state, while either charge insulator/spin insulator or cha...
Teaching Molecular Symmetry of Dihedral Point Groups by Drawing Useful 2D Projections
Chen, Lan; Sun, Hongwei; Lai, Chengming
2015-01-01
There are two main difficulties in studying molecular symmetry of dihedral point groups. One is locating the C[subscript 2] axes perpendicular to the C[subscript n] axis, while the other is finding the s[subscript]d planes which pass through the C[subscript n] axis and bisect the angles formed by adjacent C[subscript 2] axes. In this paper, a…
Constraints from conformal symmetry on the three point scalar correlator in inflation
International Nuclear Information System (INIS)
Kundu, Nilay; Shukla, Ashish; Trivedi, Sandip P.
2015-01-01
Using symmetry considerations, we derive Ward identities which relate the three point function of scalar perturbations produced during inflation to the scalar four point function, in a particular limit. The derivation assumes approximate conformal invariance, and the conditions for the slow roll approximation, but is otherwise model independent. The Ward identities allow us to deduce that the three point function must be suppressed in general, being of the same order of magnitude as in the slow roll model. They also fix the three point function in terms of the four point function, upto one constant which we argue is generically suppressed. Our approach is based on analyzing the wave function of the universe, and the Ward identities arise by imposing the requirements of spatial and time reparametrization invariance on it.
Boundary Fixed Points, Enhanced Gauge Symmetry and Singular Bundles on K3
Fuchs, J; Lerche, Wolfgang; Lütken, C A; Schweigert, C; Walcher, J
2001-01-01
We investigate certain fixed points in the boundary conformal field theory representation of type IIA D-branes on Gepner points of K3. They correspond geometrically to degenerate brane configurations, and physically lead to enhanced gauge symmetries on the world-volume. Non-abelian gauge groups arise if the stabilizer group of the fixed points is realized projectively, which is similar to D-branes on orbifolds with discrete torsion. Moreover, the fixed point boundary states can be resolved into several irreducible components. These correspond to bound states at threshold and can be viewed as (non-locally free) sub-sheaves of semi-stable sheaves. Thus, the BCFT fixed points appear to carry two-fold geometrical information: on the one hand they probe the boundary of the instanton moduli space on K3, on the other hand they probe discrete torsion in D-geometry.
Molecular symmetry: Why permutation-inversion (PI) groups don't render the point groups obsolete
Groner, Peter
2018-01-01
The analysis of spectra of molecules with internal large-amplitude motions (LAMs) requires molecular symmetry (MS) groups that are larger than and significantly different from the more familiar point groups. MS groups are described often by the permutation-inversion (PI) group method. It is shown that point groups still can and should play a significant role together with the PI groups for a class of molecules with internal rotors. In molecules of this class, several simple internal rotors are attached to a rigid molecular frame. The PI groups for this class are semidirect products like H ^ F, where the invariant subgroup H is a direct product of cyclic groups and F is a point group. This result is used to derive meaningful labels for MS groups, and to derive correlation tables between MS groups and point groups. MS groups of this class have many parallels to space groups of crystalline solids.
Mikš, Antonín; Novák, Pavel
2017-09-01
The paper is focused on the problem of determination of the point of incidence of a light ray for the case of reflection or refraction at the spherical optical surface, assuming that two fixed points in space that the sought light ray should go through are given. The requirement is that one of these points lies on the incident ray and the other point on the reflected/refracted ray. Although at first glance it seems to be a simple problem, it will be shown that it has no simple analytical solution. The basic idea of the solution is given, and it is shown that the problem leads to a nonlinear equation in one variable. The roots of the resulting nonlinear equation can be found by numerical methods of mathematical optimization. The proposed methods were implemented in MATLAB, and the proper function of these algorithms was verified on several examples.
Hidden symmetry of four-point correlation functions and amplitudes in N=4 SYM
Eden, Burkhard; Korchemsky, Gregory P; Sokatchev, Emery
2012-01-01
We study the four-point correlation function of stress-tensor supermultiplets in N=4 SYM using the method of Lagrangian insertions. We argue that, as a corollary of N=4 superconformal symmetry, the resulting all-loop integrand possesses an unexpected complete symmetry under the exchange of the four external and all the internal (integration) points. This alone allows us to predict the integrand of the three-loop correlation function up to four undetermined constants. Further, exploiting the conjectured amplitude/correlation function duality, we are able to fully determine the three-loop integrand in the planar limit. We perform an independent check of this result by verifying that it is consistent with the operator product expansion, in particular that it correctly reproduces the three-loop anomalous dimension of the Konishi operator. As a byproduct of our study, we also obtain the three-point function of two half-BPS operators and one Konishi operator at three-loop level. We use the same technique to work ou...
Symmetry properties of fractional diffusion equations
Energy Technology Data Exchange (ETDEWEB)
Gazizov, R K; Kasatkin, A A; Lukashchuk, S Yu [Ufa State Aviation Technical University, Karl Marx strausse 12, Ufa (Russian Federation)], E-mail: gazizov@mail.rb.ru, E-mail: alexei_kasatkin@mail.ru, E-mail: lsu@mail.rb.ru
2009-10-15
In this paper, nonlinear anomalous diffusion equations with time fractional derivatives (Riemann-Liouville and Caputo) of the order of 0-2 are considered. Lie point symmetries of these equations are investigated and compared. Examples of using the obtained symmetries for constructing exact solutions of the equations under consideration are presented.
Analysis of the Symmetries and Conservation Laws of the Nonlinear Jaulent-Miodek Equation
Directory of Open Access Journals (Sweden)
Mehdi Nadjafikhah
2014-01-01
Full Text Available Lie symmetry method is performed for the nonlinear Jaulent-Miodek equation. We will find the symmetry group and optimal systems of Lie subalgebras. The Lie invariants associated with the symmetry generators as well as the corresponding similarity reduced equations are also pointed out. And conservation laws of the J-M equation are presented with two steps: firstly, finding multipliers for computation of conservation laws and, secondly, symbolic computation of conservation laws will be applied.
Turok, Neil
2018-01-01
Professor David Olive was a renowned British theoretical physicist who made seminal contributions to superstrings, quantum gauge theories and mathematical physics. He was awarded the Dirac Medal by the International Centre for Theoretical Physics in Trieste in 1997, with his long-standing collaborator Peter Goddard. David Olive was a Fellow of the Royal Society and a Founding Fellow of the Learned Society of Wales. David Olive was known for his visionary conjectures, including electromagnetic duality in spontaneously broken gauge theories, as well as his exceptionally clear and insightful style of exposition. These lectures, delivered by David Olive in 1982 at the University of Virginia, provide a pedagogical, self-contained introduction to gauge theory, Lie algebras, electromagnetic duality and integrable models. Despite enormous subsequent developments, they still provide a valuable entry point to some of the deepest topics in quantum gauge theory.
Fingerprints of bosonic symmetry protected topological state in a quantum point contact
Zhang, Rui-Xing; Liu, Chao-Xing
In this work, we study the transport through a quantum point contact for two-channel interacting helical liquids that exist at the edge of a bilayer graphene under a strong magnetic field. We identify ``smoking gun'' transport signatures to distinguish bosonic symmetry protected topological (BSPT) state from fermionic two-channel quantum spin Hall (QSH) state in this system. In particular, a novel charge insulator/spin conductor phase is found for a weak repulsive interaction in the BSPT state, while either charge insulator/spin insulator or charge conductor/spin conductor phase is expected for the two-channel QSH state. In the strong interaction limit, shot noise measurement for the BSPT state is expect to reveal charge-2e instanton tunneling, in comparison with the charge-e tunneling in the two-channel QSH phase.
Fingerprints of a Bosonic Symmetry-Protected Topological State in a Quantum Point Contact
Zhang, Rui-Xing; Liu, Chao-Xing
2017-05-01
In this work, we study the transport through a quantum point contact for bosonic helical liquid that exists at the edge of a bilayer graphene under a strong magnetic field. We identify "smoking gun" transport signatures to distinguish a bosonic symmetry-protected topological (BSPT) state from a fermionic two-channel quantum spin Hall (QSH) state in this system. In particular, a novel charge-insulator-spin-conductor phase is found for the BSPT state, while either the charge-insulator-spin-insulator or the charge-conductor-spin-conductor phase is expected for the two-channel QSH state. Consequently, a simple transport measurement will reveal the fingerprint of bosonic topological physics in bilayer graphene systems.
Nonlocal Symmetries to Systems of Nonlinear Diffusion Equations
International Nuclear Information System (INIS)
Qu Changzheng; Kang Jing
2008-01-01
In this paper, we study potential symmetries to certain systems of nonlinear diffusion equations. Those systems have physical applications in soil science, mathematical biology, and invariant curve flows in R 3 . Lie point symmetries of the potential system, which cannot be projected to vector fields of the given dependent and independent variables, yield potential symmetries. The class of the system that admits potential symmetries is expanded.
A fast point-cloud computing method based on spatial symmetry of Fresnel field
Wang, Xiangxiang; Zhang, Kai; Shen, Chuan; Zhu, Wenliang; Wei, Sui
2017-10-01
Aiming at the great challenge for Computer Generated Hologram (CGH) duo to the production of high spatial-bandwidth product (SBP) is required in the real-time holographic video display systems. The paper is based on point-cloud method and it takes advantage of the propagating reversibility of Fresnel diffraction in the propagating direction and the fringe pattern of a point source, known as Gabor zone plate has spatial symmetry, so it can be used as a basis for fast calculation of diffraction field in CGH. A fast Fresnel CGH method based on the novel look-up table (N-LUT) method is proposed, the principle fringe patterns (PFPs) at the virtual plane is pre-calculated by the acceleration algorithm and be stored. Secondly, the Fresnel diffraction fringe pattern at dummy plane can be obtained. Finally, the Fresnel propagation from dummy plan to hologram plane. The simulation experiments and optical experiments based on Liquid Crystal On Silicon (LCOS) is setup to demonstrate the validity of the proposed method under the premise of ensuring the quality of 3D reconstruction the method proposed in the paper can be applied to shorten the computational time and improve computational efficiency.
Integrability from point symmetries in a family of cosmological Horndeski Lagrangians
International Nuclear Information System (INIS)
Dimakis, N.; Giacomini, Alex; Paliathanasis, Andronikos
2017-01-01
For a family of Horndeski theories, formulated in terms of a generalized Galileon model, we study the integrability of the field equations in a Friedmann-Lemaitre-Robertson-Walker space-time. We are interested in point transformations which leave invariant the field equations. Noether's theorem is applied to determine the conservation laws for a family of models that belong to the same general class. The cosmological scenarios with or without an extra perfect fluid with constant equation of state parameter are the two important cases of our study. The de Sitter universe and ideal gas solutions are derived by using the invariant functions of the symmetry generators as a demonstration of our result. Furthermore, we discuss the connection of the different models under conformal transformations while we show that when the Horndeski theory reduces to a canonical field the same holds for the conformal equivalent theory. Finally, we discuss how singular solutions provides nonsingular universes in a different frame and vice versa. (orig.)
Integrability from point symmetries in a family of cosmological Horndeski Lagrangians
Energy Technology Data Exchange (ETDEWEB)
Dimakis, N.; Giacomini, Alex [Universidad Austral de Chile, Instituto de Ciencias Fisicas y Matematicas, Valdivia (Chile); Paliathanasis, Andronikos [Universidad Austral de Chile, Instituto de Ciencias Fisicas y Matematicas, Valdivia (Chile); Durban University of Technology, Institute of Systems Science, Durban (South Africa)
2017-07-15
For a family of Horndeski theories, formulated in terms of a generalized Galileon model, we study the integrability of the field equations in a Friedmann-Lemaitre-Robertson-Walker space-time. We are interested in point transformations which leave invariant the field equations. Noether's theorem is applied to determine the conservation laws for a family of models that belong to the same general class. The cosmological scenarios with or without an extra perfect fluid with constant equation of state parameter are the two important cases of our study. The de Sitter universe and ideal gas solutions are derived by using the invariant functions of the symmetry generators as a demonstration of our result. Furthermore, we discuss the connection of the different models under conformal transformations while we show that when the Horndeski theory reduces to a canonical field the same holds for the conformal equivalent theory. Finally, we discuss how singular solutions provides nonsingular universes in a different frame and vice versa. (orig.)
Integrability from point symmetries in a family of cosmological Horndeski Lagrangians
Dimakis, N.; Giacomini, Alex; Paliathanasis, Andronikos
2017-07-01
For a family of Horndeski theories, formulated in terms of a generalized Galileon model, we study the integrability of the field equations in a Friedmann-Lemaître-Robertson-Walker space-time. We are interested in point transformations which leave invariant the field equations. Noether's theorem is applied to determine the conservation laws for a family of models that belong to the same general class. The cosmological scenarios with or without an extra perfect fluid with constant equation of state parameter are the two important cases of our study. The de Sitter universe and ideal gas solutions are derived by using the invariant functions of the symmetry generators as a demonstration of our result. Furthermore, we discuss the connection of the different models under conformal transformations while we show that when the Horndeski theory reduces to a canonical field the same holds for the conformal equivalent theory. Finally, we discuss how singular solutions provides nonsingular universes in a different frame and vice versa.
Carnovale, Giovanna; Caselli, Fabrizio; Concini, Corrado; Sole, Alberto
2017-01-01
Lie theory is a mathematical framework for encoding the concept of symmetries of a problem, and was the central theme of an INdAM intensive research period at the Centro de Giorgi in Pisa, Italy, in the academic year 2014-2015. This book gathers the key outcomes of this period, addressing topics such as: structure and representation theory of vertex algebras, Lie algebras and superalgebras, as well as hyperplane arrangements with different approaches, ranging from geometry and topology to combinatorics.
The symmetries and conservation laws of some Gordon-type ...
Indian Academy of Sciences (India)
Hq; 02.30.Jr; 02.30.Xx; 02.40.Ky. 1. Introduction. A vast amount of work has been published in the literature studying differential equations. (DEs) in terms of the Lie point symmetries admitted by them [1,2]. These symmetries play an important ...
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.
Czech Academy of Sciences Publication Activity Database
Znojil, Miloslav
2016-01-01
Roč. 8, č. 6 (2016), s. 52 ISSN 2073-8994 R&D Projects: GA ČR GA16-22945S Institutional support: RVO:61389005 Keywords : parity-time symmetry * Schrodinger equation * physical Hilbert space * inner-product metric operator * real exceptional points * solvable models * quantum Big Bang * quantum Inflation period Subject RIV: BE - Theoretical Physics Impact factor: 1.457, year: 2016
Yang, Shengfeng; Zhou, Naixie; Zheng, Hui; Ong, Shyue Ping; Luo, Jian
2018-02-01
First-order interfacial phaselike transformations that break the mirror symmetry of the symmetric ∑5 (210 ) tilt grain boundary (GB) are discovered by combining a modified genetic algorithm with hybrid Monte Carlo and molecular dynamics simulations. Density functional theory calculations confirm this prediction. This first-order coupled structural and adsorption transformation, which produces two variants of asymmetric bilayers, vanishes at an interfacial critical point. A GB complexion (phase) diagram is constructed via semigrand canonical ensemble atomistic simulations for the first time.
Directory of Open Access Journals (Sweden)
Jen-Cheng Wang
Full Text Available Lie group analysis of the photo-induced fluorescence of Drosophila oogenesis with the asymmetrically localized Gurken protein has been performed systematically to assess the roles of ligand-receptor complexes in follicle cells. The (2×2 matrix representations resulting from the polarized tissue spectra were employed to characterize the asymmetrical Gurken distributions. It was found that the fluorescence of the wild-type egg shows the Lie point symmetry X 23 at early stages of oogenesis. However, due to the morphogen regulation by intracellular proteins and extracellular proteins, the fluorescence of the embryogenesis with asymmetrically localized Gurken expansions exhibits specific symmetry features: Lie point symmetry Z 1 and Lie point symmetry X 1. The novel approach developed herein was successfully used to validate that the invariant-theoretical characterizations are consonant with the observed asymmetric fluctuations during early embryological development.
Observation of valleylike edge states of sound at a momentum away from the high-symmetry points
Xia, Bai-Zhan; Zheng, Sheng-Jie; Liu, Ting-Ting; Jiao, Jun-Rui; Chen, Ning; Dai, Hong-Qing; Yu, De-Jie; Liu, Jian
2018-04-01
In condensed matter physics, topologically protected edge transportation has drawn extensive attention over recent years. Thus far, the topological valley edge states have been produced near the Dirac cones fixed at the high-symmetry points of the Brillouin zone. In this paper, we demonstrate a unique valleylike phononic crystal (PnC) with the position-varying Dirac cones at the high-symmetry lines of the Brillouin zone boundary. The emergence of such Dirac cones, characterized by the vortex structure in a momentum space, is attributed to the unavoidable band crossing protected by the mirror symmetry. The Dirac cones can be unbuckled and a complete band gap can be induced through breaking the mirror symmetry. Interestingly, by simply rotating the square columns, we realize the valleylike vortex states and the band inversion effect which leads to the valley Hall phase transition. Along the valleylike PnC interfaces separating two distinct acoustic valley Hall phases, the valleylike protected edge transport of sound in domain walls is observed in both the simulations and the experiments. These results are promising for the exploration of alternative topological phenomena in the valleylike PnCs beyond the graphenelike lattice.
Jacobson, Nathan
1979-01-01
Lie group theory, developed by M. Sophus Lie in the 19th century, ranks among the more important developments in modern mathematics. Lie algebras comprise a significant part of Lie group theory and are being actively studied today. This book, by Professor Nathan Jacobson of Yale, is the definitive treatment of the subject and can be used as a textbook for graduate courses.Chapter I introduces basic concepts that are necessary for an understanding of structure theory, while the following three chapters present the theory itself: solvable and nilpotent Lie algebras, Carlan's criterion and its
Iachello, Francesco
2015-01-01
This course-based primer provides an introduction to Lie algebras and some of their applications to the spectroscopy of molecules, atoms, nuclei and hadrons. In the first part, it concisely presents the basic concepts of Lie algebras, their representations and their invariants. The second part includes a description of how Lie algebras are used in practice in the treatment of bosonic and fermionic systems. Physical applications considered include rotations and vibrations of molecules (vibron model), collective modes in nuclei (interacting boson model), the atomic shell model, the nuclear shell model, and the quark model of hadrons. One of the key concepts in the application of Lie algebraic methods in physics, that of spectrum generating algebras and their associated dynamic symmetries, is also discussed. The book highlights a number of examples that help to illustrate the abstract algebraic definitions and includes a summary of many formulas of practical interest, such as the eigenvalues of Casimir operators...
Energy Technology Data Exchange (ETDEWEB)
Wang, D.; Song, H.; Yu, X.; Zhang, W.; Qu, W.; Xu, Y.
2015-07-01
The key problem for picking robots is to locate the picking points of fruit. A method based on the moment of inertia and symmetry of apples is proposed in this paper to locate the picking points of apples. Image pre-processing procedures, which are crucial to improving the accuracy of the location, were carried out to remove noise and smooth the edges of apples. The moment of inertia method has the disadvantage of high computational complexity, which should be solved, so convex hull was used to improve this problem. To verify the validity of this algorithm, a test was conducted using four types of apple images containing 107 apple targets. These images were single and unblocked apple images, single and blocked apple images, images containing adjacent apples, and apples in panoramas. The root mean square error values of these four types of apple images were 6.3, 15.0, 21.6 and 18.4, respectively, and the average location errors were 4.9°, 10.2°, 16.3° and 13.8°, respectively. Furthermore, the improved algorithm was effective in terms of average runtime, with 3.7 ms and 9.2 ms for single and unblocked and single and blocked apple images, respectively. For the other two types of apple images, the runtime was determined by the number of apples and blocked apples contained in the images. The results showed that the improved algorithm could extract symmetry axes and locate the picking points of apples more efficiently. In conclusion, the improved algorithm is feasible for extracting symmetry axes and locating the picking points of apples. (Author)
Papi, Paolo; Advances in Lie Superalgebras
2014-01-01
The volume is the outcome of the conference "Lie superalgebras," which was held at the Istituto Nazionale di Alta Matematica, in 2012. The conference gathered many specialists in the subject, and the talks held provided comprehensive insights into the newest trends in research on Lie superalgebras (and related topics like vertex algebras, representation theory and supergeometry). The book contains contributions of many leading esperts in the field and provides a complete account of the newest trends in research on Lie Superalgebras.
International Nuclear Information System (INIS)
Berezin, F.A.
1977-01-01
Generalization of the Laplace-Casimir operator theory on the Lie supergroups is considered. The main result is the formula for radial parts of the Laplace operators under some general assumptions about the Lie supergroup. In particular these assumptions are valid for the Lie suppergroups U(p,g) and C (m,n). The first one is the analogue of the unitary group, the second one is the analogue of the linear group of canonical transformations
Institute of Scientific and Technical Information of China (English)
李凯辉; 刘汉泽; 辛祥鹏
2016-01-01
The symmetries, conservation laws and exact solutions to the nonlinear partial differential equations play a signif-icant role in nonlinear science and mathematical physics. Symmetry is derived from physics, and it is a mathematical description for invariance. Symmetry group theory plays an important role in constructing explicit solutions, whether the equations are integrable or not. By using the symmetry method, an original nonlinear system can be reduced to a system with fewer independent variables through any given subgroup. But, since there are almost always an infinite number of such subgroups, it is usually not feasible to list all possible group invariant solutions to the system. It is anticipated to find all those equivalent group invariant solutions, that is to say, to construct the one-dimensional optimal system for the Lie algebra. Construction of explicit forms of conservation laws is meaningful, as they are used for developing the appropriate numerical methods and for making mathematical analyses, in particular, of existence, uniqueness and stability. In addition, the existence of a large number of conservation laws of a partial differential equation (system) is a strong indication of its integrability. The similarity solutions are of importance for investigating the long-time behavior, blow-up profile and asymptotic phenomena of a non-linear system. For instance, in some circumstance, the asymptotic behaviors of finite-mass solutions of non-linear diffusion equation with non-linear source term are described by an explicit self-similar solution, etc. However, how to tackle these matters is a complicated problem that challenges researchers to be solved. In this paper, by using the symmetry method, we obtain the symmetry reduction, optimal systems, and many new exact group invariant solution of a fifth-order nonlinear wave equation. By Lie symmetry analysis method, the point symmetries and an optimal system of the equation are obtained. The exact power
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.
Energy Technology Data Exchange (ETDEWEB)
Albaladejo, M.; Fernandez-Soler, P.; Nieves, J.; Ortega, P.G. [Centro Mixto CSIC-Universidad de Valencia, Instituto de Fisica Corpuscular (IFIC), Institutos de Investigacion de Paterna, Aptd. 22085, Valencia (Spain)
2017-03-15
The discovery of the D{sup *}{sub s0}(2317) and D{sub s1}(2460) resonances in the charmed-strange meson spectra revealed that formerly successful constituent quark models lose predictability in the vicinity of two-meson thresholds. The emergence of non-negligible effects due to meson loops requires an explicit evaluation of the interplay between Q anti q and (Q anti q)(q anti q) Fock components. In contrast to the c anti s sector, there is no experimental evidence of J{sup P} = 0{sup +}, 1{sup +} bottom-strange states yet. Motivated by recent lattice studies, in this work the heavy-quark partners of the D{sub s0}{sup *}(2317) and D{sub s1}(2460) states are analyzed within a heavy meson chiral unitary scheme. As a novelty, the coupling between the constituent quark-model P-wave anti B{sub s} scalar and axial mesons and the anti B{sup (*)}K channels is incorporated employing an effective interaction, consistent with heavy-quark spin symmetry, constrained by the lattice energy levels. (orig.)
Directory of Open Access Journals (Sweden)
Tosca eBallerini
2015-02-01
Full Text Available Atmosphere-Ocean General Circulation Models (AOGCMs predict changes in the sea ice environment and in atmospheric precipitations over larger areas of Antarctica. These changes are expected to affect the population dynamics of seabirds and marine mammals, but the extent of this influence is not clear. We investigated the future population trajectories of the colony of Adélie penguins at Edmonson Point, in the Ross Sea, from 2010 to 2100. To do so, we incorporated the relationship between sea ice and demographic parameters of the studied colony into a matrix population model. Specifically, we used sea ice projections from AOGCMs and a proxy for snowfall precipitation. Simulations of population persistence under future climate change scenarios showed that a reduction in sea ice extent and an increase in precipitation events during the breeding season will drive the population to extinction. However, the population growth rate estimated by the model was lower than the population growth rate observed during the last decades, suggesting that recruits from other colonies maintain the observed population dynamics at Edmonson Point. This local ‘rescue’ effect is consistent with a metapopulation dynamic for Adélie penguins in the Ross Sea, in which neighboring colonies might exhibit contrasting population trends and different density-dependent effects. In the hypothesis that connectivity with larger source colonies or that local recruitment would decrease, the sink colony at Edmonson Point is predicted to disappear.
Scale-chiral symmetry, ω meson, and dense baryonic matter
Ma, Yong-Liang; Rho, Mannque
2018-05-01
It is shown that explicitly broken scale symmetry is essential for dense skyrmion matter in hidden local symmetry theory. Consistency with the vector manifestation fixed point for the hidden local symmetry of the lowest-lying vector mesons and the dilaton limit fixed point for scale symmetry in dense matter is found to require that the anomalous dimension (|γG2| ) of the gluon field strength tensor squared (G2 ) that represents the quantum trace anomaly should be 1.0 ≲|γG2|≲3.5 . The magnitude of |γG2| estimated here will be useful for studying hadron and nuclear physics based on the scale-chiral effective theory. More significantly, that the dilaton limit fixed point can be arrived at with γG2≠0 at some high density signals that scale symmetry can arise in dense medium as an "emergent" symmetry.
Directory of Open Access Journals (Sweden)
Avraham eMerzel
2015-10-01
Full Text Available Do we feel bound by our own misrepresentations? Does one act of cheating compel the cheater to make subsequent choices that maintain the false image even at a cost? To answer these questions we employed a two-task paradigm such that in the first task the participants could benefit from false reporting of private observations whereas in the second they could benefit from making a prediction in line with their actual, rather than their previously reported observations. Thus, for those participants who inflated their report during the first task, sticking with that report for the second task was likely to lead to a loss, whereas deviating from it would imply that they had lied. Data from three experiments (total N=116 indicate that, having lied, participants were ready to suffer future loss rather than admit, even if implicitly, that they had lied.
Symmetry Reductions of a 1.5-Layer Ocean Circulation Model
International Nuclear Information System (INIS)
Huang Fei; Lou Senyue
2007-01-01
The (2+1)-dimensional nonlinear 1.5-layer ocean circulation model without external wind stress forcing is analyzed by using the classical Lie group approach. Some Lie point symmetries and their corresponding two-dimensional reduction equations are obtained.
MIRROR AND POINT SYMMETRIES IN A BALLISTIC JET FROM A BINARY SYSTEM
International Nuclear Information System (INIS)
Raga, A. C.; Esquivel, A.; Velazquez, P. F.; Haro-Corzo, S.; RodrIguez-Gonzalez, A.; Canto, J.; Riera, A.
2009-01-01
Models of accretion disks around a star in a binary system predict that the disk will have a retrograde precession with a period a factor of ∼10 times the orbital period. If the star+disk system ejects a bipolar outflow, this outflow will be subject to the effects of both the orbital motion and the precession. We present an analytic, ballistic model and a three-dimensional gasdynamical simulation of a bipolar outflow from a source in a circular orbit, and with a precessing outflow axis. We find that this combination results in a jet/counterjet system with a small spatial scale, reflection-symmetric spiral (resulting from the orbital motion) and a larger-scale, point-symmetric spiral (resulting from the longer period precession). These results provide interesting possibilities for modeling specific Herbig-Haro jets and bipolar planetary nebulae.
Algebraic Properties of First Integrals for Scalar Linear Third-Order ODEs of Maximal Symmetry
Directory of Open Access Journals (Sweden)
K. S. Mahomed
2013-01-01
Full Text Available By use of the Lie symmetry group methods we analyze the relationship between the first integrals of the simplest linear third-order ordinary differential equations (ODEs and their point symmetries. It is well known that there are three classes of linear third-order ODEs for maximal cases of point symmetries which are 4, 5, and 7. The simplest scalar linear third-order equation has seven-point symmetries. We obtain the classifying relation between the symmetry and the first integral for the simplest equation. It is shown that the maximal Lie algebra of a first integral for the simplest equation y′′′=0 is unique and four-dimensional. Moreover, we show that the Lie algebra of the simplest linear third-order equation is generated by the symmetries of the two basic integrals. We also obtain counting theorems of the symmetry properties of the first integrals for such linear third-order ODEs. Furthermore, we provide insights into the manner in which one can generate the full Lie algebra of higher-order ODEs of maximal symmetry from two of their basic integrals.
ON PARTIAL DIFFERENTIAL AND DIFFERENCE EQUATIONS WITH SYMMETRIES DEPENDING ON ARBITRARY FUNCTIONS
Directory of Open Access Journals (Sweden)
Giorgio Gubbiotti
2016-06-01
Full Text Available In this note we present some ideas on when Lie symmetries, both point and generalized, can depend on arbitrary functions. We show a few examples, both in partial differential and partial difference equations where this happens. Moreover we show that the infinitesimal generators of generalized symmetries depending on arbitrary functions, both for continuous and discrete equations, effectively play the role of master symmetries.
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.
The symmetries and conservation laws of some Gordon-type
Indian Academy of Sciences (India)
Conservation laws; Milne space-time; Gordon-type equations. Abstract. In this letter, the Lie point symmetries of a class of Gordon-type wave equations that arise in the Milne space-time are presented ... Pramana – Journal of Physics | News.
Group formalism of Lie transformations to time-fractional partial ...
Indian Academy of Sciences (India)
Lie symmetry analysis; Fractional partial differential equation; Riemann–Liouville fractional derivative ... science and engineering. It is known that while ... differential equations occurring in different areas of applied science [11,14]. The Lie ...
Sun, Li-Chung; Chang, Young-Fo; Chang, Chih-Hsiung; Chung, Chia-Lung
2012-05-01
In reflection seismology, detailed knowledge of how seismic waves propagate in anisotropic media is important for locating reservoirs accurately. The SH-wave possesses a pure mode polarization which does not convert to P- and SV-waves when reflecting from a horizontal interface, and vice versa. The simplicity of the SH-wave thus provides an easy way to view the details of SH-wave propagation in anisotropic media. In this study, we attempt to inspect the theoretical reflection moveouts of SH-waves reflected from transversely isotropic (TI) layers with tilted symmetry axes and to verify the reflection point, which could be shifted away from the common midpoint (CMP), by numerical calculations and physical modelling. In travel time-offset analyses, the moveout curves of SH-waves reflected from horizontal TI media (TIM) with different tilted angles of symmetry axes are computed by the TI modified hyperbolic equation and Fermat's principle, respectively. It turns out that both the computed moveout curves are similar and fit well to the observed physical data. The reflection points of SH-waves for a CMP gather computed by Fermat's principle show that they are close to the CMP for TIM with the vertical and horizontal symmetry axes, but they shift away from the CMP for the other tilted angles of symmetry axes. The shifts of the reflection points of the SH-waves from the CMP were verified by physical modelling.
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.)
Approximate and renormgroup symmetries
International Nuclear Information System (INIS)
Ibragimov, Nail H.; Kovalev, Vladimir F.
2009-01-01
''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.)
8x8 and 10x10 Hyperspace Representations of SU(3) and 10-fold Point-Symmetry Group of Quasicrystals
Animalu, Alexander
2012-02-01
In order to further elucidate the unexpected 10-fold point-symmetry group structure of quasi-crystals for which the 2011 Nobel Prize in chemistry was awarded to Daniel Shechtman, we explore a correspondence principle between the number of (projective) geometric elements (points[vertices] + lines[edges] + planes[faces]) of primitive cells of periodic or quasi-periodic arrangement of hard or deformable spheres in 3-dimensional space of crystallography and elements of quantum field theory of particle physics [points ( particles, lines ( particles, planes ( currents] and hence construct 8x8 =64 = 28+36 = 26 + 38, and 10x10 =100= 64 + 36 = 74 + 26 hyperspace representations of the SU(3) symmetry of elementary particle physics and quasicrystals of condensed matter (solid state) physics respectively, As a result, we predict the Cabibbo-like angles in leptonic decay of hadrons in elementary-particle physics and the observed 10-fold symmetric diffraction pattern of quasi-crystals.
Construction of Difference Equations Using Lie Groups
International Nuclear Information System (INIS)
Axford, R.A.
1998-01-01
The theory of prolongations of the generators of groups of point transformations to the grid point values of dependent variables and grid spacings is developed and applied to the construction of group invariant numerical algorithms. The concepts of invariant difference operators and generalized discrete sources are introduced for the discretization of systems of inhomogeneous differential equations and shown to produce exact difference equations. Invariant numerical flux functions are constructed from the general solutions of first order partial differential equations that come out of the evaluation of the Lie derivatives of conservation forms of difference schemes. It is demonstrated that invariant numerical flux functions with invariant flux or slope limiters can be determined to yield high resolution difference schemes. The introduction of an invariant flux or slope limiter can be done so as not to break the symmetry properties of a numerical flux-function
Quasi-Lie algebras and Lie groups
International Nuclear Information System (INIS)
Momo Bangoura
2006-07-01
In this work, we define the quasi-Poisson Lie quasigroups, dual objects to the quasi-Poisson Lie groups and we establish the correspondence between the local quasi-Poisson Lie quasigoups and quasi-Lie bialgebras (up to isomorphism). (author) [fr
Lie groups and Lie algebras for physicists
Das, Ashok
2015-01-01
The book is intended for graduate students of theoretical physics (with a background in quantum mechanics) as well as researchers interested in applications of Lie group theory and Lie algebras in physics. The emphasis is on the inter-relations of representation theories of Lie groups and the corresponding Lie algebras.
International Nuclear Information System (INIS)
Baeuerle, G.G.A.; Kerf, E.A. de
1990-01-01
The structure of the laws in physics is largely based on symmetries. This book is on Lie algebras, the mathematics of symmetry. It gives a thorough mathematical treatment of finite dimensional Lie algebras and Kac-Moody algebras. Concepts such as Cartan matrix, root system, Serre's construction are carefully introduced. Although the book can be read by an undergraduate with only an elementary knowledge of linear algebra, the book will also be of use to the experienced researcher. Experience has shown that students who followed the lectures are well-prepared to take on research in the realms of string-theory, conformal field-theory and integrable systems. 48 refs.; 66 figs.; 3 tabs
International Nuclear Information System (INIS)
Pradeep, R Gladwin; Chandrasekar, V K; Senthilvelan, M; Lakshmanan, M
2011-01-01
In this paper, we devise a systematic procedure to obtain nonlocal symmetries of a class of scalar nonlinear ordinary differential equations (ODEs) of arbitrary order related to linear ODEs through nonlocal relations. The procedure makes use of the Lie point symmetries of the linear ODEs and the nonlocal connection to deduce the nonlocal symmetries of the corresponding nonlinear ODEs. Using these nonlocal symmetries, we obtain reduction transformations and reduced equations to specific examples. We find that the reduced equations can be explicitly integrated to deduce the general solutions for these cases. We also extend this procedure to coupled higher order nonlinear ODEs with specific reference to second-order nonlinear ODEs. (paper)
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.
Rubio Martí, Vicente
2016-01-01
En el presente proyecto definimos lo que es un grupo de Lie, así como su respectiva álgebra de Lie canónica como aproximación lineal a dicho grupo de Lie. El proceso de linealización, que es hallar el algebra de Lie de un grupo de Lie dado, tiene su
Symmetry and symmetry breaking
International Nuclear Information System (INIS)
Balian, R.; Lambert, D.; Brack, A.; Lachieze-Rey, M.; Emery, E.; Cohen-Tannoudji, G.; Sacquin, Y.
1999-01-01
The symmetry concept is a powerful tool for our understanding of the world. It allows a reduction of the volume of information needed to apprehend a subject thoroughly. Moreover this concept does not belong to a particular field, it is involved in the exact sciences but also in artistic matters. Living beings are characterized by a particular asymmetry: the chiral asymmetry. Although this asymmetry is visible in whole organisms, it seems it comes from some molecules that life always produce in one chirality. The weak interaction presents also the chiral asymmetry. The mass of particles comes from the breaking of a fundamental symmetry and the void could be defined as the medium showing as many symmetries as possible. The texts put together in this book show to a great extent how symmetry goes far beyond purely geometrical considerations. Different aspects of symmetry ideas are considered in the following fields: the states of matter, mathematics, biology, the laws of Nature, quantum physics, the universe, and the art of music. (A.C.)
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.
International Nuclear Information System (INIS)
Wu Ming-Zhong; Bai Cheng-Ming
2015-01-01
A compatible Lie algebra is a pair of Lie algebras such that any linear combination of the two Lie brackets is a Lie bracket. We construct a bialgebra theory of compatible Lie algebras as an analogue of a Lie bialgebra. They can also be regarded as a “compatible version” of Lie bialgebras, that is, a pair of Lie bialgebras such that any linear combination of the two Lie bialgebras is still a Lie bialgebra. Many properties of compatible Lie bialgebras as the “compatible version” of the corresponding properties of Lie bialgebras are presented. In particular, there is a coboundary compatible Lie bialgebra theory with a construction from the classical Yang–Baxter equation in compatible Lie algebras as a combination of two classical Yang–Baxter equations in Lie algebras. Furthermore, a notion of compatible pre-Lie algebra is introduced with an interpretation of its close relation with the classical Yang–Baxter equation in compatible Lie algebras which leads to a construction of the solutions of the latter. As a byproduct, the compatible Lie bialgebras fit into the framework to construct non-constant solutions of the classical Yang–Baxter equation given by Golubchik and Sokolov. (paper)
Dynamics of symmetry breaking during quantum real-time evolution in a minimal model system.
Heyl, Markus; Vojta, Matthias
2014-10-31
One necessary criterion for the thermalization of a nonequilibrium quantum many-particle system is ergodicity. It is, however, not sufficient in cases where the asymptotic long-time state lies in a symmetry-broken phase but the initial state of nonequilibrium time evolution is fully symmetric with respect to this symmetry. In equilibrium, one particular symmetry-broken state is chosen as a result of an infinitesimal symmetry-breaking perturbation. From a dynamical point of view the question is: Can such an infinitesimal perturbation be sufficient for the system to establish a nonvanishing order during quantum real-time evolution? We study this question analytically for a minimal model system that can be associated with symmetry breaking, the ferromagnetic Kondo model. We show that after a quantum quench from a completely symmetric state the system is able to break its symmetry dynamically and discuss how these features can be observed experimentally.
Recursions of Symmetry Orbits and Reduction without Reduction
Directory of Open Access Journals (Sweden)
Andrei A. Malykh
2011-04-01
Full Text Available We consider a four-dimensional PDE possessing partner symmetries mainly on the example of complex Monge-Ampère equation (CMA. We use simultaneously two pairs of symmetries related by a recursion relation, which are mutually complex conjugate for CMA. For both pairs of partner symmetries, using Lie equations, we introduce explicitly group parameters as additional variables, replacing symmetry characteristics and their complex conjugates by derivatives of the unknown with respect to group parameters. We study the resulting system of six equations in the eight-dimensional space, that includes CMA, four equations of the recursion between partner symmetries and one integrability condition of this system. We use point symmetries of this extended system for performing its symmetry reduction with respect to group parameters that facilitates solving the extended system. This procedure does not imply a reduction in the number of physical variables and hence we end up with orbits of non-invariant solutions of CMA, generated by one partner symmetry, not used in the reduction. These solutions are determined by six linear equations with constant coefficients in the five-dimensional space which are obtained by a three-dimensional Legendre transformation of the reduced extended system. We present algebraic and exponential examples of such solutions that govern Legendre-transformed Ricci-flat Kähler metrics with no Killing vectors. A similar procedure is briefly outlined for Husain equation.
On double reductions from symmetries and conservation laws for a damped Boussinesq equation
International Nuclear Information System (INIS)
Gandarias, M.L.; Rosa, M.
2016-01-01
In this work, we study a Boussinesq equation with a strong damping term from the point of view of the Lie theory. We derive the classical Lie symmetries admitted by the equation as well as the reduced ordinary differential equations. Some nontrivial conservation laws are derived by using the multipliers method. Taking into account the relationship between symmetries and conservation laws and applying the double reduction method, we obtain a direct reduction of order of the ordinary differential equations and in particular a kink solution.
Finch, Peter E.; Flohr, Michael; Frahm, Holger
2018-02-01
We study two families of quantum models which have been used previously to investigate the effect of topological symmetries in one-dimensional correlated matter. Various striking similarities are observed between certain {Z}n quantum clock models, spin chains generalizing the Ising model, and chains of non-Abelian anyons constructed from the so(n)2 fusion category for odd n, both subject to periodic boundary conditions. In spite of the differences between these two types of quantum chains, e.g. their Hilbert spaces being spanned by tensor products of local spin states or fusion paths of anyons, the symmetries of the lattice models are shown to be closely related. Furthermore, under a suitable mapping between the parameters describing the interaction between spins and anyons the respective Hamiltonians share part of their energy spectrum (although their degeneracies may differ). This spin-anyon correspondence can be extended by fine-tuning of the coupling constants leading to exactly solvable models. We show that the algebraic structures underlying the integrability of the clock models and the anyon chain are the same. For n = 3,5,7 we perform an extensive finite size study—both numerical and based on the exact solution—of these models to map out their ground state phase diagram and to identify the effective field theories describing their low energy behaviour. We observe that the continuum limit at the integrable points can be described by rational conformal field theories with extended symmetry algebras which can be related to the discrete ones of the lattice models.
Lie algebras and linear differential equations.
Brockett, R. W.; Rahimi, A.
1972-01-01
Certain symmetry properties possessed by the solutions of linear differential equations are examined. For this purpose, some basic ideas from the theory of finite dimensional linear systems are used together with the work of Wei and Norman on the use of Lie algebraic methods in differential equation theory.
An introduction to Yangian symmetries
International Nuclear Information System (INIS)
Bernard, D.
1992-01-01
Some aspects of the quantum Yangians as symmetry algebras of two-dimensional quantum field theories are reviewed. They include two main issues: the first is the classical Heisenberg model, covering non-Abelian symmetries, generators of the symmetries and the semi-classical Yangians, an alternative presentation of the semi-classical Yangians, digression on Poisson-Lie groups. The second is the quantum Heisenberg chain, covering non-Abelian symmetries and the quantum Yangians, the transfer matrix and an alternative presentation of the Yangians, digression on the double Yangians. (K.A.) 15 refs
Nonlocal symmetry and explicit solutions from the CRE method of the Boussinesq equation
Zhao, Zhonglong; Han, Bo
2018-04-01
In this paper, we analyze the integrability of the Boussinesq equation by using the truncated Painlevé expansion and the CRE method. Based on the truncated Painlevé expansion, the nonlocal symmetry and Bäcklund transformation of this equation are obtained. A prolonged system is introduced to localize the nonlocal symmetry to the local Lie point symmetry. It is proved that the Boussinesq equation is CRE solvable. The two-solitary-wave fusion solutions, single soliton solutions and soliton-cnoidal wave solutions are presented by means of the Bäcklund transformations.
Quantum Space-Time Deformed Symmetries Versus Broken Symmetries
Amelino-Camelia, G
2002-01-01
Several recent studies have concerned the faith of classical symmetries in quantum space-time. In particular, it appears likely that quantum (discretized, noncommutative,...) versions of Minkowski space-time would not enjoy the classical Lorentz symmetries. I compare two interesting cases: the case in which the classical symmetries are "broken", i.e. at the quantum level some classical symmetries are lost, and the case in which the classical symmetries are "deformed", i.e. the quantum space-time has as many symmetries as its classical counterpart but the nature of these symmetries is affected by the space-time quantization procedure. While some general features, such as the emergence of deformed dispersion relations, characterize both the symmetry-breaking case and the symmetry-deformation case, the two scenarios are also characterized by sharp differences, even concerning the nature of the new effects predicted. I illustrate this point within an illustrative calculation concerning the role of space-time symm...
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
On a Lie-isotopic theory of gravity
International Nuclear Information System (INIS)
Gasperini, M.
1984-01-01
Starting from the isotopic lifting of the Poincare algebra, a Lie-isotopic theory of gravity is formulated, its physical interpretation is given in terms of a generalized principle of equivalence, and it is shown that a local Lorentz-isotopic symmetry motivates the introduction of a generalized metric-affine geometrical structure. Finally, possible applications of a Lie-isotopic theory to the problem of unifying gravity with internal symmetries, in four and more than four dimensions, are discussed
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.
Gravitation, Symmetry and Undergraduates
Jorgensen, Jamie
2001-04-01
This talk will discuss "Project Petrov" Which is designed to investigate gravitational fields with symmetry. Project Petrov represents a collaboration involving physicists, mathematicians as well as graduate and undergraduate math and physics students. An overview of Project Petrov will be given, with an emphasis on students' contributions, including software to classify and generate Lie algebras, to classify isometry groups, and to compute the isometry group of a given metric.
Symmetries and casimir of an extended classical long wave system
Indian Academy of Sciences (India)
Keywords. Dispersionless equations; symmetries; casimir; conserved quantities. ... Application of Lie symmetry analysis to integro-differential equations or infinite systems ..... The financial support in the form of Senior Research Fellowship.
Transitive Lie algebras of vector fields: an overview
Draisma, J.
2011-01-01
This overview paper is intended as a quick introduction to Lie algebras of vector fields. Originally introduced in the late 19th century by Sophus Lie to capture symmetries of ordinary differential equations, these algebras, or infinitesimal groups, are a recurring theme in 20th-century research on
Bakhurst, D
1992-01-01
This article challenges Jennifer Jackson's recent defence of doctors' rights to deceive patients. Jackson maintains there is a general moral difference between lying and intentional deception: while doctors have a prima facie duty not to lie, there is no such obligation to avoid deception. This paper argues 1) that an examination of cases shows that lying and deception are often morally equivalent, and 2) that Jackson's position is premised on a species of moral functionalism that misconstrue...
Symmetry and symmetry breaking in quantum mechanics
International Nuclear Information System (INIS)
Chomaz, Philippe
1998-01-01
In the world of infinitely small, the world of atoms, nuclei and particles, the quantum mechanics enforces its laws. The discovery of Quanta, this unbelievable castration of the Possible in grains of matter and radiation, in discrete energy levels compels us of thinking the Single to comprehend the Universal. Quantum Numbers, magic Numbers and Numbers sign the wave. The matter is vibration. To describe the music of the world one needs keys, measures, notes, rules and partition: one needs quantum mechanics. The particles reduce themselves not in material points as the scholars of the past centuries thought, but they must be conceived throughout the space, in the accomplishment of shapes of volumes. When Einstein asked himself whether God plays dice, there was no doubt among its contemporaries that if He exists He is a geometer. In a Nature reduced to Geometry, the symmetries assume their role in servicing the Harmony. The symmetries allow ordering the energy levels to make them understandable. They impose there geometrical rules to the matter waves, giving them properties which sometimes astonish us. Hidden symmetries, internal symmetries and newly conceived symmetries have to be adopted subsequently to the observation of some order in this world of Quanta. In turn, the symmetries provide new observables which open new spaces of observation
Lagrangian submanifolds and dynamics on Lie algebroids
International Nuclear Information System (INIS)
Leon, Manuel de; Marrero, Juan C; MartInez, Eduardo
2005-01-01
In some previous papers, a geometric description of Lagrangian mechanics on Lie algebroids has been developed. In this topical review, we give a Hamiltonian description of mechanics on Lie algebroids. In addition, we introduce the notion of a Lagrangian submanifold of a symplectic Lie algebroid and we prove that the Lagrangian (Hamiltonian) dynamics on Lie algebroids may be described in terms of Lagrangian submanifolds of symplectic Lie algebroids. The Lagrangian (Hamiltonian) formalism on Lie algebroids permits us to deal with Lagrangian (Hamiltonian) functions not defined necessarily on tangent (cotangent) bundles. Thus, we may apply our results to the projection of Lagrangian (Hamiltonian) functions which are invariant under the action of a symmetry Lie group. As a consequence, we obtain that Lagrange-Poincare (Hamilton-Poincare) equations are the Euler-Lagrange (Hamilton) equations associated with the corresponding Atiyah algebroid. Moreover, we prove that Lagrange-Poincare (Hamilton-Poincare) equations are the local equations defining certain Lagrangian submanifolds of symplectic Atiyah algebroids. (topical review)
Directory of Open Access Journals (Sweden)
Miloslav Znojil
2016-06-01
Full Text Available For a given operator D ( t of an observable in theoretical parity-time symmetric quantum physics (or for its evolution-generator analogues in the experimental gain-loss classical optics, etc. the instant t c r i t i c a l of a spontaneous breakdown of the parity-time alias gain-loss symmetry should be given, in the rigorous language of mathematics, the Kato’s name of an “exceptional point”, t c r i t i c a l = t ( E P . In the majority of conventional applications the exceptional point (EP values are not real. In our paper, we pay attention to several exactly tractable toy-model evolutions for which at least some of the values of t ( E P become real. These values are interpreted as “instants of a catastrophe”, be it classical or quantum. In the classical optical setting the discrete nature of our toy models might make them amenable to simulations. In the latter context the instant of Big Bang is mentioned as an illustrative sample of possible physical meaning of such an EP catastrophe in quantum cosmology.
Hsiang, Wu-Yi
2017-01-01
This volume consists of nine lectures on selected topics of Lie group theory. We provide the readers a concise introduction as well as a comprehensive 'tour of revisiting' the remarkable achievements of S Lie, W Killing, É Cartan and H Weyl on structural and classification theory of semi-simple Lie groups, Lie algebras and their representations; and also the wonderful duet of Cartans' theory on Lie groups and symmetric spaces.With the benefit of retrospective hindsight, mainly inspired by the outstanding contribution of H Weyl in the special case of compact connected Lie groups, we develop the above theory via a route quite different from the original methods engaged by most other books.We begin our revisiting with the compact theory which is much simpler than that of the general semi-simple Lie theory; mainly due to the well fittings between the Frobenius-Schur character theory and the maximal tori theorem of É Cartan together with Weyl's reduction (cf. Lectures 1-4). It is a wonderful reality of the Lie t...
Verschuere, B.; Spruyt, A.; Meijer, E.H.; Otgaar, H.
2011-01-01
Brain imaging studies suggest that truth telling constitutes the default of the human brain and that lying involves intentional suppression of the predominant truth response. By manipulating the truth proportion in the Sheffield lie test, we investigated whether the dominance of the truth response
Biyogmam, Guy Roger
2011-01-01
In this paper, we introduce the category of Lie $n$-racks and generalize several results known on racks. In particular, we show that the tangent space of a Lie $n$-Rack at the neutral element has a Leibniz $n$-algebra structure. We also define a cohomology theory of $n$-racks..
Vrij, Aldert; Taylor, Paul J.; Picornell, Isabel; Oxburgh, Gavin; Myklebust, Trond; Grant, Tim; Milne, Rebecca
2015-01-01
In this chapter, we discuss verbal lie detection and will argue that speech content can be revealing about deception. Starting with a section discussing the, in our view, myth that non-verbal behaviour would be more revealing about deception than speech, we then provide an overview of verbal lie
Medicine, lies and deceptions.
Benn, P
2001-04-01
This article offers a qualified defence of the view that there is a moral difference between telling lies to one's patients, and deceiving them without lying. However, I take issue with certain arguments offered by Jennifer Jackson in support of the same conclusion. In particular, I challenge her claim that to deny that there is such a moral difference makes sense only within a utilitarian framework, and I cast doubt on the aptness of some of her examples of non-lying deception. But I argue that lies have a greater tendency to damage trust than does non-lying deception, and suggest that since many doctors do believe there is a moral boundary between the two types of deception, encouraging them to violate that boundary may have adverse general effects on their moral sensibilities.
Fermion dynamical symmetry and identical bands
International Nuclear Information System (INIS)
Guidry, M.
1994-01-01
Recent general attention has been directed to the phenomenon of identical bands in both normally deformed and superdeformed nuclei. This paper discusses the possibility that such behavior results from a dynamical symmetry of the nuclear many-body system. Phenomenology and the basic principles of Lie algebras are used to place conditions on the acceptable properties of a candidate symmetry. We find that quite general arguments require that such a symmetry have a minimum of 21 generators with a microscopic fermion interpretation
Killing symmetries in neutron transport
International Nuclear Information System (INIS)
Lukacs, B.; Racz, A.
1992-10-01
Although inside the reactor zone there is no exact continuous spatial symmetry, in certain configurations neutron flux distribution is close to a symmetrical one. In such cases the symmetrical solution could provide a good starting point to determine the non-symmetrical power distribution. All possible symmetries are determined in the 3-dimensional Euclidean space, and the form of the transport equation is discussed in such a coordinate system which is adapted to the particular symmetry. Possible spontaneous symmetry breakings are pointed out. (author) 6 refs
Bakhurst, D
1992-06-01
This article challenges Jennifer Jackson's recent defence of doctors' rights to deceive patients. Jackson maintains there is a general moral difference between lying and intentional deception: while doctors have a prima facie duty not to lie, there is no such obligation to avoid deception. This paper argues 1) that an examination of cases shows that lying and deception are often morally equivalent, and 2) that Jackson's position is premised on a species of moral functionalism that misconstrues the nature of moral obligation. Against Jackson, it is argued that both lying and intentional deception are wrong where they infringe a patient's right to autonomy or his/her right to be treated with dignity. These rights represent 'deontological constraints' on action, defining what we must not do whatever the functional value of the consequences. Medical ethics must recognise such constraints if it is to contribute to the moral integrity of medical practice.
Chevalley, Claude
2018-01-01
The standard text on the subject for many years, this introductory treatment covers classical linear groups, topological groups, manifolds, analytic groups, differential calculus of Cartan, and compact Lie groups and their representations. 1946 edition.
Bakhurst, D
1992-01-01
This article challenges Jennifer Jackson's recent defence of doctors' rights to deceive patients. Jackson maintains there is a general moral difference between lying and intentional deception: while doctors have a prima facie duty not to lie, there is no such obligation to avoid deception. This paper argues 1) that an examination of cases shows that lying and deception are often morally equivalent, and 2) that Jackson's position is premised on a species of moral functionalism that misconstrues the nature of moral obligation. Against Jackson, it is argued that both lying and intentional deception are wrong where they infringe a patient's right to autonomy or his/her right to be treated with dignity. These rights represent 'deontological constraints' on action, defining what we must not do whatever the functional value of the consequences. Medical ethics must recognise such constraints if it is to contribute to the moral integrity of medical practice. PMID:1619626
Infinitesimal symmetries: a computational approach
International Nuclear Information System (INIS)
Kersten, P.H.M.
1985-01-01
This thesis is concerned with computational aspects in the determination of infinitesimal symmetries and Lie-Baecklund transformations of differential equations. Moreover some problems are calculated explicitly. A brief introduction to some concepts in the theory of symmetries and Lie-Baecklund transformations, relevant for this thesis, are given. The mathematical formalism is shortly reviewed. The jet bundle formulation is chosen, in which, by its algebraic nature, objects can be described very precisely. Consequently it is appropriate for implementation. A number of procedures are discussed, which enable to carry through computations with the help of a computer. These computations are very extensive in practice. The Lie algebras of infinitesimal symmetries of a number of differential equations in Mathematical Physics are established and some of their applications are discussed, i.e., Maxwell equations, nonlinear diffusion equation, nonlinear Schroedinger equation, nonlinear Dirac equations and self dual SU(2) Yang-Mills equations. Lie-Baecklund transformations of Burgers' equation, Classical Boussinesq equation and the Massive Thirring Model are determined. Furthermore, nonlocal Lie-Baecklund transformations of the last equation are derived. (orig.)
Aniello, Paolo; Chruściński, Dariusz
2017-07-01
A symmetry witness is a suitable subset of the space of selfadjoint trace class operators that allows one to determine whether a linear map is a symmetry transformation, in the sense of Wigner. More precisely, such a set is invariant with respect to an injective densely defined linear operator in the Banach space of selfadjoint trace class operators (if and) only if this operator is a symmetry transformation. According to a linear version of Wigner’s theorem, the set of pure states—the rank-one projections—is a symmetry witness. We show that an analogous result holds for the set of projections with a fixed rank (with some mild constraint on this rank, in the finite-dimensional case). It turns out that this result provides a complete classification of the sets of projections with a fixed rank that are symmetry witnesses. These particular symmetry witnesses are projectable; i.e. reasoning in terms of quantum states, the sets of ‘uniform’ density operators of corresponding fixed rank are symmetry witnesses too.
Institute of Scientific and Technical Information of China (English)
郑世旺; 王建波; 陈向炜; 李彦敏; 解加芳
2012-01-01
航天器运行系统大都属于变质量力学系统,变质量力学系统的对称性和守恒量隐含着航天系统更深刻的物理规律.本文首先导出了变质量非完整力学系统的Tzénoff方程,然后研究了变质量非完整力学系统Tzénoff方程的Lie对称性及其所导出的守恒量,给出了这种守恒量的函数表达式和导出这种守恒量的判据方程.该研究结果对进一步探究变质量系统所遵循的守恒规律具有一定的理论价值.%The operational system of the spacecraft is general a variable mass one,of which the symmetry and the conserved quantity imply physical rules of the space system.In this paper,Tzénoff equations of the variable mass nonholonomic system are derived,from which the Lie symmetries of Tzénoff equations for the variable mass nonholonomic system and conserved quantities are derived and are researched.The function expressions of conserved quantities and the criterion equations which deduce these conserved quantities are presented.This result has some theoretical value for further research of the conservation laws obeyed by the variable mass system.
Yan, Xue-Wei; Tian, Shou-Fu; Dong, Min-Jie; Wang, Xiu-Bin; Zhang, Tian-Tian
2018-05-01
We consider the generalised dispersive modified Benjamin-Bona-Mahony equation, which describes an approximation status for long surface wave existed in the non-linear dispersive media. By employing the truncated Painlevé expansion method, we derive its non-local symmetry and Bäcklund transformation. The non-local symmetry is localised by a new variable, which provides the corresponding non-local symmetry group and similarity reductions. Moreover, a direct method can be provided to construct a kind of finite symmetry transformation via the classic Lie point symmetry of the normal prolonged system. Finally, we find that the equation is a consistent Riccati expansion solvable system. With the help of the Jacobi elliptic function, we get its interaction solutions between solitary waves and cnoidal periodic waves.
Symmetry chains and adaptation coefficients
International Nuclear Information System (INIS)
Fritzer, H.P.; Gruber, B.
1985-01-01
Given a symmetry chain of physical significance it becomes necessary to obtain states which transform properly with respect to the symmetries of the chain. In this article we describe a method which permits us to calculate symmetry-adapted quantum states with relative ease. The coefficients for the symmetry-adapted linear combinations are obtained, in numerical form, in terms of the original states of the system and can thus be represented in the form of numerical tables. In addition, one also obtains automatically the matrix elements for the operators of the symmetry groups which are involved, and thus for any physical operator which can be expressed either as an element of the algebra or of the enveloping algebra. The method is well suited for computers once the physically relevant symmetry chain, or chains, have been defined. While the method to be described is generally applicable to any physical system for which semisimple Lie algebras play a role we choose here a familiar example in order to illustrate the method and to illuminate its simplicity. We choose the nuclear shell model for the case of two nucleons with orbital angular momentum l = 1. While the states of the entire shell transform like the smallest spin representation of SO(25) we restrict our attention to its subgroup SU(6) x SU(2)/sub T/. We determine the symmetry chains which lead to total angular momentum SU(2)/sub J/ and obtain the symmetry-adapted states for these chains
Additional symmetries of supersymmetric KP hierarchies
International Nuclear Information System (INIS)
Stanciu, S.
1993-09-01
We investigate the additional symmetries of several supersymmetric KP hierarchies: The SKP hierarchy of Manin and Radul, the SKP 2 hierarchy, and the Jacobian SKP hierarchy. The main technical tool is the supersymmetric generalisation of a map originally due to Radul between the Lie algebra of superdifferential operators and the Lie algebra of vector fields on the space of supersymmetric Lax operators. In the case of the Manin-Radul SKP hierarchy we identify additional symmetries which form an algebra isomorphic to a subalgebra of superdifferential operators; whereas in the case of the Jacobian SKP, the (additional) symmetries are identified with the algebra itself. (orig.)
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 ...
Implications of an arithmetical symmetry of the commutant for modular invariants
International Nuclear Information System (INIS)
Ruelle, P.; Thiran, E.; Weyers, J.
1993-01-01
We point out the existence of an arithmetical symmetry for the commutant of the modular matrices S and T. This symmetry holds for all affine simple Lie algebras at all levels and implies the equality of certain coefficients in any modular invariant. Particularizing to SU(3) k , we classify the modular invariant partition functions when k+3 is an integer coprime with 6 and when it is a power of either 2 or 3. Our results imply that no detailed knowledge of the commutant is needed to undertake a classification of all modular invariants. (orig.)
A model of intrinsic symmetry breaking
International Nuclear Information System (INIS)
Ge, Li; Li, Sheng; George, Thomas F.; Sun, Xin
2013-01-01
Different from the symmetry breaking associated with a phase transition, which occurs when the controlling parameter is manipulated across a critical point, the symmetry breaking presented in this Letter does not need parameter manipulation. Instead, the system itself suddenly undergoes symmetry breaking at a certain time during its evolution, which is intrinsic symmetry breaking. Through a polymer model, it is revealed that the origin of the intrinsic symmetry breaking is nonlinearity, which produces instability at the instance when the evolution crosses an inflexion point, where this instability breaks the original symmetry
Seron, X
2014-10-01
The issue of lying occurs in neuropsychology especially when examinations are conducted in a forensic context. When a subject intentionally either presents non-existent deficits or exaggerates their severity to obtain financial or material compensation, this behaviour is termed malingering. Malingering is discussed in the general framework of lying in psychology, and the different procedures used by neuropsychologists to evidence a lack of collaboration at examination are briefly presented and discussed. When a lack of collaboration is observed, specific emphasis is placed on the difficulty in unambiguously establishing that this results from the patient's voluntary decision. Copyright © 2014. Published by Elsevier SAS.
Energy Technology Data Exchange (ETDEWEB)
Sati, Hisham [University of Pittsburgh,Pittsburgh, PA, 15260 (United States); Mathematics Program, Division of Science and Mathematics, New York University Abu Dhabi,Saadiyat Island, Abu Dhabi (United Arab Emirates); Schreiber, Urs [Mathematics Institute of the Academy,Žitna 25, Praha 1, 115 67 (Czech Republic)
2017-03-16
We uncover higher algebraic structures on Noether currents and BPS charges. It is known that equivalence classes of conserved currents form a Lie algebra. We show that at least for target space symmetries of higher parameterized WZW-type sigma-models this naturally lifts to a Lie (p+1)-algebra structure on the Noether currents themselves. Applied to the Green-Schwarz-type action functionals for super p-brane sigma-models this yields super Lie (p+1)-algebra refinements of the traditional BPS brane charge extensions of supersymmetry algebras. We discuss this in the generality of higher differential geometry, where it applies also to branes with (higher) gauge fields on their worldvolume. Applied to the M5-brane sigma-model we recover and properly globalize the M-theory super Lie algebra extension of 11-dimensional superisometries by 2-brane and 5-brane charges. Passing beyond the infinitesimal Lie theory we find cohomological corrections to these charges in higher analogy to the familiar corrections for D-brane charges as they are lifted from ordinary cohomology to twisted K-theory. This supports the proposal that M-brane charges live in a twisted cohomology theory.
Du, Xia-Xia; Tian, Bo; Chai, Jun; Sun, Yan; Yuan, Yu-Qiang
2017-11-01
In this paper, we investigate a (3+1)-dimensional modified Zakharov-Kuznetsov equation, which describes the nonlinear plasma-acoustic waves in a multicomponent magnetised plasma. With the aid of the Hirota method and symbolic computation, bilinear forms and one-, two- and three-soliton solutions are derived. The characteristics and interaction of the solitons are discussed graphically. We present the effects on the soliton's amplitude by the nonlinear coefficients which are related to the ratio of the positive-ion mass to negative-ion mass, number densities, initial densities of the lower- and higher-temperature electrons and ratio of the lower temperature to the higher temperature for electrons, as well as by the dispersion coefficient, which is related to the ratio of the positive-ion mass to the negative-ion mass and number densities. Moreover, using the Lie symmetry group theory, we derive the Lie point symmetry generators and the corresponding symmetry reductions, through which certain analytic solutions are obtained via the power series expansion method and the (G'/G) expansion method. We demonstrate that such an equation is strictly self-adjoint, and the conservation laws associated with the Lie point symmetry generators are derived.
Some general constraints on identical band symmetries
International Nuclear Information System (INIS)
Guidry, M.W.; Strayer, M.R.; Wu, C.; Feng, D.H.
1993-01-01
We argue on general grounds that nearly identical bands observed for superdeformation and less frequently for normal deformation must be explicable in terms of a symmetry having a microscopic basis. We assume that the unknown symmetry is associated with a Lie algebra generated by terms bilinear in fermion creation and annihilation operators. Observed features of these bands and the general properties of Lie groups are then used to place constraints on acceptable algebras. Additional constraints are placed by assuming that the collective spectrum is associated with a dynamical symmetry, and examining the subgroup structure required by phenomenology. We observe that requisite symmetry cannot be unitary, and that the simplest known group structures consistent with these minimal criteria are associated with the Ginocchio algebras employed in the fermion dynamical symmetry model. However, our arguments are general in nature, and we propose that they imply model-independent constraints on any candidate explanation for identical bands
Collective states and crossing symmetry
International Nuclear Information System (INIS)
Heiss, W.D.
1977-01-01
Collective states are usually described in simple terms but with the use of effective interactions which are supposed to contain more or less complicated contributions. The significance of crossing symmetry is discussed in this connection. Formal problems encountered in the attempts to implement crossing symmetry are pointed out
Lie transforms and their use in Hamiltonian perturbation theory
International Nuclear Information System (INIS)
Cary, J.R.
1978-06-01
A review is presented of the theory of Lie transforms as applied to Hamiltonian systems. We begin by presenting some general background on the Hamiltonian formalism and by introducing the operator notation for canonical transformations. We then derive the general theory of Lie transforms. We derive the formula for the new Hamiltonian when one uses a Lie transform to effect a canonical transformation, and we use Lie transforms to prove a very general version of Noether's theorem, or the symmetry-equals-invariant theorem. Next we use the general Lie transform theory to derive Deprit's perturbation theory. We illustrate this perturbation theory by application to two well-known problems in classical mechanics. Finally we present a chapter on conventions. There are many ways to develop Lie transforms. The last chapter explains the reasons for the choices made here
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.
A Lie based 4-dimensional higher Chern-Simons theory
Zucchini, Roberto
2016-05-01
We present and study a model of 4-dimensional higher Chern-Simons theory, special Chern-Simons (SCS) theory, instances of which have appeared in the string literature, whose symmetry is encoded in a skeletal semistrict Lie 2-algebra constructed from a compact Lie group with non discrete center. The field content of SCS theory consists of a Lie valued 2-connection coupled to a background closed 3-form. SCS theory enjoys a large gauge and gauge for gauge symmetry organized in an infinite dimensional strict Lie 2-group. The partition function of SCS theory is simply related to that of a topological gauge theory localizing on flat connections with degree 3 second characteristic class determined by the background 3-form. Finally, SCS theory is related to a 3-dimensional special gauge theory whose 2-connection space has a natural symplectic structure with respect to which the 1-gauge transformation action is Hamiltonian, the 2-curvature map acting as moment map.
Directory of Open Access Journals (Sweden)
Debra Lewis
2013-05-01
Full Text Available Relative equilibria of Lagrangian and Hamiltonian systems with symmetry are critical points of appropriate scalar functions parametrized by the Lie algebra (or its dual of the symmetry group. Setting aside the structures – symplectic, Poisson, or variational – generating dynamical systems from such functions highlights the common features of their construction and analysis, and supports the construction of analogous functions in non-Hamiltonian settings. If the symmetry group is nonabelian, the functions are invariant only with respect to the isotropy subgroup of the given parameter value. Replacing the parametrized family of functions with a single function on the product manifold and extending the action using the (coadjoint action on the algebra or its dual yields a fully invariant function. An invariant map can be used to reverse the usual perspective: rather than selecting a parametrized family of functions and finding their critical points, conditions under which functions will be critical on specific orbits, typically distinguished by isotropy class, can be derived. This strategy is illustrated using several well-known mechanical systems – the Lagrange top, the double spherical pendulum, the free rigid body, and the Riemann ellipsoids – and generalizations of these systems.
International Nuclear Information System (INIS)
Kumar, Vikas; Gupta, R. K.; Jiwari, Ram
2014-01-01
In this paper, the variable-coefficient diffusion—advection (DA) equation, which arises in modeling various physical phenomena, is studied by the Lie symmetry approach. The similarity reductions are derived by determining the complete sets of point symmetries of this equation, and then exact and numerical solutions are reported for the reduced second-order nonlinear ordinary differential equations. Further, an extended (G'/G)-expansion method is applied to the DA equation to construct some new non-traveling wave solutions
Symmetry broken and restored coupled-cluster theory: I. Rotational symmetry and angular momentum
International Nuclear Information System (INIS)
Duguet, T
2015-01-01
We extend coupled-cluster (CC) theory performed on top of a Slater determinant breaking rotational symmetry to allow for the exact restoration of the angular momentum at any truncation order. The main objective relates to the description of near-degenerate finite quantum systems with an open-shell character. As such, the newly developed many-body formalism offers a wealth of potential applications and further extensions dedicated to the ab initio description of, e.g., doubly open-shell atomic nuclei and molecule dissociation. The formalism, which encompasses both single-reference CC theory and projected Hartree–Fock theory as particular cases, permits the computation of usual sets of connected diagrams while consistently incorporating static correlations through the highly non-perturbative restoration of rotational symmetry. Interestingly, the yrast spectroscopy of the system, i.e. the lowest energy associated with each angular momentum, is accessed within a single calculation. A key difficulty presently overcome relates to the necessity to handle generalized energy and norm kernels for which naturally terminating CC expansions could be eventually obtained. The present work focuses on SU(2) but can be extended to any (locally) compact Lie group and to discrete groups, such as most point groups. In particular, the formalism will be soon generalized to U(1) symmetry associated with particle number conservation. This is relevant to Bogoliubov CC theory that was recently applied to singly open-shell nuclei. (paper)
Lie bialgebras with triangular decomposition
International Nuclear Information System (INIS)
Andruskiewitsch, N.; Levstein, F.
1992-06-01
Lie bialgebras originated in a triangular decomposition of the underlying Lie algebra are discussed. The explicit formulas for the quantization of the Heisenberg Lie algebra and some motion Lie algebras are given, as well as the algebra of rational functions on the quantum Heisenberg group and the formula for the universal R-matrix. (author). 17 refs
Unified Symmetry and Conserved Quantities of Mechanical System in Phase Space
International Nuclear Information System (INIS)
Fang Jianhui; Ding Ning; Wang Peng
2006-01-01
In this paper, a new symmetry and its conserved quantities of a mechanical system in phase space are studied. The definition of this new symmetry, i.e., a unified one is presented, and the criterion of this symmetry is also given. The Noether, the generalized Hojman and the Mei conserved quantities of the unified symmetry of the system are obtained. The unified symmetry contains the Noether, the Lie and the Mei symmetries, and has more generalized significance.
Lie groups, lie algebras, and representations an elementary introduction
Hall, Brian
2015-01-01
This textbook treats Lie groups, Lie algebras and their representations in an elementary but fully rigorous fashion requiring minimal prerequisites. In particular, the theory of matrix Lie groups and their Lie algebras is developed using only linear algebra, and more motivation and intuition for proofs is provided than in most classic texts on the subject. In addition to its accessible treatment of the basic theory of Lie groups and Lie algebras, the book is also noteworthy for including: a treatment of the Baker–Campbell–Hausdorff formula and its use in place of the Frobenius theorem to establish deeper results about the relationship between Lie groups and Lie algebras motivation for the machinery of roots, weights and the Weyl group via a concrete and detailed exposition of the representation theory of sl(3;C) an unconventional definition of semisimplicity that allows for a rapid development of the structure theory of semisimple Lie algebras a self-contained construction of the representations of compac...
Symmetries, Integrals and Solutions of Ordinary Differential ...
Indian Academy of Sciences (India)
Second-and third-order scalar ordinary differential equations of maximal symmetry in the traditional sense of point, respectively contact, symmetry are examined for the mappings they produce in solutions and fundamental first integrals. The properties of the `exceptional symmetries', i.e. those not considered to be generic to ...
International Nuclear Information System (INIS)
Souriau, J.M.
1984-01-01
The sky uniformity can be noticed in studying the repartition of objects far enough. The sky isotropy description uses space rotations. The group theory elements will allow to give a meaning at the same time precise and general to the word a ''symmetry''. Universe models are reviewed, which must have both of the following qualities: - conformity with the physic known laws; - rigorous symmetry following one of the permitted groups. Each of the models foresees that universe evolution obeys an evolution equation. Expansion and big-bang theory are recalled. Is universe an open or closed space. Universe is also electrically neutral. That leads to a work hypothesis: the existing matter is not given data of universe but it appeared by evolution from nothing. Problem of matter and antimatter is then raised up together with its place in universe [fr
Lipkin, Harry J
2002-01-01
According to the author of this concise, high-level study, physicists often shy away from group theory, perhaps because they are unsure which parts of the subject belong to the physicist and which belong to the mathematician. However, it is possible for physicists to understand and use many techniques which have a group theoretical basis without necessarily understanding all of group theory. This book is designed to familiarize physicists with those techniques. Specifically, the author aims to show how the well-known methods of angular momentum algebra can be extended to treat other Lie group
Energy Technology Data Exchange (ETDEWEB)
NONE
1996-02-01
The Department of Energy has prepared an Environmental Assessment (DOE/EA-1143) evaluating the construction, equipping and operation of the proposed Lied Transplant Center at the University of Nebraska Medical Center in Omaha, Nebraska. Based on the analysis in the EA, the DOE has determined that the proposed action does not constitute a major federal action significantly affecting the quality of the human environment within the meaning of the National Environmental Policy Act of 1969 (NEPA). Therefore, the preparation of an Environmental Statement in not required.
Energy Technology Data Exchange (ETDEWEB)
Salam, A. [Imperial College of Science and Technology, London (United Kingdom)
1963-01-15
Throughout the history of quantum theory, a battle has raged between the amateurs and professional group theorists. The amateurs have maintained that everything one needs in the theory of groups can be discovered by the light of nature provided one knows how to multiply two matrices. In support of this claim, they of course, justifiably, point to the successes of that prince of amateurs in this field, Dirac, particularly with the spinor representations of the Lorentz group. As an amateur myself, I strongly believe in the truth of the non-professionalist creed. I think perhaps there is not much one has to learn in the way of methodology from the group theorists except caution. But this does not mean one should not be aware of the riches which have been amassed over the course of years particularly in that most highly developed of all mathematical disciplines - the theory of Lie groups. My lectures then are an amateur's attempt to gather some of the fascinating results for compact simple Lie groups which are likely to be of physical interest. I shall state theorems; and with a physicist's typical unconcern rarely, if ever, shall I prove these. Throughout, the emphasis will be to show the close similarity of these general groups with that most familiar of all groups, the group of rotations in three dimensions.
Hyperbolic-symmetry vector fields.
Gao, Xu-Zhen; Pan, Yue; Cai, Meng-Qiang; Li, Yongnan; Tu, Chenghou; Wang, Hui-Tian
2015-12-14
We present and construct a new kind of orthogonal coordinate system, hyperbolic coordinate system. We present and design a new kind of local linearly polarized vector fields, which is defined as the hyperbolic-symmetry vector fields because the points with the same polarization form a series of hyperbolae. We experimentally demonstrate the generation of such a kind of hyperbolic-symmetry vector optical fields. In particular, we also study the modified hyperbolic-symmetry vector optical fields with the twofold and fourfold symmetric states of polarization when introducing the mirror symmetry. The tight focusing behaviors of these vector fields are also investigated. In addition, we also fabricate micro-structures on the K9 glass surfaces by several tightly focused (modified) hyperbolic-symmetry vector fields patterns, which demonstrate that the simulated tightly focused fields are in good agreement with the fabricated micro-structures.
Extended nonabelian symmetries for free fermionic model
International Nuclear Information System (INIS)
Zaikov, R.P.
1993-08-01
The higher spin symmetry for both Dirac and Majorana massless free fermionic field models are considered. An infinite Lie algebra which is a linear realization of the higher spin extension of the cross products of the Virasoro and affine Kac-Moody algebras is obtained. The corresponding current algebra is closed which is not the case of analogous current algebra in the WZNW model. The gauging procedure for the higher spin symmetry is also given. (author). 12 refs
International Nuclear Information System (INIS)
French, J.B.
1974-01-01
The concepts of statistical behavior and symmetry are presented from the point of view of many body spectroscopy. Remarks are made on methods for the evaluation of moments, particularly widths, for the purpose of giving a feeling for the types of mathematical structures encountered. Applications involving ground state energies, spectra, and level densities are discussed. The extent to which Hamiltonian eigenstates belong to irreducible representations is mentioned. (4 figures, 1 table) (U.S.)
Lie Quasi-Bialgebras and Cohomology of Lie algebra
International Nuclear Information System (INIS)
Bangoura, Momo
2010-05-01
Lie quasi-bialgebras are natural generalisations of Lie bialgebras introduced by Drinfeld. To any Lie quasi-bialgebra structure of finite-dimensional (G, μ, γ, φ), corresponds one Lie algebra structure on D = G + G*, called the double of the given Lie quasi-bialgebra. We show that there exist on ΛG, the exterior algebra of G, a D-module structure and we establish an isomorphism of D-modules between ΛD and End(ΛG), D acting on ΛD by the adjoint action. (author) [fr
Renormalized Lie perturbation theory
International Nuclear Information System (INIS)
Rosengaus, E.; Dewar, R.L.
1981-07-01
A Lie operator method for constructing action-angle transformations continuously connected to the identity is developed for area preserving mappings. By a simple change of variable from action to angular frequency a perturbation expansion is obtained in which the small denominators have been renormalized. The method is shown to lead to the same series as the Lagrangian perturbation method of Greene and Percival, which converges on KAM surfaces. The method is not superconvergent, but yields simple recursion relations which allow automatic algebraic manipulation techniques to be used to develop the series to high order. It is argued that the operator method can be justified by analytically continuing from the complex angular frequency plane onto the real line. The resulting picture is one where preserved primary KAM surfaces are continuously connected to one another
Debey, E.; De Houwer, J.; Verschuere, B.
2014-01-01
Cognitive models of deception focus on the conflict-inducing nature of the truth activation during lying. Here we tested the counterintuitive hypothesis that the truth can also serve a functional role in the act of lying. More specifically, we examined whether the construction of a lie can involve a
Purposes and Effects of Lying.
Hample, Dale
Three exploratory studies were aimed at describing the purposes of lies and the consequences of lying. Data were collected through a partly open-ended questionnaire, a content analysis of several tape-recorded interviews, and a large-scale survey. The results showed that two of every three lies were told for selfish reasons, while three of every…
Point form relativistic quantum mechanics and relativistic SU(6)
Klink, W. H.
1993-01-01
The point form is used as a framework for formulating a relativistic quantum mechanics, with the mass operator carrying the interactions of underlying constituents. A symplectic Lie algebra of mass operators is introduced from which a relativistic harmonic oscillator mass operator is formed. Mass splittings within the degenerate harmonic oscillator levels arise from relativistically invariant spin-spin, spin-orbit, and tensor mass operators. Internal flavor (and color) symmetries are introduced which make it possible to formulate a relativistic SU(6) model of baryons (and mesons). Careful attention is paid to the permutation symmetry properties of the hadronic wave functions, which are written as polynomials in Bargmann spaces.
Discrete finite nilpotent Lie analogs: New models for unified gauge field theory
International Nuclear Information System (INIS)
Kornacker, K.
1978-01-01
To each finite dimensional real Lie algebra with integer structure constants there corresponds a countable family of discrete finite nilpotent Lie analogs. Each finite Lie analog maps exponentially onto a finite unipotent group G, and is isomorphic to the Lie algebra of G. Reformulation of quantum field theory in discrete finite form, utilizing nilpotent Lie analogs, should elminate all divergence problems even though some non-Abelian gauge symmetry may not be spontaneously broken. Preliminary results in the new finite representation theory indicate that a natural hierarchy of spontaneously broken symmetries can arise from a single unbroken non-Abelian gauge symmetry, and suggest the possibility of a new unified group theoretic interpretation for hadron colors and flavors
Symmetry of quantum intramolecular dynamics
International Nuclear Information System (INIS)
Burenin, Alexander V
2002-01-01
The paper reviews the current progress in describing quantum intramolecular dynamics using merely symmetry principles as a basis. This closed qualitative approach is of particular interest because it is the only method currently available for a broad class of topical problems in the internal dynamics of molecules. Moreover, a molecule makes a physical system whose collective internal motions are geometrically structured, so that its description by perturbation methods requires a symmetry analysis of this structure. The nature of the geometrical symmetry groups crucial for the closed formulation of the qualitative approach is discussed. In particular, the point group of a molecule is of this type. (methodological notes)
Symbolic Detection of Permutation and Parity Symmetries of Evolution Equations
Alghamdi, Moataz
2017-01-01
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
Fermion dynamical symmetry and identical bands
International Nuclear Information System (INIS)
Guidry, M.
1995-01-01
Recent general attention has been directed to the phenomenon of identical bands in both normally deformed and superdeformed nuclei. This paper discusses the possibility that such behavior results from a dynamical symmetry of the nuclear many-body system. Phenomenology and the basis principles of Lie algebras are used to place conditions on the acceptable properties of a candidate symmetry. We find that quite general arguments require that such a symmetry have a minimum of 21 generators with a microscopic fermion interpretation. (author). 9 refs., 11 figs., 1 tab
Lie Algebras and Integrable Systems
International Nuclear Information System (INIS)
Zhang Yufeng; Mei Jianqin
2012-01-01
A 3 × 3 matrix Lie algebra is first introduced, its subalgebras and the generated Lie algebras are obtained, respectively. Applications of a few Lie subalgebras give rise to two integrable nonlinear hierarchies of evolution equations from their reductions we obtain the nonlinear Schrödinger equations, the mKdV equations, the Broer-Kaup (BK) equation and its generalized equation, etc. The linear and nonlinear integrable couplings of one integrable hierarchy presented in the paper are worked out by casting a 3 × 3 Lie subalgebra into a 2 × 2 matrix Lie algebra. Finally, we discuss the elliptic variable solutions of a generalized BK equation. (general)
Celse, Jérémy; Chang, Kirk
2017-11-30
This research analyzed whether political leaders make people lie via priming experiments. Priming is a non-conscious and implicit memory effect in which exposure to one stimulus affects the response to another. Following priming theories, we proposed an innovative concept that people who perceive leaders to be dishonest (such as liars) are likely to lie themselves. We designed three experiments to analyze and critically discussed the potential influence of prime effect on lying behavior, through the prime effect of French political leaders (including general politicians, presidents and parties). Experiment 1 discovered that participants with non-politician-prime were less likely to lie (compared to politician-prime). Experiment 2A discovered that, compared to Hollande-prime, Sarkozy-prime led to lying behavior both in gravity (i.e., bigger lies) and frequency (i.e., lying more frequently). Experiment 2B discovered that Republicans-prime yielded an impact on more lying behavior, and Sarkozy-prime made such impact even stronger. Overall, the research findings suggest that lying can be triggered by external influencers such as leaders, presidents and politicians in the organizations. Our findings have provided valuable insights into organizational leaders and managers in their personnel management practice, especially in the intervention of lying behavior. Our findings also have offered new insights to explain non-conscious lying behavior.
BOOK REVIEW: Symmetry Breaking
Ryder, L. H.
2005-11-01
have to be rather clever to recognize that the particle interactions were rotationally invariant. Nambu and Goldstone showed that the spontaneous breakdown of a (continuous) symmetry implied the existence of massless scalar particles, referred to as Nambu Goldstone bosons, or simply Goldstone bosons. Meanwhile Anderson, in his study of (non-relativistic) superconductivity, showed that the exclusion of magnetic flux (Meissner effect) corresponds to a finite range for the electromagnetic field and hence to a `massive photon'. In a relativistic context Englert, Brout, Guralnik and more particularly Higgs showed that a spontaneous breaking of a gauge symmetry resulted in a massive, instead of a massless, gauge particle and no Goldstone particle; in the jargon of the day, the massless gauge particle had `eaten' the massless Goldstone boson and become massive; exactly Anderson's observation. It is this phenomenon which has been invoked so successfully to explain the masses of the W and Z bosons of weak interactions. Spontaneous symmetry breaking, therefore, has played a major role in the development of the Standard Model of particle physics, and it has also proved an important tool in condensed matter physics, for example in the understanding of phase transitions. At the same time, however, in the understanding of most (or all) particle physicists, and perhaps also condensed matter physicists, the notion of spontaneous symmetry breaking has been inexorably linked to that of a degenerate vacuum. This is the background and the starting point for Strocchi's book. Recognizing the power and importance of the concept of spontaneous symmetry breaking in theoretical physics, he defines it in a more refined and general way than usual. `Despite the many popular accounts', he writes, `the phenomenon of spontaneous symmetry breaking is deep and subtle and it is not without [reason] that it has been fully understood only in recent times.' Strocchi's main emphasis is on the fact that the
Lie groups and grand unified theories
International Nuclear Information System (INIS)
Gubitoso, M.D.
1987-01-01
This work presents some concepts in group theory and Lie algebras and, at same time, shows a method to study and work with semisimple Lie groups, based on Dynkin diagrams. The aproach taken is not completely formal, but it presents the main points of the elaboration of the method, so its mathematical basis is designed with the purpose of making the reading not so cumbersome to those who are interested only in a general picture of the method and its usefulness. At the end it is shown a brief review of gauge theories and two grand-unification models based on SO(13) and E 7 gauge groups. (author) [pt
A search for symmetries in the genetic code
International Nuclear Information System (INIS)
Hornos, J.E.M.; Hornos, Y.M.M.
1991-01-01
A search for symmetries based on the classification theorem of Cartan for the compact simple Lie algebras is performed to verify to what extent the genetic code is a manifestation of some underlying symmetry. An exact continuous symmetry group cannot be found to reproduce the present, universal code. However a unique approximate symmetry group is compatible with codon assignment for the fundamental amino acids and the termination codon. In order to obtain the actual genetic code, the symmetry must be slightly broken. (author). 27 refs, 3 figs, 6 tabs
Directory of Open Access Journals (Sweden)
Decio Levi
2013-10-01
Full Text Available We briefly review two different methods of applying Lie group theory in the numerical solution of ordinary differential equations. On specific examples we show how the symmetry preserving discretization provides difference schemes for which the “first differential approximation” is invariant under the same Lie group as the original ordinary differential equation.
Residual symmetries in the presence of an EM background
International Nuclear Information System (INIS)
Carrion, H.L.; Rojas, M.; Toppan, F.
2002-08-01
The symmetry algebra of a QFT in the presence of an external EM background (named 'residual symmetry') is investigated within a Lie-algebraic, model independent scheme. Some results previously encountered in the literature are here extended. In particular we compute the symmetry algebra for a constant EM background in D = 3 and D = 4 dimensions. In D = 3 dimensions the residual symmetry algebra is isomorphic to u(1) +P c (2), with P c (2) the centrally extended 2-dimensional Poincare algebra. In D = 4 dimension the generic residual symmetry algebra is given by a seven-dimensional solvable Lie algebra which is explicitly computed. residual symmetry algebras are also computed for specific non-constant EM backgrounds. (author)
Residual symmetries in the presence of an EM background
Energy Technology Data Exchange (ETDEWEB)
Rojas Leyva, Moises Porfirio; Salazar, Hector Leny Carrion; Toppan, Francesco [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil)]. E-mail: mrojas, hleny, toppan@cbpf.br
2001-07-01
The symmetry algebra of a QFT in the presence of an external EM background (named 'residual symmetry') is investigated within a Lie-algebraic, model independent scheme. Some results previously encountered in the literature are here extended. In particular we compute the symmetry algebra for a constant EM background in D = 3 and D = 4 dimensions. In D = 3 dimensions the residual symmetry algebra is isomorphic to u(1) + P{sub c} (2) the centrally extended 2-dimensional Poincare algebra. In D=4 dimensions the generic residual symmetry algebra is given by a 7 dimensional solvable Lie algebra which is explicitly computed. Residual symmetry algebras are also computed for specific non-constant EM backgrounds. (author)
Residual symmetries in the presence of an EM background
Energy Technology Data Exchange (ETDEWEB)
Carrion, H.L.; Rojas, M.; Toppan, F. [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil)]. E-mail: hleny@cbpf.br; mrojas@cbpf.br; toppan@cbpf.br
2002-08-01
The symmetry algebra of a QFT in the presence of an external EM background (named 'residual symmetry') is investigated within a Lie-algebraic, model independent scheme. Some results previously encountered in the literature are here extended. In particular we compute the symmetry algebra for a constant EM background in D = 3 and D = 4 dimensions. In D = 3 dimensions the residual symmetry algebra is isomorphic to u(1) +P{sub c}(2), with P{sub c}(2) the centrally extended 2-dimensional Poincare algebra. In D = 4 dimension the generic residual symmetry algebra is given by a seven-dimensional solvable Lie algebra which is explicitly computed. residual symmetry algebras are also computed for specific non-constant EM backgrounds. (author)
Nonflexible Lie-admissible algebras
International Nuclear Information System (INIS)
Myung, H.C.
1978-01-01
We discuss the structure of Lie-admissible algebras which are defined by nonflexible identities. These algebras largely arise from the antiflexible algebras, 2-varieties and associator dependent algebras. The nonflexible Lie-admissible algebras in our discussion are in essence byproducts of the study of nonassociative algebras defined by identities of degree 3. The main purpose is to discuss the classification of simple Lie-admissible algebras of nonflexible type
Non-Hermitian systems of Euclidean Lie algebraic type with real energy spectra
International Nuclear Information System (INIS)
Dey, Sanjib; Fring, Andreas; Mathanaranjan, Thilagarajah
2014-01-01
We study several classes of non-Hermitian Hamiltonian systems, which can be expressed in terms of bilinear combinations of Euclidean–Lie algebraic generators. The classes are distinguished by different versions of antilinear (PT)-symmetries exhibiting various types of qualitative behaviour. On the basis of explicitly computed non-perturbative Dyson maps we construct metric operators, isospectral Hermitian counterparts for which we solve the corresponding time-independent Schrödinger equation for specific choices of the coupling constants. In these cases general analytical expressions for the solutions are obtained in the form of Mathieu functions, which we analyze numerically to obtain the corresponding energy spectra. We identify regions in the parameter space for which the corresponding spectra are entirely real and also domains where the PT symmetry is spontaneously broken and sometimes also regained at exceptional points. In some cases it is shown explicitly how the threshold region from real to complex spectra is characterized by the breakdown of the Dyson maps or the metric operator. We establish the explicit relationship to models currently under investigation in the context of beam dynamics in optical lattices. -- Highlights: •Different PT-symmetries lead to qualitatively different systems. •Construction of non-perturbative Dyson maps and isospectral Hermitian counterparts. •Numerical discussion of the eigenvalue spectra for one of the E(2)-systems. •Established link to systems studied in the context of optical lattices. •Setup for the E(3)-algebra is provided
Lie families: theory and applications
International Nuclear Information System (INIS)
Carinena, Jose F; Grabowski, Janusz; De Lucas, Javier
2010-01-01
We analyze the families of non-autonomous systems of first-order ordinary differential equations admitting a common time-dependent superposition rule, i.e. a time-dependent map expressing any solution of each of these systems in terms of a generic set of particular solutions of the system and some constants. We next study the relations of these families, called Lie families, with the theory of Lie and quasi-Lie systems and apply our theory to provide common time-dependent superposition rules for certain Lie families.
Lying in business : Insights from Hanna Arendt's 'Lying in Politics'
Eenkhoorn, P.; Graafland, J.J.
2011-01-01
The political philosopher Hannah Arendt develops several arguments regarding why truthfulness cannot be counted among the political virtues. This article shows that similar arguments apply to lying in business. Based on Hannah Arendt's theory, we distinguish five reasons why lying is a structural
On symmetries and exact solutions of the Einstein–Maxwell field equations via the symmetry approach
International Nuclear Information System (INIS)
Kaur, Lakhveer; Gupta, R K
2013-01-01
Using the Lie symmetry approach, we have examined herein the system of partial differential equations corresponding to the Einstein–Maxwell equations for a static axially symmetric spacetime. The method used reduces the system of partial differential equations to a system of ordinary differential equations according to the Lie symmetry admitted. In particular, we found the relevant system of ordinary differential equations is all optimal subgroups. The system of ordinary differential equations is further solved in general to obtain exact solutions. Several new physically important families of exact solutions are derived. (paper)
International Nuclear Information System (INIS)
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
Directory of Open Access Journals (Sweden)
Nadjafikhah M.
2017-07-01
Full Text Available Lie group method is applicable to both linear and non-linear partial differential equations, which leads to find new solutions for partial differential equations. Lie symmetry group method is applied to study Newtonian incompressible fluid’s equations flow in turbulent boundary layers. The symmetry group and its optimal system are given, and group invariant solutions associated to the symmetries are obtained. Finally the structure of the Lie algebra such as Levi decomposition, radical subalgebra, solvability and simplicity of symmetries is given.
Introduction to vertex algebras, Borcherds algebras and the Monster Lie algebras
International Nuclear Information System (INIS)
Gebert, R.W.
1993-09-01
The theory of vertex algebras constitutes a mathematically rigorous axiomatic formulation of the algebraic origins of conformal field theory. In this context Borcherds algebras arise as certain ''physical'' subspaces of vertex algebras. The aim of this review is to give a pedagogical introduction into this rapidly-developing area of mathematics. Based on the machinery of formal calculus we present the axiomatic definition of vertex algebras. We discuss the connection with conformal field theory by deriving important implications of these axioms. In particular, many explicit calculations are presented to stress the eminent role of the Jacobi identity axiom for vertex algebras. As a class of concrete examples the vertex algebras associated with even lattices are constructed and it is shown in detail how affine Lie algebras and the fake Monster Lie algebra naturally appear. This leads us to the abstract definition of Borcherds algebras as generalized Kac-Moody algebras and their basic properties. Finally, the results about the simplest generic Borcherds algebras are analysed from the point of view of symmetry in quantum theory and the construction of the Monster Lie algebra is sketched. (orig.)
Spontaneously broken spacetime symmetries and the role of inessential Goldstones
Klein, Remko; Roest, Diederik; Stefanyszyn, David
2017-10-01
In contrast to internal symmetries, there is no general proof that the coset construction for spontaneously broken spacetime symmetries leads to universal dynamics. One key difference lies in the role of Goldstone bosons, which for spacetime symmetries includes a subset which are inessential for the non-linear realisation and hence can be eliminated. In this paper we address two important issues that arise when eliminating inessential Goldstones. The first concerns the elimination itself, which is often performed by imposing so-called inverse Higgs constraints. Contrary to claims in the literature, there are a series of conditions on the structure constants which must be satisfied to employ the inverse Higgs phenomenon, and we discuss which parametrisation of the coset element is the most effective in this regard. We also consider generalisations of the standard inverse Higgs constraints, which can include integrating out inessential Goldstones at low energies, and prove that under certain assumptions these give rise to identical effective field theories for the essential Goldstones. Secondly, we consider mappings between non-linear realisations that differ both in the coset element and the algebra basis. While these can always be related to each other by a point transformation, remarkably, the inverse Higgs constraints are not necessarily mapped onto each other under this transformation. We discuss the physical implications of this non-mapping, with a particular emphasis on the coset space corresponding to the spontaneous breaking of the Anti-De Sitter isometries by a Minkowski probe brane.
Gradings on simple Lie algebras
Elduque, Alberto
2013-01-01
Gradings are ubiquitous in the theory of Lie algebras, from the root space decomposition of a complex semisimple Lie algebra relative to a Cartan subalgebra to the beautiful Dempwolff decomposition of E_8 as a direct sum of thirty-one Cartan subalgebras. This monograph is a self-contained exposition of the classification of gradings by arbitrary groups on classical simple Lie algebras over algebraically closed fields of characteristic not equal to 2 as well as on some nonclassical simple Lie algebras in positive characteristic. Other important algebras also enter the stage: matrix algebras, the octonions, and the Albert algebra. Most of the presented results are recent and have not yet appeared in book form. This work can be used as a textbook for graduate students or as a reference for researchers in Lie theory and neighboring areas.
Approximate Noether symmetries and collineations for regular perturbative Lagrangians
Paliathanasis, Andronikos; Jamal, Sameerah
2018-01-01
Regular perturbative Lagrangians that admit approximate Noether symmetries and approximate conservation laws are studied. Specifically, we investigate the connection between approximate Noether symmetries and collineations of the underlying manifold. In particular we determine the generic Noether symmetry conditions for the approximate point symmetries and we find that for a class of perturbed Lagrangians, Noether symmetries are related to the elements of the Homothetic algebra of the metric which is defined by the unperturbed Lagrangian. Moreover, we discuss how exact symmetries become approximate symmetries. Finally, some applications are presented.
Lie groups, Lie algebras, and some of their applications
Gilmore, Robert
1974-01-01
Lie group theory plays an increasingly important role in modern physical theories. Many of its calculations remain fundamentally unchanged from one field of physics to another, altering only in terms of symbols and the language. Using the theory of Lie groups as a unifying vehicle, concepts and results from several fields of physics can be expressed in an extremely economical way. With rigor and clarity, this text introduces upper-level undergraduate students to Lie group theory and its physical applications.An opening discussion of introductory concepts leads to explorations of the classical
Chiral symmetry and chiral-symmetry breaking
International Nuclear Information System (INIS)
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
Cherniha, Roman
2017-01-01
This book presents several fundamental results in solving nonlinear reaction-diffusion equations and systems using symmetry-based methods. Reaction-diffusion systems are fundamental modeling tools for mathematical biology with applications to ecology, population dynamics, pattern formation, morphogenesis, enzymatic reactions and chemotaxis. The book discusses the properties of nonlinear reaction-diffusion systems, which are relevant for biological applications, from the symmetry point of view, providing rigorous definitions and constructive algorithms to search for conditional symmetry (a nontrivial generalization of the well-known Lie symmetry) of nonlinear reaction-diffusion systems. In order to present applications to population dynamics, it focuses mainly on two- and three-component diffusive Lotka-Volterra systems. While it is primarily a valuable guide for researchers working with reaction-diffusion systems and those developing the theoretical aspects of conditional symmetry conception,...
International Nuclear Information System (INIS)
Prakash, M.
1985-01-01
The theory of supergravity has attracted increasing attention in the recent years as a unified theory of elementary particle interactions. The superspace formulation of the theory is highly suggestive of an underlying geometrical structure of superspace. It also incorporates the beautifully geometrical general theory of relativity. It leads us to believe that a better understanding of its geometry would result in a better understanding of the theory itself, and furthermore, that the geometry of superspace would also have physical consequences. As a first step towards that goal, we develop here a theory of super Lie groups. These are groups that have the same relation to a super Lie algebra as Lie groups have to a Lie algebra. More precisely, a super Lie group is a super-manifold and a group such that the group operations are super-analytic. The super Lie algebra of a super Lie group is related to the local properties of the group near the identity. This work develops the algebraic and super-analytical tools necessary for our theory, including proofs of a set of existence and uniqueness theorems for a class of super-differential equations
CERN. Geneva
2011-01-01
- The discovery of subatomic structures and of the concomitant weak and strong short-range forces raised the question of how to cope with short-range forces in relativistic quantum field theory. The Fermi theory of weak interactions, formulated in terms of point-like current-current interaction, was well-defined in lowest order perturbation theory and accounted for existing experimental data.However, it was inconsistent in higher orders because of uncontrollable divergent quant...
International Nuclear Information System (INIS)
Henley, E.M.
1987-01-01
Nuclei are very useful for testing symmetries, and for studies of symmetry breaking. This thesis is illustrated for two improper space-time transformations, parity and time-reversal and for one internal symmetry: charge symmetry and independence. Recent progress and present interest is reviewed. 23 refs., 8 figs., 2 tabs
Thiese, Matthew S; Walker, Skyler; Lindsey, Jenna
2017-10-01
Distribution of valuable research discoveries are needed for the continual advancement of patient care. Publication and subsequent reliance of false study results would be detrimental for patient care. Unfortunately, research misconduct may originate from many sources. While there is evidence of ongoing research misconduct in all it's forms, it is challenging to identify the actual occurrence of research misconduct, which is especially true for misconduct in clinical trials. Research misconduct is challenging to measure and there are few studies reporting the prevalence or underlying causes of research misconduct among biomedical researchers. Reported prevalence estimates of misconduct are probably underestimates, and range from 0.3% to 4.9%. There have been efforts to measure the prevalence of research misconduct; however, the relatively few published studies are not freely comparable because of varying characterizations of research misconduct and the methods used for data collection. There are some signs which may point to an increased possibility of research misconduct, however there is a need for continued self-policing by biomedical researchers. There are existing resources to assist in ensuring appropriate statistical methods and preventing other types of research fraud. These included the "Statistical Analyses and Methods in the Published Literature", also known as the SAMPL guidelines, which help scientists determine the appropriate method of reporting various statistical methods; the "Strengthening Analytical Thinking for Observational Studies", or the STRATOS, which emphases on execution and interpretation of results; and the Committee on Publication Ethics (COPE), which was created in 1997 to deliver guidance about publication ethics. COPE has a sequence of views and strategies grounded in the values of honesty and accuracy.
Institute of Scientific and Technical Information of China (English)
王丹丹; 徐越; 宋怀波; 何东健
2015-01-01
果实采摘点的精确定位是采摘机器人必须解决的关键问题。鉴于苹果目标具有良好对称性的特点，利用转动惯量所具有的平移、旋转不变性及其在对称轴方向取得极值的特性，提出了一种基于轮廓对称轴法的苹果目标采摘点定位方法。为了解决分割后苹果目标边缘不够平滑而导致定位精度偏低的问题，提出了一种苹果目标轮廓平滑方法。为了验证算法的有效性，对随机选取的20幅无遮挡的单果苹果图像分别利用轮廓平滑和未进行轮廓平滑的算法进行试验，试验结果表明，未进行轮廓平滑算法的平均定位误差为20.678°，而轮廓平滑后算法平均定位误差为4.542°，比未进行轮廓平滑算法平均定位误差降低了78.035%，未进行轮廓平滑算法的平均运行时间为10.2 ms，而轮廓平滑后算法的平均运行时间为7.5 ms，比未进行轮廓平滑算法平均运行时间降低了25.839%，表明平滑轮廓算法可以提高定位精度和运算效率。利用平滑轮廓对称轴算法可以较好地找到苹果目标的对称轴并实现采摘点定位，表明将该方法应用于苹果目标的对称轴提取及采摘点定位是可行的。%The localization of picking points of fruits is one of the key problems for picking robots, and it is the first step of implementation of the picking task for picking robots. In view of a good symmetry of apples, and characteristics of shift, rotation invariance, and reaching the extreme values in symmetry axis direction which moment of inertia possesses, a new method based on a contour symmetry axis was proposed to locate the picking point of apples. In order to solve the problem of low localization accuracy which results from the rough edge of apples after segmentation, a method of smoothing contour algorithm was presented. The steps of the algorithm were as follow, first, the image was transformed from RGB color space into
Applications of chiral symmetry
International Nuclear Information System (INIS)
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 χ implies that the ρ and a 1 vector mesons are degenerate in mass. In a gauged linear sigma model the ρ mass increases with temperature, m ρ (T χ ) > m ρ (0). The author conjectures that at T χ the thermal ρ - a 1 , peak is relatively high, at about ∼1 GeV, with a width approximately that at zero temperature (up to standard kinematic factors). The ω meson also increases in mass, nearly degenerate with the ρ, but its width grows dramatically with temperature, increasing to at least ∼100 MeV by T χ . 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 quenchedclose 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
Quantum group and quantum symmetry
International Nuclear Information System (INIS)
Chang Zhe.
1994-05-01
This is a self-contained review on the theory of quantum group and its applications to modern physics. A brief introduction is given to the Yang-Baxter equation in integrable quantum field theory and lattice statistical physics. The quantum group is primarily introduced as a systematic method for solving the Yang-Baxter equation. Quantum group theory is presented within the framework of quantum double through quantizing Lie bi-algebra. Both the highest weight and the cyclic representations are investigated for the quantum group and emphasis is laid on the new features of representations for q being a root of unity. Quantum symmetries are explored in selected topics of modern physics. For a Hamiltonian system the quantum symmetry is an enlarged symmetry that maintains invariance of equations of motion and allows a deformation of the Hamiltonian and symplectic form. The configuration space of the integrable lattice model is analyzed in terms of the representation theory of quantum group. By means of constructing the Young operators of quantum group, the Schroedinger equation of the model is transformed to be a set of coupled linear equations that can be solved by the standard method. Quantum symmetry of the minimal model and the WZNW model in conformal field theory is a hidden symmetry expressed in terms of screened vertex operators, and has a deep interplay with the Virasoro algebra. In quantum group approach a complete description for vibrating and rotating diatomic molecules is given. The exact selection rules and wave functions are obtained. The Taylor expansion of the analytic formulas of the approach reproduces the famous Dunham expansion. (author). 133 refs, 20 figs
Invariants of triangular Lie algebras
International Nuclear Information System (INIS)
Boyko, Vyacheslav; Patera, Jiri; Popovych, Roman
2007-01-01
Triangular Lie algebras are the Lie algebras which can be faithfully represented by triangular matrices of any finite size over the real/complex number field. In the paper invariants ('generalized Casimir operators') are found for three classes of Lie algebras, namely those which are either strictly or non-strictly triangular, and for so-called special upper triangular Lie algebras. Algebraic algorithm of Boyko et al (2006 J. Phys. A: Math. Gen.39 5749 (Preprint math-ph/0602046)), developed further in Boyko et al (2007 J. Phys. A: Math. Theor.40 113 (Preprint math-ph/0606045)), is used to determine the invariants. A conjecture of Tremblay and Winternitz (2001 J. Phys. A: Math. Gen.34 9085), concerning the number of independent invariants and their form, is corroborated
The low-lying collective multipole response of atomic nuclei
Energy Technology Data Exchange (ETDEWEB)
Spieker, Mark; Derya, Vera; Hennig, Andreas; Pickstone, Simon G.; Prill, Sarah; Vielmetter, Vera; Weinert, Michael; Wilhelmy, Julius; Zilges, Andreas [Institute for Nuclear Physics, University of Cologne, Cologne (Germany); Petkov, Pavel [Institute for Nuclear Physics, University of Cologne, Cologne (Germany); INRNE, Bulgarian Academy of Sciences, Sofia (Bulgaria); National Institute for Physics and Nuclear Engineering, Bucharest (Romania)
2016-07-01
We present experimental results on the low-lying multipole response, which were obtained with the recently established DSA-method in Cologne. Nuclear level lifetimes in the sub-ps regime are extracted by means of centroid-shifts utilizing the (p,p{sup '}γ) reaction at the 10 MV FN-Tandem accelerator in Cologne. The scattered protons are coincidently detected with the deexciting γ rays using the SONIC rate at HORUS detector array, which allows for a precise determination of the reaction kinematics. In addition to the pioneering results on octupole and hexadecapole mixed-symmetry states of {sup 96}Ru, this contribution will feature new results on low-lying quadrupole-octupole coupled states and on the low-lying E2 strength of {sup 112,114}Sn, which was recently discussed to be generated due to a quadrupole-type oscillation of the neutron skin against the isospin-saturated core.
Cheng, Wen-Guang; Qiu, De-Qin; Yu, Bo
2017-06-01
This paper is concerned with the fifth-order modified Korteweg-de Vries (fmKdV) equation. It is proved that the fmKdV equation is consistent Riccati expansion (CRE) solvable. Three special form of soliton-cnoidal wave interaction solutions are discussed analytically and shown graphically. Furthermore, based on the consistent tanh expansion (CTE) method, the nonlocal symmetry related to the consistent tanh expansion (CTE) is investigated, we also give the relationship between this kind of nonlocal symmetry and the residual symmetry which can be obtained with the truncated Painlevé method. We further study the spectral function symmetry and derive the Lax pair of the fmKdV equation. The residual symmetry can be localized to the Lie point symmetry of an enlarged system and the corresponding finite transformation group is computed. Supported by National Natural Science Foundation of China under Grant No. 11505090, and Research Award Foundation for Outstanding Young Scientists of Shandong Province under Grant No. BS2015SF009
Symmetries of Ginsparg-Wilson chiral fermions
International Nuclear Information System (INIS)
Mandula, Jeffrey E.
2009-01-01
The group structure of the variant chiral symmetry discovered by Luescher 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 invariant 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, noncommuting 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 noncanonical elements of lattice chiral symmetry are related to complex energy singularities that violate reflection positivity and impede continuation to Minkowski space.
Duality and self-duality (energy reflection symmetry) of quasi-exactly solvable periodic potentials
International Nuclear Information System (INIS)
Dunne, Gerald V.; Shifman, M.
2002-01-01
A class of spectral problems with a hidden Lie-algebraic structure is considered. We define a duality transformation which maps the spectrum of one quasi-exactly solvable (QES) periodic potential to that of another QES periodic potential. The self-dual point of this transformation corresponds to the energy-reflection symmetry found previously for certain QES systems. The duality transformation interchanges bands at the bottom (top) of the spectrum of one potential with gaps at the top (bottom) of the spectrum of the other, dual, potential. Thus, the duality transformation provides an exact mapping between the weak coupling (perturbative) and semiclassical (nonperturbative) sectors
Symmetries and groups in particle physics
International Nuclear Information System (INIS)
Scherer, Stefan
2016-01-01
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
Reflection symmetry-integrated image segmentation.
Sun, Yu; Bhanu, Bir
2012-09-01
This paper presents a new symmetry-integrated region-based image segmentation method. The method is developed to obtain improved image segmentation by exploiting image symmetry. It is realized by constructing a symmetry token that can be flexibly embedded into segmentation cues. Interesting points are initially extracted from an image by the SIFT operator and they are further refined for detecting the global bilateral symmetry. A symmetry affinity matrix is then computed using the symmetry axis and it is used explicitly as a constraint in a region growing algorithm in order to refine the symmetry of the segmented regions. A multi-objective genetic search finds the segmentation result with the highest performance for both segmentation and symmetry, which is close to the global optimum. The method has been investigated experimentally in challenging natural images and images containing man-made objects. It is shown that the proposed method outperforms current segmentation methods both with and without exploiting symmetry. A thorough experimental analysis indicates that symmetry plays an important role as a segmentation cue, in conjunction with other attributes like color and texture.
"Lie to me"-Oxytocin impairs lie detection between sexes.
Pfundmair, Michaela; Erk, Wiebke; Reinelt, Annika
2017-10-01
The hormone oxytocin modulates various aspects of social behaviors and even seems to lead to a tendency for gullibility. The aim of the current study was to investigate the effect of oxytocin on lie detection. We hypothesized that people under oxytocin would be particularly susceptible to lies told by people of the opposite sex. After administration of oxytocin or a placebo, male and female participants were asked to judge the veracity of statements from same- vs. other-sex actors who either lied or told the truth. Results showed that oxytocin decreased the ability of both male and female participants to correctly classify other-sex statements as truths or lies compared to placebo. This effect was based on a lower ability to detect lies and not a stronger bias to regard truth statements as false. Revealing a new effect of oxytocin, the findings may support assumptions about the hormone working as a catalyst for social adaption. Copyright © 2017. Published by Elsevier Ltd.
Symmetry analysis in parametrisation of complex systems
International Nuclear Information System (INIS)
Sikora, W; Malinowski, J
2010-01-01
The symmetry analysis method based on the theory of group representations is used for description of complex systems and their behavior in this work. The first trial of using the symmetry analysis in modeling of behavior of complex social system is presented. The evacuation of large building scenarios are discussed as transition from chaotic to ordered states, described as movements of individuals according to fields of displacements, calculated correspondingly to given scenario. The symmetry of the evacuation space is taken into account in calculation of displacements field - the displacements related to every point of this space are presented in the coordinate frame in the best way adapted to given symmetry space group, which is the set of basic vectors of irreducible representation of given symmetry group. The results got with using the symmetry consideration are compared with corresponding results calculated under assumption of shortest way to exits (Voronoi assumption).
Symmetry analysis in parametrisation of complex systems
Energy Technology Data Exchange (ETDEWEB)
Sikora, W; Malinowski, J, E-mail: sikora@novell.ftj.agh.edu.p [Faculty of Physics and Applied Computer Science, AGH - University of Science and Technology, Al. Mickiewicza 30, 30-059 Krakow (Poland)
2010-03-01
The symmetry analysis method based on the theory of group representations is used for description of complex systems and their behavior in this work. The first trial of using the symmetry analysis in modeling of behavior of complex social system is presented. The evacuation of large building scenarios are discussed as transition from chaotic to ordered states, described as movements of individuals according to fields of displacements, calculated correspondingly to given scenario. The symmetry of the evacuation space is taken into account in calculation of displacements field - the displacements related to every point of this space are presented in the coordinate frame in the best way adapted to given symmetry space group, which is the set of basic vectors of irreducible representation of given symmetry group. The results got with using the symmetry consideration are compared with corresponding results calculated under assumption of shortest way to exits (Voronoi assumption).
Discrete symmetries in periodic-orbit theory
International Nuclear Information System (INIS)
Robbins, J.M.
1989-01-01
The application of periodic-orbit theory to systems which possess a discrete symmetry is considered. A semiclassical expression for the symmetry-projected Green's function is obtained; it involves a sum over classical periodic orbits on a symmetry-reduced phase space, weighted by characters of the symmetry group. These periodic orbits correspond to trajectories on the full phase space which are not necessarily periodic, but whose end points are related by symmetry. If the symmetry-projected Green's functions are summed, the contributions of the unperiodic orbits cancel, and one recovers the usual periodic-orbit sum for the full Green's function. Several examples are considered, including the stadium billiard, a particle in a periodic potential, the Sinai billiard, the quartic oscillator, and the rotational spectrum of SF 6
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.
Causality and symmetry in cosmology and the conformal group
International Nuclear Information System (INIS)
Segal, I.E.
1977-01-01
A new theoretic postulate in fundamental physics is considered which is called the chronometric principle because it deals primarily with the nature of time, or its dual or conjugate, energy. Conformality is equivalent to causality. Thus, the group of all local causality-preserving transformations in the vicinity of a point of Minkowski space is, as a local Lie group, identical with the conformal group. The same statement made globally on Minkowski space is: The set of all vector fields on Minkowski space which generate smooth local causality-preserving transformations is identical with the set of all conformal vector fields. The main validation for the chronometric principle is in cosmology or ultramacroscopic physics. Therefore this principle is illustrated along the lines of the red shift. This principle in combination with quantum field theory leads to a convergent and causal description of particle production in which nonlinearities are supplanted by more sophisticated and comprehensive actions for the fundamental symmetry groups. 11 references
Super-Laplacians and their symmetries
International Nuclear Information System (INIS)
Howe, P.S.; Lindström, University
2017-01-01
A super-Laplacian is a set of differential operators in superspace whose highest-dimensional component is given by the spacetime Laplacian. Symmetries of super-Laplacians are given by linear differential operators of arbitrary finite degree and are determined by superconformal Killing tensors. We investigate these in flat superspaces. The differential operators determining the symmetries give rise to algebras which can be identified in many cases with the tensor algebras of the relevant superconformal Lie algebras modulo certain ideals. They have applications to Higher Spin theories.
Super-Laplacians and their symmetries
Energy Technology Data Exchange (ETDEWEB)
Howe, P.S. [Department of Mathematics, King’s College London,The Strand, London, WC2R 2LS (United Kingdom); Lindström, University [Department of Physics and Astronomy, Theoretical Physics, Uppsala University,Uppsala, SE-751 20 (Sweden); Theoretical Physics, Imperial College London,Prince Consort Road, London, SW7 2AZ (United Kingdom)
2017-05-22
A super-Laplacian is a set of differential operators in superspace whose highest-dimensional component is given by the spacetime Laplacian. Symmetries of super-Laplacians are given by linear differential operators of arbitrary finite degree and are determined by superconformal Killing tensors. We investigate these in flat superspaces. The differential operators determining the symmetries give rise to algebras which can be identified in many cases with the tensor algebras of the relevant superconformal Lie algebras modulo certain ideals. They have applications to Higher Spin theories.
Deformations of spacetime and internal symmetries
Directory of Open Access Journals (Sweden)
Gresnigt Niels G.
2017-01-01
Full Text Available Algebraic deformations provide a systematic approach to generalizing the symmetries of a physical theory through the introduction of new fundamental constants. The applications of deformations of Lie algebras and Hopf algebras to both spacetime and internal symmetries are discussed. As a specific example we demonstrate how deforming the classical flavor group S U(3 to the quantum group S Uq(3 ≡ U q (su(3 (a Hopf algebra and taking into account electromagnetic mass splitting within isospin multiplets leads to new and exceptionally accurate baryon mass sum rules that agree perfectly with experimental data.
International Nuclear Information System (INIS)
Becker, R.L.; Svenne, J.P.
1975-12-01
Energy levels of states connected by a symmetry of the Hamiltonian normally should be degenerate. In self-consistent field theories, when only one of a pair of single-particle levels connected by a symmetry of the full Hamiltonian is occupied, the degeneracy is split and the unoccupied level often lies below the occupied one. Inversions of neutron-proton (charge) and time-reversal doublets in odd nuclei, charge doublets in even nuclei with a neutron excess, and spin-orbit doublets in spherical configurations with spin-unsaturated shells are examined. The origin of the level inversion is investigated, and the following explanation offered. Unoccupied single-particle levels, from a calculation in an A-particle system, should be interpreted as levels of the (A + 1)-particle system. When the symmetry-related level, occupied in the A-particle system, is also calculated in the (A + 1)-particle system it is degenerate with or lies lower than the other. That is, when both levels are calculated in the (A + 1)-particle system, they are not inverted. It is demonstrated that the usual prescription to occupy the lowest-lying orbitals should be modified to refer to the single-particle energies calculated in the (A + 1)- or the (A - 1)-particle system. This observation is shown to provide a justification for avoiding an oscillation of occupancy between symmetry-related partners in successive iterations leading to a self-consistency. It is pointed out that two degenerate determinants arise from occupying one or the other partner of an initially degenerate pair of levels and then iterating to self-consistency. The existence of the degenerate determinants indicates the need for introducing correlations, either by mixing the two configurations or by allowing additional symmetry-breaking (resulting in a more highly deformed non-degenerate configuration). 2 figures, 3 tables, 43 references
Structural symmetry and protein function.
Goodsell, D S; Olson, A J
2000-01-01
The majority of soluble and membrane-bound proteins in modern cells are symmetrical oligomeric complexes with two or more subunits. The evolutionary selection of symmetrical oligomeric complexes is driven by functional, genetic, and physicochemical needs. Large proteins are selected for specific morphological functions, such as formation of rings, containers, and filaments, and for cooperative functions, such as allosteric regulation and multivalent binding. Large proteins are also more stable against denaturation and have a reduced surface area exposed to solvent when compared with many individual, smaller proteins. Large proteins are constructed as oligomers for reasons of error control in synthesis, coding efficiency, and regulation of assembly. Symmetrical oligomers are favored because of stability and finite control of assembly. Several functions limit symmetry, such as interaction with DNA or membranes, and directional motion. Symmetry is broken or modified in many forms: quasisymmetry, in which identical subunits adopt similar but different conformations; pleomorphism, in which identical subunits form different complexes; pseudosymmetry, in which different molecules form approximately symmetrical complexes; and symmetry mismatch, in which oligomers of different symmetries interact along their respective symmetry axes. Asymmetry is also observed at several levels. Nearly all complexes show local asymmetry at the level of side chain conformation. Several complexes have reciprocating mechanisms in which the complex is asymmetric, but, over time, all subunits cycle through the same set of conformations. Global asymmetry is only rarely observed. Evolution of oligomeric complexes may favor the formation of dimers over complexes with higher cyclic symmetry, through a mechanism of prepositioned pairs of interacting residues. However, examples have been found for all of the crystallographic point groups, demonstrating that functional need can drive the evolution of
Flavor physics without flavor symmetries
Buchmuller, Wilfried; Patel, Ketan M.
2018-04-01
We quantitatively analyze a quark-lepton flavor model derived from a six-dimensional supersymmetric theory with S O (10 )×U (1 ) gauge symmetry, compactified on an orbifold with magnetic flux. Two bulk 16 -plets charged under the U (1 ) provide the three quark-lepton generations whereas two uncharged 10 -plets yield two Higgs doublets. At the orbifold fixed points mass matrices are generated with rank one or two. Moreover, the zero modes mix with heavy vectorlike split multiplets. The model possesses no flavor symmetries. Nevertheless, there exist a number of relations between Yukawa couplings, remnants of the underlying grand unified theory symmetry and the wave function profiles of the zero modes, which lead to a prediction of the light neutrino mass scale, mν 1˜10-3 eV and heavy Majorana neutrino masses in the range from 1 012 to 1 014 GeV . The model successfully includes thermal leptogenesis.
Symmetry Analysis and Exact Solutions of (2+1)-Dimensional Sawada-Kotera Equation
International Nuclear Information System (INIS)
Zhi Hongyan; Zhang Hongqing
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.
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.
A cyclic symmetry principle in physics
International Nuclear Information System (INIS)
Green, H.S.; Adelaide Univ., SA
1994-01-01
Many areas of modern physics are illuminated by the application of a symmetry principle, requiring the invariance of the relevant laws of physics under a group of transformations. This paper examines the implications and some of the applications of the principle of cyclic symmetry, especially in the areas of statistical mechanics and quantum mechanics, including quantized field theory. This principle requires invariance under the transformations of a finite group, which may be a Sylow π-group, a group of Lie type, or a symmetric group. The utility of the principle of cyclic invariance is demonstrated in finding solutions of the Yang-Baxter equation that include and generalize known solutions. It is shown that the Sylow π-groups have other uses, in providing a basis for a type of generalized quantum statistics, and in parametrising a new generalization of Lie groups, with associated algebras that include quantized algebras. 31 refs
Invariants of generalized Lie algebras
International Nuclear Information System (INIS)
Agrawala, V.K.
1981-01-01
Invariants and invariant multilinear forms are defined for generalized Lie algebras with arbitrary grading and commutation factor. Explicit constructions of invariants and vector operators are given by contracting invariant forms with basic elements of the generalized Lie algebra. The use of the matrix of a linear map between graded vector spaces is emphasized. With the help of this matrix, the concept of graded trace of a linear operator is introduced, which is a rich source of multilinear forms of degree zero. To illustrate the use of invariants, a characteristic identity similar to that of Green is derived and a few Racah coefficients are evaluated in terms of invariants
Symmetries and conservation laws of the damped harmonic oscillator
Indian Academy of Sciences (India)
We work with a formulation of Noether-symmetry analysis which uses the properties of infinitesimal point transformations in the space-time variables to establish the association between symmetries and conservation laws of a dynamical system. Here symmetries are expressed in the form of generators. We have studied the ...
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
On nonlocal symmetries of some shallow water equations
Energy Technology Data Exchange (ETDEWEB)
Reyes, Enrique G [Departamento de Matematicas y Ciencia de la Computacion, Universidad de Santiago de Chile, Casilla 307 Correo 2 Santiago (Chile)
2007-04-27
A recent construction of nonlocal symmetries for the Korteweg-de Vries, Camassa-Holm and Hunter-Saxton equations is reviewed, and it is pointed out that-in the Camassa-Holm and Hunter-Saxton case-these symmetries can be considered as (nonlocal) symmetries of integro-differential equations.
International Nuclear Information System (INIS)
Nilles, Hans Peter
2012-04-01
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.
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.
Symmetry, asymmetry and dissymmetry
International Nuclear Information System (INIS)
Wackenheim, A.; Zollner, G.
1987-01-01
The authors discuss the concept of symmetry and defect of symmetry in radiological imaging and recall the definition of asymmetry (congenital or constitutional) and dissymmetry (acquired). They then describe a rule designed for the cognitive method of automatic evaluation of shape recognition data and propose the use of reversal symmetry [fr
International Nuclear Information System (INIS)
Fuentes Cobas, L.E.; Font Hernandez, R.
1993-01-01
An analytical treatment of electrostatic and magnetostatic field symmetry, as a function of charge and current distribution symmetry, is proposed. The Newmann Principle, related to the cause-effect symmetry relation, is presented and applied to the characterization of simple configurations. (Author) 5 refs
Rehren, K. -H.
1996-01-01
Weak C* Hopf algebras can act as global symmetries in low-dimensional quantum field theories, when braid group statistics prevents group symmetries. Possibilities to construct field algebras with weak C* Hopf symmetry from a given theory of local observables are discussed.
International Nuclear Information System (INIS)
Weinberg, S.
1976-01-01
The problem of how gauge symmetries of the weak interactions get broken is discussed. Some reasons why such a heirarchy of gauge symmetry breaking is needed, the reason gauge heirarchies do not seem to arise in theories of a given and related type, and the implications of theories with dynamical symmetry breaking, which can exhibit a gauge hierarchy
Matrix Elements in Fermion Dynamical Symmetry Model
Institute of Scientific and Technical Information of China (English)
LIU Guang-Zhou; LIU Wei
2002-01-01
In a neutron-proton system, the matrix elements of the generators for SO(8) × SO(8) symmetry areconstructed explicitly, and with these matrix elements the low-lying excitation spectra obtained by diagonalization arepresented. The excitation spectra for SO(7) nuclei Pd and Ru isotopes and SO(6) r-soft rotational nuclei Xe, Ba, andCe isotopes are calculated, and comparison with the experimental results is carried out.
Matrix Elements in Fermion Dynamical Symmetry Model
Institute of Scientific and Technical Information of China (English)
LIUGuang－Zhou; LIUWei
2002-01-01
In a neutron-proton system,the matrix elements of the generators for SO(8)×SO(8) symmetry are constructed exp;icitly,and with these matrix elements the low-lying excitation spsectra obtained by diagonalization are presented.The excitation spectra for SO(7) nuclei Pd and Ru isotopes and SO(6) r-soft rotational nuclei Xe,Ba,and Ce isotopes are calculated,and comparison with the experimental results is carried out.
Isomorphism of Intransitive Linear Lie Equations
Directory of Open Access Journals (Sweden)
Jose Miguel Martins Veloso
2009-11-01
Full Text Available We show that formal isomorphism of intransitive linear Lie equations along transversal to the orbits can be extended to neighborhoods of these transversal. In analytic cases, the word formal is dropped from theorems. Also, we associate an intransitive Lie algebra with each intransitive linear Lie equation, and from the intransitive Lie algebra we recover the linear Lie equation, unless of formal isomorphism. The intransitive Lie algebra gives the structure functions introduced by É. Cartan.
MINAMI, Haruo
2016-01-01
For a compact simple Lie group $G$, we show that the element $[G, \\mathcal{L}] \\in \\pi^S_*(S^0)$ represented by the pair $(G, \\mathcal{L})$ is zero, where $\\mathcal{L}$ denotes the left invariant framing of $G$. The proof relies on the method of E. Ossa [Topology, 21 (1982), 315–323].
String Topology for Lie Groups
DEFF Research Database (Denmark)
A. Hepworth, Richard
2010-01-01
In 1999 Chas and Sullivan showed that the homology of the free loop space of an oriented manifold admits the structure of a Batalin-Vilkovisky algebra. In this paper we give a direct description of this Batalin-Vilkovisky algebra in the case that the manifold is a compact Lie group G. Our answer ...
Lie groups and algebraic groups
Indian Academy of Sciences (India)
We give an exposition of certain topics in Lie groups and algebraic groups. This is not a complete ... of a polynomial equation is equivalent to the solva- bility of the equation ..... to a subgroup of the group of roots of unity in k (in particular, it is a ...
Cartan Connections and Lie Algebroids
Directory of Open Access Journals (Sweden)
Michael Crampin
2009-06-01
Full Text Available This paper is a study of the relationship between two constructions associated with Cartan geometries, both of which involve Lie algebroids: the Cartan algebroid, due to [Blaom A.D., Trans. Amer. Math. Soc. 358 (2006, 3651–3671], and tractor calculus [Cap A., Gover A.R., Trans. Amer. Math. Soc. 354 (2001, 1511–1548].
Non-Hermitian systems of Euclidean Lie algebraic type with real energy spectra
Dey, Sanjib; Fring, Andreas; Mathanaranjan, Thilagarajah
2014-07-01
We study several classes of non-Hermitian Hamiltonian systems, which can be expressed in terms of bilinear combinations of Euclidean-Lie algebraic generators. The classes are distinguished by different versions of antilinear (PT)-symmetries exhibiting various types of qualitative behaviour. On the basis of explicitly computed non-perturbative Dyson maps we construct metric operators, isospectral Hermitian counterparts for which we solve the corresponding time-independent Schrödinger equation for specific choices of the coupling constants. In these cases general analytical expressions for the solutions are obtained in the form of Mathieu functions, which we analyze numerically to obtain the corresponding energy spectra. We identify regions in the parameter space for which the corresponding spectra are entirely real and also domains where the PT symmetry is spontaneously broken and sometimes also regained at exceptional points. In some cases it is shown explicitly how the threshold region from real to complex spectra is characterized by the breakdown of the Dyson maps or the metric operator. We establish the explicit relationship to models currently under investigation in the context of beam dynamics in optical lattices.
Non-relativistic conformal symmetries and Newton-Cartan structures
International Nuclear Information System (INIS)
Duval, C; Horvathy, P A
2009-01-01
This paper provides us with a unifying classification of the conformal infinitesimal symmetries of non-relativistic Newton-Cartan spacetime. The Lie algebras of non-relativistic conformal transformations are introduced via the Galilei structure. They form a family of infinite-dimensional Lie algebras labeled by a rational 'dynamical exponent', z. The Schroedinger-Virasoro algebra of Henkel et al corresponds to z = 2. Viewed as projective Newton-Cartan symmetries, they yield, for timelike geodesics, the usual Schroedinger Lie algebra, for which z = 2. For lightlike geodesics, they yield, in turn, the Conformal Galilean Algebra (CGA) of Lukierski, Stichel and Zakrzewski (alias 'alt' of Henkel), with z = 1. Physical systems realizing these symmetries include, e.g. classical systems of massive and massless non-relativistic particles, and also hydrodynamics, as well as Galilean electromagnetism.
Vector fields and nilpotent Lie algebras
Grayson, Matthew; Grossman, Robert
1987-01-01
An infinite-dimensional family of flows E is described with the property that the associated dynamical system: x(t) = E(x(t)), where x(0) is a member of the set R to the Nth power, is explicitly integrable in closed form. These flows E are of the form E = E1 + E2, where E1 and E2 are the generators of a nilpotent Lie algebra, which is either free, or satisfies some relations at a point. These flows can then be used to approximate the flows of more general types of dynamical systems.
Strings, Branes and Symmetries
International Nuclear Information System (INIS)
Westerberg, A.
1997-01-01
Recent dramatic progress in the understanding of the non-perturbative structure of superstring theory shows that extended objects of various kinds, collectively referred to as p-branes, are an integral part of the theory. In this thesis, comprising an introductory text and seven appended research papers, we study various aspects of p-branes with relevance for superstring theory. The first part of the introductory text is a brief review of string theory focussing on the role of p-branes. In particular, we consider the so-called D-branes which currently are attracting a considerable amount of attention. The purpose of this part is mainly to put into context the results of paper 4, 5 and 6 concerning action functionals describing the low-energy dynamics of D-branes. The discussion of perturbative string theory given in this part of the introduction is also intended to provide some background to paper 2 which contains an application of the Reggeon-sewing approach to the construction of string vertices. The second part covers a rather different subject, namely higher-dimensional loop algebras and their cohomology, with the aim of facilitating the reading of papers 1, 3 and 7. The relation to p-branes is to be found in paper 1 where we introduce a certain higher-dimensional generalization of the loop algebra and discuss its potential applicability as a symmetry algebra for p-branes. Papers 3 and 7 are mathematically oriented out-growths of this paper addressing the issue of realizing algebras of this kind, known in physics as current algebras, in terms of pseudo differential operators (PSDOs). The main result of paper 3 is a proof of the equivalence between certain Lie-algebra cocycles on the space of second-quantizable PSDOs
Raibert, M H
1986-03-14
Symmetry plays a key role in simplifying the control of legged robots and in giving them the ability to run and balance. The symmetries studied describe motion of the body and legs in terms of even and odd functions of time. A legged system running with these symmetries travels with a fixed forward speed and a stable upright posture. The symmetries used for controlling legged robots may help in elucidating the legged behavior of animals. Measurements of running in the cat and human show that the feet and body sometimes move as predicted by the even and odd symmetry functions.
Kemeth, Felix P.; Haugland, Sindre W.; Krischer, Katharina
2018-05-01
Symmetry broken states arise naturally in oscillatory networks. In this Letter, we investigate chaotic attractors in an ensemble of four mean-coupled Stuart-Landau oscillators with two oscillators being synchronized. We report that these states with partially broken symmetry, so-called chimera states, have different setwise symmetries in the incoherent oscillators, and in particular, some are and some are not invariant under a permutation symmetry on average. This allows for a classification of different chimera states in small networks. We conclude our report with a discussion of related states in spatially extended systems, which seem to inherit the symmetry properties of their counterparts in small networks.
Parastatistics and gauge symmetries
International Nuclear Information System (INIS)
Govorkov, A.B.
1982-01-01
A possible formulation of gauge symmetries in the Green parafield theory is analysed and the SO(3) gauge symmetry is shown to be on a distinct status. The Greenberg paraquark hypothesis turns out to be not equivalent to the hypothesis of quark colour SU(3)sub(c) symmetry. Specific features of the gauge SO(3) symmetry are discussed, and a possible scheme where it is an exact subgroup of the broken SU(3)sub(c) symmetry is proposed. The direct formulation of the gauge principle for the parafield represented by quaternions is also discussed
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...
Knot wormholes and the dimensional invariant of exceptional Lie groups and Stein space hierarchies
International Nuclear Information System (INIS)
Elokaby, Ayman
2009-01-01
The present short note points out a most interesting and quite unexpected connection between the number of distinct knot as a function of their crossing number and exceptional Lie groups and Stein space hierarchies. It is found that the crossing number 7 plays the role of threshold similar to 4 and 5 in E-infinity theory and for the 11 crossing the number of distinct knots is very close to 4α-bar 0 +1=548+1=549, where α-bar 0 =137 is the inverse integer electromagnetic fine structure constant. This is particularly intriguing in view of a similar relation pertinent to the 17 two and three Stein spaces where the total dimension is Σ 1 17 Stein=5α-bar 0 +1=685+1=686, as well as the sum of the eight exceptional Lie symmetry groups Σ i=1 8 |E i |=4α-bar 0 =548. The slight discrepancy of one is explained in both cases by the inclusion of El Naschie's transfinite corrections leading to Σ i=1 8 |E i |=(4)(137+k 0 )=548.328157 and Σ i=1 17 Stein=(5)(137+k 0 )=685.41097, where k o = φ 5 (1 - φ 5 ) and φ=(√(5)-1)/2.
International Nuclear Information System (INIS)
Gaiotto, Davide; Kapustin, Anton; Seiberg, Nathan; Willett, Brian
2015-01-01
A q-form global symmetry is a global symmetry for which the charged operators are of space-time dimension q; e.g. Wilson lines, surface defects, etc., and the charged excitations have q spatial dimensions; e.g. strings, membranes, etc. Many of the properties of ordinary global symmetries (q=0) apply here. They lead to Ward identities and hence to selection rules on amplitudes. Such global symmetries can be coupled to classical background fields and they can be gauged by summing over these classical fields. These generalized global symmetries can be spontaneously broken (either completely or to a subgroup). They can also have ’t Hooft anomalies, which prevent us from gauging them, but lead to ’t Hooft anomaly matching conditions. Such anomalies can also lead to anomaly inflow on various defects and exotic Symmetry Protected Topological phases. Our analysis of these symmetries gives a new unified perspective of many known phenomena and uncovers new results.
Atomic Nuclei with Tetrahedral and Octahedral Symmetries
International Nuclear Information System (INIS)
Dudek, J.; Gozdz, A.; Schunck, N.
2003-01-01
We present possible manifestations of octahedral and tetrahedral symmetries in nuclei. These symmetries are associated with the O D h and T D d double point groups. Both of them have very characteristic finger-prints in terms of the nucleonic level properties - unique in the Fermionic universe. The tetrahedral symmetry leads to the four-fold degeneracies in the nucleonic spectra; it does not preserve the parity. The octahedral symmetry leads to the four-fold degeneracies in the nucleonic spectra as well but it does preserve the parity. Microscopic predictions have been obtained using mean-field theory based on the relativistic equations and confirmed by using ''traditional'' Schrodinger equation formalism. Calculations are performed in multidimensional deformation spaces using newly designed algorithms. We discuss some experimental fingerprints of the hypothetical new symmetries and possibilities of their verification through experiments. (author)
Quantum group and symmetry of the heat equation
International Nuclear Information System (INIS)
Jha, P.K.; Tripathy, K.C.
1992-07-01
The symmetry associated with the heat equation is re-examined using Lie's method. Under suitable choice of the arbitrary parameters in the Lie field, it is shown that the system exhibits SL(2,R) symmetry. On inspection of the q-analogue of the principal solution, we find broadening of the Gaussian-flow curve when q is varied from 1 to 0.002. The q-analogue of the general solution predicts the existence of additional degeneracy. (author). 8 refs, 1 fig
Pomeranchuk conjecture and symmetry schemes
Energy Technology Data Exchange (ETDEWEB)
Galindo, A.; Morales, A.; Ruegg, H. [Junta de Energia Nuclear, Madrid (Spain); European Organization for Nuclear Research, Geneva (Switzerland); University of Geneva, Geneva (Switzerland)
1963-01-15
Pomeranchuk has conjectured that the cross-sections for charge-exchange processes vanish asymptotically as the energy tends to infinity. (By ''charge'' it is meant any internal quantum number, like electric charge, hypercharge, .. . ). It has been stated by several people that this conjecture implies equalities among the total cross-sections whenever any symmetry scheme is invoked for the strong interactions. But to our knowledge no explicit general proof of this statement has been given so far. We want to give this proof for any compact Lie group. We also prove, under certain assumptions, that the equality of the total cross-sections implies that s{sup -l} times the charge-exchange forward scattering absorptive amplitudes tend to zero as s -> ∞.
International Nuclear Information System (INIS)
Mainzer, K.
1988-01-01
Symmetry, disymmetry, chirality etc. are well-known topics in chemistry. But they cannot only be found on the molecular level of matter. Atoms and elementary particles in physics are also characterized by particular symmetry groups. Even living organisms and populations on the macroscopic level have functional properties of symmetry. The whole physical, chemical, and biological evolution seems to be regulated by the emergence of new symmetries and the breaking down of old ones. One is reminded of Heisenberg's famous statement: 'Die letzte Wurzel der Erscheinungen ist also nicht die Materie, sondern das mathematische Gesetz, die Symmetrie, die mathematische Form' (Wandlungen in den Grundlagen der Naturwissenschaften, 1959). Historically the belief in symmetry and simplicity of nature has a long philosophical tradition from the Pythagoreans, Plato and Greek astronomers to Kepler and modern scientists. Today, 'symmetries in nature' is a common topic of mathematics, physics, chemistry, and biology. A lot of Nobel prizes were given in honour of inquiries concerning symmetries in nature. The fascination of symmetries is not only motivated by science, but by art and religion too. Therefore 'symmetris in nature' is an interdisciplinary topic which may help to overcome C.P. Snow's 'Two Cultures' of natural sciences and humanities. (author) 17 refs., 21 figs
Energy Technology Data Exchange (ETDEWEB)
Mainzer, K
1988-05-01
Symmetry, disymmetry, chirality etc. are well-known topics in chemistry. But they cannot only be found on the molecular level of matter. Atoms and elementary particles in physics are also characterized by particular symmetry groups. Even living organisms and populations on the macroscopic level have functional properties of symmetry. The whole physical, chemical, and biological evolution seems to be regulated by the emergence of new symmetries and the breaking down of old ones. One is reminded of Heisenberg's famous statement: 'Die letzte Wurzel der Erscheinungen ist also nicht die Materie, sondern das mathematische Gesetz, die Symmetrie, die mathematische Form' (Wandlungen in den Grundlagen der Naturwissenschaften, 1959). Historically the belief in symmetry and simplicity of nature has a long philosophical tradition from the Pythagoreans, Plato and Greek astronomers to Kepler and modern scientists. Today, 'symmetries in nature' is a common topic of mathematics, physics, chemistry, and biology. A lot of Nobel prizes were given in honour of inquiries concerning symmetries in nature. The fascination of symmetries is not only motivated by science, but by art and religion too. Therefore 'symmetris in nature' is an interdisciplinary topic which may help to overcome C.P. Snow's 'Two Cultures' of natural sciences and humanities. (author) 17 refs., 21 figs.
International Nuclear Information System (INIS)
Arima, A.
2003-01-01
(1) There are symmetries in nature, and the concept of symmetry has been used in art and architecture. The symmetry is evaluated high in the European culture. In China, the symmetry is broken in the paintings but it is valued in the architecture. In Japan, however, the symmetry has been broken everywhere. The serious and interesting question is why these differences happens? (2) In this lecture, I reviewed from the very beginning the importance of the rotational symmetry in quantum mechanics. I am sorry to be too fundamental for specialists of nuclear physics. But for people who do not use these theories, I think that you could understand the mathematical aspects of quantum mechanics and the relation between the angular momentum and the rotational symmetry. (3) To the specialists of nuclear physics, I talked about my idea as follows: dynamical treatment of collective motions in nuclei by IBM, especially the meaning of the degeneracy observed in the rotation bands top of γ vibration and β vibration, and the origin of pseudo-spin symmetry. Namely, if there is a symmetry, a degeneracy occurs. Conversely, if there is a degeneracy, there must be a symmetry. I discussed some details of the observed evidence and this correspondence is my strong belief in physics. (author)
Superdeformations and fermion dynamical symmetries
International Nuclear Information System (INIS)
Wu, Cheng-Li
1990-01-01
In this talk, I will present a link between nuclear collective motions and their underlying fermion dynamical symmetries. In particular, I will focus on the microscopic understanding of deformations. It is shown that the SU 3 of the one major shell fermion dynamical symmetry model (FDSM) is responsible for the physics of low and high spins in normal deformation. For the recently observed phenomena of superdeformation, the physics of the problem dictates a generalization to a supershell structure (SFDSM), which also has an SU 3 fermion dynamical symmetry. Many recently discovered feature of superdeformation are found to be inherent in such an SU 3 symmetry. In both cases the dynamical Pauli effect plays a vital role. A particularly noteworthy discovery from this model is that the superdeformed ground band is not the usual unaligned band but the D-pair aligned (DPA) band, which sharply crosses the excited bands. The existence of such DPA band is a key point to understand many properties of superdeformation. Our studies also poses new experimental challenge. This is particularly interesting since there are now plans to build new and exciting γ-ray detecting systems, like the GAMMASPHERE, which could provide answers to some of these challenges. 34 refs., 11 figs., 5 tabs
On discretization of tori of compact simple Lie groups: II
International Nuclear Information System (INIS)
Hrivnák, Jiří; Motlochová, Lenka; Patera, Jiří
2012-01-01
The discrete orthogonality of special function families, called C- and S-functions, which are derived from the characters of compact simple Lie groups, is described in Hrivnák and Patera (2009 J. Phys. A: Math. Theor. 42 385208). Here, the results of Hrivnák and Patera are extended to two additional recently discovered families of special functions, called S s - and S l -functions. The main result is an explicit description of their pairwise discrete orthogonality within each family, when the functions are sampled on finite fragments F s M and F l M of a lattice in any dimension n ⩾ 2 and of any density controlled by M, and of the symmetry of the weight lattice of any compact simple Lie group with two different lengths of roots. (paper)
Advances in geometry and Lie algebras from supergravity
Frè, Pietro Giuseppe
2018-01-01
This book aims to provide an overview of several topics in advanced Differential Geometry and Lie Group Theory, all of them stemming from mathematical problems in supersymmetric physical theories. It presents a mathematical illustration of the main development in geometry and symmetry theory that occurred under the fertilizing influence of supersymmetry/supergravity. The contents are mainly of mathematical nature, but each topic is introduced by historical information and enriched with motivations from high energy physics, which help the reader in getting a deeper comprehension of the subject. .
Fractional supersymmetry and infinite dimensional lie algebras
International Nuclear Information System (INIS)
Rausch de Traubenberg, M.
2001-01-01
In an earlier work extensions of supersymmetry and super Lie algebras were constructed consistently starting from any representation D of any Lie algebra g. Here it is shown how infinite dimensional Lie algebras appear naturally within the framework of fractional supersymmetry. Using a differential realization of g this infinite dimensional Lie algebra, containing the Lie algebra g as a sub-algebra, is explicitly constructed
Gapless Symmetry-Protected Topological Order
Directory of Open Access Journals (Sweden)
Thomas Scaffidi
2017-11-01
Full Text Available We introduce exactly solvable gapless quantum systems in d dimensions that support symmetry-protected topological (SPT edge modes. Our construction leads to long-range entangled, critical points or phases that can be interpreted as critical condensates of domain walls “decorated” with dimension (d-1 SPT systems. Using a combination of field theory and exact lattice results, we argue that such gapless SPT systems have symmetry-protected topological edge modes that can be either gapless or symmetry broken, leading to unusual surface critical properties. Despite the absence of a bulk gap, these edge modes are robust against arbitrary symmetry-preserving local perturbations near the edges. In two dimensions, we construct wave functions that can also be interpreted as unusual quantum critical points with diffusive scaling in the bulk but ballistic edge dynamics.
From physical symmetries to emergent gauge symmetries
International Nuclear Information System (INIS)
Barceló, Carlos; Carballo-Rubio, Raúl; 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 gravity program, such as the Weinberg-Witten theorem, are discussed.
Symmetry and bifurcations of momentum mappings
International Nuclear Information System (INIS)
Arms, J.M.; Marsden, J.E.; Moncrief, V.
1981-01-01
The zero set of a momentum mapping is shown to have a singularity at each point with symmetry. The zero set is diffeomorphic to the product of a manifold and the zero set of a homogeneous quadratic function. The proof uses the Kuranishi theory of deformations. Among the applications, it is shown that the set of all solutions of the Yang-Mills equations on a Lorentz manifold has a singularity at any solution with symmetry, in the sense of a pure gauge symmetry. Similarly, the set of solutions of Einstein's equations has a singularity at any solution that has spacelike Killing fields, provided the spacetime has a compact Cauchy surface. (orig.)
Symmetry and bifurcations of momentum mappings
Arms, Judith M.; Marsden, Jerrold E.; Moncrief, Vincent
1981-01-01
The zero set of a momentum mapping is shown to have a singularity at each point with symmetry. The zero set is diffeomorphic to the product of a manifold and the zero set of a homogeneous quadratic function. The proof uses the Kuranishi theory of deformations. Among the applications, it is shown that the set of all solutions of the Yang-Mills equations on a Lorentz manifold has a singularity at any solution with symmetry, in the sense of a pure gauge symmetry. Similarly, the set of solutions of Einstein's equations has a singularity at any solution that has spacelike Killing fields, provided the spacetime has a compact Cauchy surface.
International Nuclear Information System (INIS)
Kashaev, R.M.; Savel'ev, M.V.; Savel'eva, S.A.
1990-01-01
Nonlinear equations associated through a zero curvature type representation with Lie algebras S 0 Diff T 2 and of infinitesimal diffeomorphisms of (S 1 ) 2 , and also with a new infinite-dimensional Lie algebras. In particular, the general solution (in the sense of the Goursat problem) of the heavently equation which describes self-dual Einstein spaces with one rotational Killing symmetry is discussed, as well as the solutions to a generalized equation. The paper is supplied with Appendix containing the definition of the continuum graded Lie algebras and the general construction of the nonlinear equations associated with them. 11 refs
Essays in the history of Lie groups and algebraic groups
Borel, Armand
2001-01-01
Lie groups and algebraic groups are important in many major areas of mathematics and mathematical physics. We find them in diverse roles, notably as groups of automorphisms of geometric structures, as symmetries of differential systems, or as basic tools in the theory of automorphic forms. The author looks at their development, highlighting the evolution from the almost purely local theory at the start to the global theory that we know today. Starting from Lie's theory of local analytic transformation groups and early work on Lie algebras, he follows the process of globalization in its two main frameworks: differential geometry and topology on one hand, algebraic geometry on the other. Chapters II to IV are devoted to the former, Chapters V to VIII, to the latter. The essays in the first part of the book survey various proofs of the full reducibility of linear representations of \\mathbf{SL}_2{(\\mathbb{C})}, the contributions of H. Weyl to representations and invariant theory for semisimple Lie groups, and con...
Particle-like structure of Lie algebras
Vinogradov, A. M.
2017-07-01
If a Lie algebra structure 𝔤 on a vector space is the sum of a family of mutually compatible Lie algebra structures 𝔤i's, we say that 𝔤 is simply assembled from the 𝔤i's. Repeating this procedure with a number of Lie algebras, themselves simply assembled from the 𝔤i's, one obtains a Lie algebra assembled in two steps from 𝔤i's, and so on. We describe the process of modular disassembling of a Lie algebra into a unimodular and a non-unimodular part. We then study two inverse questions: which Lie algebras can be assembled from a given family of Lie algebras, and from which Lie algebras can a given Lie algebra be assembled. We develop some basic assembling and disassembling techniques that constitute the elements of a new approach to the general theory of Lie algebras. The main result of our theory is that any finite-dimensional Lie algebra over an algebraically closed field of characteristic zero or over R can be assembled in a finite number of steps from two elementary constituents, which we call dyons and triadons. Up to an abelian summand, a dyon is a Lie algebra structure isomorphic to the non-abelian 2-dimensional Lie algebra, while a triadon is isomorphic to the 3-dimensional Heisenberg Lie algebra. As an example, we describe constructions of classical Lie algebras from triadons.
On symmetry reduction and exact solutions of the linear one-dimensional Schroedinger equation
International Nuclear Information System (INIS)
Barannik, L.L.
1996-01-01
Symmetry reduction of the Schroedinger equation with potential is carried out on subalgebras of the Lie algebra which is the direct sum of the special Galilei algebra and one-dimensional algebra. Some new exact solutions are obtained
Harris, A. Brooks
2006-01-01
This paper represents a detailed instruction manual for constructing the Landau expansion for magnetoelectric coupling in incommensurate ferroelectric magnets. The first step is to describe the magnetic ordering in terms of symmetry adapted coordinates which serve as complex valued magnetic order parameters whose transformation properties are displayed. In so doing we use the previously proposed technique to exploit inversion symmetry, since this symmetry had been universally overlooked. Havi...
Surveying the quantum group symmetries of integrable open spin chains
Nepomechie, Rafael I.; Retore, Ana L.
2018-05-01
Using anisotropic R-matrices associated with affine Lie algebras g ˆ (specifically, A2n(2), A2n-1 (2) , Bn(1), Cn(1), Dn(1)) and suitable corresponding K-matrices, we construct families of integrable open quantum spin chains of finite length, whose transfer matrices are invariant under the quantum group corresponding to removing one node from the Dynkin diagram of g ˆ . We show that these transfer matrices also have a duality symmetry (for the cases Cn(1) and Dn(1)) and additional Z2 symmetries that map complex representations to their conjugates (for the cases A2n-1 (2) , Bn(1) and Dn(1)). A key simplification is achieved by working in a certain "unitary" gauge, in which only the unbroken symmetry generators appear. The proofs of these symmetries rely on some new properties of the R-matrices. We use these symmetries to explain the degeneracies of the transfer matrices.
Transformation groups and Lie algebras
Ibragimov, Nail H
2013-01-01
This book is based on the extensive experience of teaching for mathematics, physics and engineering students in Russia, USA, South Africa and Sweden. The author provides students and teachers with an easy to follow textbook spanning a variety of topics. The methods of local Lie groups discussed in the book provide universal and effective method for solving nonlinear differential equations analytically. Introduction to approximate transformation groups also contained in the book helps to develop skills in constructing approximate solutions for differential equations with a small parameter.
Filiform Lie algebras of order 3
International Nuclear Information System (INIS)
Navarro, R. M.
2014-01-01
The aim of this work is to generalize a very important type of Lie algebras and superalgebras, i.e., filiform Lie (super)algebras, into the theory of Lie algebras of order F. Thus, the concept of filiform Lie algebras of order F is obtained. In particular, for F = 3 it has been proved that by using infinitesimal deformations of the associated model elementary Lie algebra it can be obtained families of filiform elementary lie algebras of order 3, analogously as that occurs into the theory of Lie algebras [M. Vergne, “Cohomologie des algèbres de Lie nilpotentes. Application à l’étude de la variété des algèbres de Lie nilpotentes,” Bull. Soc. Math. France 98, 81–116 (1970)]. Also we give the dimension, using an adaptation of the sl(2,C)-module Method, and a basis of such infinitesimal deformations in some generic cases
Filiform Lie algebras of order 3
Navarro, R. M.
2014-04-01
The aim of this work is to generalize a very important type of Lie algebras and superalgebras, i.e., filiform Lie (super)algebras, into the theory of Lie algebras of order F. Thus, the concept of filiform Lie algebras of order F is obtained. In particular, for F = 3 it has been proved that by using infinitesimal deformations of the associated model elementary Lie algebra it can be obtained families of filiform elementary lie algebras of order 3, analogously as that occurs into the theory of Lie algebras [M. Vergne, "Cohomologie des algèbres de Lie nilpotentes. Application à l'étude de la variété des algèbres de Lie nilpotentes," Bull. Soc. Math. France 98, 81-116 (1970)]. Also we give the dimension, using an adaptation of the {sl}(2,{C})-module Method, and a basis of such infinitesimal deformations in some generic cases.
Bismut's way of the Malliavin calculus for large order generators on a Lie group
Léandre, Rémi
2018-01-01
We adapt Bismut's mechanism of the Malliavin Calculus to right invariant big order generator on a Lie group. We use deeply the symmetry in order to avoid the use of the Malliavin matrix. As an application, we deduce logarithmic estimates in small time of the heat kernel.
A density matrix renormalization group study of low-lying excitations ...
Indian Academy of Sciences (India)
Symmetrized density-matrix-renormalization-group calculations have been carried out, within Pariser-Parr-Pople Hamiltonian, to explore the nature of the ground and low-lying excited states of long polythiophene oligomers. We have exploited 2 symmetry and spin parity of the system to obtain excited states of ...
Description of a class of superstring compactifications related to semi-simple Lie algebras
International Nuclear Information System (INIS)
Markushevich, D.I.; Ol'shanetskij, M.A.; Perelomov, A.M.
1986-01-01
A class of vacuum configurations in the superstring theory obtained by compactification of physical dimensions from ten to four is constructed. The compactification scheme involves taking quotients of tori of semisimple Lie algebras by finite symmetry group actions. The complete list of such configurations arising from actions by a Coxeter transformation is given. Some topological invariants having physical interpretations are calculated
Using local symmetry for landmark selection
Kootstra, Geert; de Jong, Sjoerd; Schomaker, Lambert R. B.
2009-01-01
Most visual Simultaneous Localization And Mapping (SLAM) methods use interest points as landmarks in their maps of the environment. Often the interest points are detected using contrast features, for instance those of the Scale Invariant Feature Transform (SIFT). The SIFT interest points, however, have problems with stability, and noise robustness. Taking our inspiration from human vision, we therefore propose the use of local symmetry to select interest points. Our method, the MUlti-scale Sy...
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.
Olver, Peter J; the American Mathematical Society on Lie Algebras, Cohomology and New Applications to Quantum Mechanics
1994-01-01
This volume is devoted to a range of important new ideas arising in the applications of Lie groups and Lie algebras to Schrödinger operators and associated quantum mechanical systems. In these applications, the group does not appear as a standard symmetry group, but rather as a "hidden" symmetry group whose representation theory can still be employed to analyze at least part of the spectrum of the operator. In light of the rapid developments in this subject, a Special Session was organized at the AMS meeting at Southwest Missouri State University in March 1992 in order to bring together, perhaps for the first time, mathematicians and physicists working in closely related areas. The contributions to this volume cover Lie group methods, Lie algebras and Lie algebra cohomology, representation theory, orthogonal polynomials, q-series, conformal field theory, quantum groups, scattering theory, classical invariant theory, and other topics. This volume, which contains a good balance of research and survey papers, p...
International Nuclear Information System (INIS)
Ghikas, D.K.P.; Ktorides, C.N.; Papaloukas, L.
1980-01-01
This mathematical note is motivated by an assessment concerning our current understanding of the role of Lie-admissible symmetries in connection with quantum structures. We identify the problem of representations of the universal enveloping (lambda, μ)-mutation algebra of a given Lie algebra on a suitable algebra of operators, as constituting a fundamental first step for improving the situation. We acknowledge a number of difficulties which are peculiar to the adopted nonassociative product for the operator algebra. In view of these difficulties, we are presently content in establishing the generalization, to the Lie-admissible case, of a certain theorem by Nelson. This theorem has been very instrumental in Nelson's treatment concerning the Lie symmetry content of quantum structures. It is hoped that a similar situation will eventually prevail for the Lie-admissible case. We offer a number of relevant suggestions
Ji, Q.; Xin, C.; Tang, S. X.; Huang, J. P.
2018-02-01
Crowd panic has incurred massive injuries or deaths throughout the world, and thus understanding it is particularly important. It is now a common knowledge that crowd panic induces "symmetry break" in which some exits are jammed while others are underutilized. Amazingly, here we show, by experiment, simulation and theory, that a class of symmetry patterns come to appear for ants and humans escaping from multiple-exit rooms while the symmetry break exists. Our symmetry pattern is described by the fact that the ratio between the ensemble-averaging numbers of ants or humans escaping from different exits is equal to the ratio between the widths of the exits. The mechanism lies in the effect of heterogeneous preferences of agents with limited information for achieving the Nash equilibrium. This work offers new insights into how to improve public safety because large public areas are always equipped with multiple exits, and it also brings an ensemble-averaging method for seeking symmetry associated with symmetry breaking.
International Nuclear Information System (INIS)
Thierry-Mieg, Jean
2006-01-01
In Yang-Mills theory, the charges of the left and right massless Fermions are independent of each other. We propose a new paradigm where we remove this freedom and densify the algebraic structure of Yang-Mills theory by integrating the scalar Higgs field into a new gauge-chiral 1-form which connects Fermions of opposite chiralities. Using the Bianchi identity, we prove that the corresponding covariant differential is associative if and only if we gauge a Lie-Kac super-algebra. In this model, spontaneous symmetry breakdown naturally occurs along an odd generator of the super-algebra and induces a representation of the Connes-Lott non commutative differential geometry of the 2-point finite space
International Nuclear Information System (INIS)
Haxton, W.C.
1988-01-01
I discuss a number of the themes of the Symmetries and Spin session of the 8th International Symposium on High Energy Spin Physics: parity nonconservation, CP/T nonconservation, and tests of charge symmetry and charge independence. 28 refs., 1 fig
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.
Quantum symmetry for pedestrians
International Nuclear Information System (INIS)
Mack, G.; Schomerus, V.
1992-03-01
Symmetries more general than groups are possible in quantum therory. Quantum symmetries in the narrow sense are compatible with braid statistics. They are theoretically consistent much as supersymmetry is, and they could lead to degenerate multiplets of excitations with fractional spin in thin films. (orig.)
Wigner's Symmetry Representation Theorem
Indian Academy of Sciences (India)
IAS Admin
At the Heart of Quantum Field Theory! Aritra Kr. ... principle of symmetry was not held as something very fundamental ... principle of local symmetry: the laws of physics are invariant un- .... Next, we would show that different coefficients of a state ...
Charged fluids with symmetries
Indian Academy of Sciences (India)
It is possible to introduce many types of symmetries on the manifold which restrict the ... metric tensor field and generate constants of the motion along null geodesics .... In this analysis we have studied the role of symmetries for charged perfect ...
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.
Symmetry and symmetry breaking in modern physics
International Nuclear Information System (INIS)
Barone, M; Theophilou, A K
2008-01-01
In modern physics, the theory of symmetry, i.e. group theory, is a basic tool for understanding and formulating the fundamental principles of Physics, like Relativity, Quantum Mechanics and Particle Physics. In this work we focus on the relation between Mathematics, Physics and objective reality
Geometry of Majorana neutrino and new symmetries
Volkov, G G
2006-01-01
Experimental observation of Majorana fermion matter gives a new impetus to the understanding of the Lorentz symmetry and its extension, the geometrical properties of the ambient space-time structure, matter--antimatter symmetry and some new ways to understand the baryo-genesis problem in cosmology. Based on the primordial Majorana fermion matter assumption, we discuss a possibility to solve the baryo-genesis problem through the the Majorana-Diraco genesis in which we have a chance to understand creation of Q(em) charge and its conservation in our D=1+3 Universe after the Big Bang. In the Majorana-Diraco genesis approach there appears a possibility to check the proton and electron non-stability on the very low energy scale. In particle physics and in our space-time geometry, the Majorana nature of the neutrino can be related to new types of symmetries which are lying beyond the binary Cartan-Killing-Lie algebras/superalgebras. This can just support a conjecture about the non-completeness of the SM in terms of ...
Symmetry breaking by bifundamentals
Schellekens, A. N.
2018-03-01
We derive all possible symmetry breaking patterns for all possible Higgs fields that can occur in intersecting brane models: bifundamentals and rank-2 tensors. This is a field-theoretic problem that was already partially solved in 1973 by Ling-Fong Li [1]. In that paper the solution was given for rank-2 tensors of orthogonal and unitary group, and U (N )×U (M ) and O (N )×O (M ) bifundamentals. We extend this first of all to symplectic groups. When formulated correctly, this turns out to be straightforward generalization of the previous results from real and complex numbers to quaternions. The extension to mixed bifundamentals is more challenging and interesting. The scalar potential has up to six real parameters. Its minima or saddle points are described by block-diagonal matrices built out of K blocks of size p ×q . Here p =q =1 for the solutions of Ling-Fong Li, and the number of possibilities for p ×q is equal to the number of real parameters in the potential, minus 1. The maximum block size is p ×q =2 ×4 . Different blocks cannot be combined, and the true minimum occurs for one choice of basic block, and for either K =1 or K maximal, depending on the parameter values.
On generalized Melvin solution for the Lie algebra E6
International Nuclear Information System (INIS)
Bolokhov, S.V.; Ivashchuk, V.D.
2017-01-01
A multidimensional generalization of Melvin's solution for an arbitrary simple Lie algebra G is considered. The gravitational model in D dimensions, D ≥ 4, contains n 2-forms and l ≥ n scalar fields, where n is the rank of G. The solution is governed by a set of n functions H s (z) obeying n ordinary differential equations with certain boundary conditions imposed. It was conjectured earlier that these functions should be polynomials (the so-called fluxbrane polynomials). The polynomials H s (z), s = 1,.., 6, for the Lie algebra E 6 are obtained and a corresponding solution for l = n = 6 is presented. The polynomials depend upon integration constants Q s , s = 1,.., 6. They obey symmetry and duality identities. The latter ones are used in deriving asymptotic relations for solutions at large distances. The power-law asymptotic relations for E 6 -polynomials at large z are governed by the integer-valued matrix ν = A -1 (I + P), where A -1 is the inverse Cartan matrix, I is the identity matrix and P is a permutation matrix, corresponding to a generator of the Z 2 -group of symmetry of the Dynkin diagram. The 2-form fluxes Φ s , s = 1,.., 6, are calculated. (orig.)
A review on symmetries for certain Aedes aegypti models
Freire, Igor Leite; Torrisi, Mariano
2015-04-01
We summarize our results related with mathematical modeling of Aedes aegypti and its Lie symmetries. Moreover, some explicit, group-invariant solutions are also shown. Weak equivalence transformations of more general reaction diffusion systems are also considered. New classes of solutions are obtained.
Simple mathematical models of symmetry breaking. Application to particle physics
International Nuclear Information System (INIS)
Michel, L.
1976-01-01
Some mathematical facts relevant to symmetry breaking are presented. A first mathematical model deals with the smooth action of compact Lie groups on real manifolds, a second model considers linear action of any group on real or complex finite dimensional vector spaces. Application of the mathematical models to particle physics is considered. (B.R.H.)
Jacobi's last multiplier and symmetries for the Kepler problem plus a lineal story
International Nuclear Information System (INIS)
Nucci, M C; Leach, P G L
2004-01-01
We calculate the first integrals of the Kepler problem by the method of Jacobi's last multiplier using the symmetries for the equations of motion. Also we provide another example which shows that Jacobi's last multiplier together with Lie symmetries unveils many first integrals neither necessarily algebraic nor rational whereas other published methods may yield just one
Nonlocal symmetries and a Darboux transformation for the Camassa-Holm equation
International Nuclear Information System (INIS)
Hernandez-Heredero, Rafael; Reyes, Enrique G
2009-01-01
We announce two new structures associated with the Camassa-Holm (CH) equation: a Lie algebra of nonlocal symmetries, and a Darboux transformation for this important equation, which we construct using only our symmetries. We also extend our results to the associated Camassa-Holm equation introduced by J Schiff (1998 Physica D 121 24-43). (fast track communication)
Nonlocal symmetries and a Darboux transformation for the Camassa-Holm equation
Energy Technology Data Exchange (ETDEWEB)
Hernandez-Heredero, Rafael [Departamento de Matematica Aplicada, EUIT de Telecomunicacion, Universidad Politecnica de Madrid, Campus Sur Ctra de Valencia Km. 7. 28031, Madrid (Spain); Reyes, Enrique G [Departamento de Matematica y Ciencia de la Computacion, Universidad de Santiago de Chile, Casilla 307 Correo 2, Santiago (Chile)], E-mail: rafahh@euitt.upm.es, E-mail: ereyes@fermat.usach.cl
2009-05-08
We announce two new structures associated with the Camassa-Holm (CH) equation: a Lie algebra of nonlocal symmetries, and a Darboux transformation for this important equation, which we construct using only our symmetries. We also extend our results to the associated Camassa-Holm equation introduced by J Schiff (1998 Physica D 121 24-43). (fast track communication)
Symmetries of the triple degenerate DNLS equations for weakly nonlinear dispersive MHD waves
International Nuclear Information System (INIS)
Webb, G. M.; Brio, M.; Zank, G. P.
1996-01-01
A formulation of Hamiltonian and Lagrangian variational principles, Lie point symmetries and conservation laws for the triple degenerate DNLS equations describing the propagation of weakly nonlinear dispersive MHD waves along the ambient magnetic field, in β∼1 plasmas is given. The equations describe the interaction of the Alfven and magnetoacoustic modes near the triple umbilic point, where the fast magnetosonic, slow magnetosonic and Alfven speeds coincide and a g 2 =V A 2 where a g is the gas sound speed and V A is the Alfven speed. A discussion is given of the travelling wave similarity solutions of the equations, which include solitary wave and periodic traveling waves. Strongly compressible solutions indicate the necessity for the insertion of shocks in the flow, whereas weakly compressible, near Alfvenic solutions resemble similar, shock free travelling wave solutions of the DNLS equation
Lie algebroids in derived differential topology
Nuiten, J.J.
2018-01-01
A classical principle in deformation theory asserts that any formal deformation problem is controlled by a differential graded Lie algebra. This thesis studies a generalization of this principle to Lie algebroids, and uses this to examine the interactions between the theory of Lie algebroids and the
The Centroid of a Lie Triple Algebra
Directory of Open Access Journals (Sweden)
Xiaohong Liu
2013-01-01
Full Text Available General results on the centroids of Lie triple algebras are developed. Centroids of the tensor product of a Lie triple algebra and a unitary commutative associative algebra are studied. Furthermore, the centroid of the tensor product of a simple Lie triple algebra and a polynomial ring is completely determined.
The First Honest Book about Lies.
Kincher, Jonni; Espeland, Pamela, Ed.
Readers learn how to discern the truth from lies through a series of activities, games, and experiments. This book invites young students to look at lies in a fair and balanced way. Different types of lies are examined and the purposes they serve and discussed. Problem solving activities are given. The book is organized in nine chapters,…
Infinite symmetry in the quantum Hall effect
Directory of Open Access Journals (Sweden)
Lütken C.A.
2014-04-01
Full Text Available The new states of matter and concomitant quantum critical phenomena revealed by the quantum Hall effect appear to be accompanied by an emergent modular symmetry. The extreme rigidity of this infinite symmetry makes it easy to falsify, but two decades of experiments have failed to do so, and the location of quantum critical points predicted by the symmetry is in increasingly accurate agreement with scaling experiments. The symmetry severely constrains the structure of the effective quantum field theory that encodes the low energy limit of quantum electrodynamics of 1010 charges in two dirty dimensions. If this is a non-linear σ-model the target space is a torus, rather than the more familiar sphere. One of the simplest toroidal models gives a critical (correlation length exponent that agrees with the value obtained from numerical simulations of the quantum Hall effect.
Spacetime symmetries and topology in bimetric relativity
Torsello, Francesco; Kocic, Mikica; Högâs, Marcus; Mörtsell, Edvard
2018-04-01
We explore spacetime symmetries and topologies of the two metric sectors in Hassan-Rosen bimetric theory. We show that, in vacuum, the two sectors can either share or have separate spacetime symmetries. If stress-energy tensors are present, a third case can arise, with different spacetime symmetries within the same sector. This raises the question of the best definition of spacetime symmetry in Hassan-Rosen bimetric theory. We emphasize the possibility of imposing ansatzes and looking for solutions having different Killing vector fields or different isometries in the two sectors, which has gained little attention so far. We also point out that the topology of spacetime imposes a constraint on possible metric combinations.
Symmetry and fermion degeneracy on a lattice
International Nuclear Information System (INIS)
Raszillier, H.
1982-03-01
In this paper we consider the general form of finite difference approximation to the Dirac (Weyl) Hamiltonian on a lattice and investigate systematically the dependence on symmetry of the number of particles described by it. Our result is, that to a symmetry - expressed by a crystallographic space group - there corresponds a minimal number of particles, which are associated to prescribed points of momentum space (the unit cell of the reciprocal lattice). For convenience of the reader we show, using the existing detailed descriptions of space groups, how these results look for all the relevant (symmorphic) symmetry groups. Only for lattice Hamiltonians with a momentum dependent mass term can this degeneracy be reduced and even eliminated without reducing the symmetry. (orig./HSI)
Symmetry-preserving perturbations of the Bateman Lagrangian and dissipative systems
Campoamor-Stursberg, Rutwig
2017-03-01
Perturbations of the classical Bateman Lagrangian preserving a certain subalgebra of Noether symmetries are studied, and conservative perturbations are characterized by the Lie algebra sl(2, ℝ) ⊕ so(2). Non-conservative albeit integrable perturbations are determined by the simple Lie algebra sl(2,ℝ), showing further the relation of the corresponding non-linear systems with the notion of generalized Ermakov systems.
Symmetry-preserving perturbations of the Bateman Lagrangian and dissipative systems
International Nuclear Information System (INIS)
Campoamor-Stursberg, Rutwig
2017-01-01
Perturbations of the classical Bateman Lagrangian preserving a certain subalgebra of Noether symmetries are studied, and conservative perturbations are characterized by the Lie algebra sl(2, ℝ) ⊕ so(2). Non-conservative albeit integrable perturbations are determined by the simple Lie algebra sl(2,ℝ), showing further the relation of the corresponding non-linear systems with the notion of generalized Ermakov systems.
Symmetry-preserving perturbations of the Bateman Lagrangian and dissipative systems
Energy Technology Data Exchange (ETDEWEB)
Campoamor-Stursberg, Rutwig, E-mail: rutwig@ucm.es [Faculted de Ciencias Matematicas Universidad Complutense, Instituto de Matemática Interdisciplinar and Departamento Geometría y Topología (Spain)
2017-03-15
Perturbations of the classical Bateman Lagrangian preserving a certain subalgebra of Noether symmetries are studied, and conservative perturbations are characterized by the Lie algebra sl(2, ℝ) ⊕ so(2). Non-conservative albeit integrable perturbations are determined by the simple Lie algebra sl(2,ℝ), showing further the relation of the corresponding non-linear systems with the notion of generalized Ermakov systems.
International Nuclear Information System (INIS)
O'Raifeartaigh, L.
1979-01-01
This review describes the principles of hidden gauge symmetry and of its application to the fundamental interactions. The emphasis is on the structure of the theory rather than on the technical details and, in order to emphasise the structure, gauge symmetry and hidden symmetry are first treated as independent phenomena before being combined into a single (hidden gauge symmetric) theory. The main application of the theory is to the weak and electromagnetic interactions of the elementary particles, and although models are used for comparison with experiment and for illustration, emphasis is placed on those features of the application which are model-independent. (author)
Sequential flavor symmetry breaking
International Nuclear Information System (INIS)
Feldmann, Thorsten; Jung, Martin; Mannel, Thomas
2009-01-01
The gauge sector of the standard model exhibits a flavor symmetry that allows for independent unitary transformations of the fermion multiplets. In the standard model the flavor symmetry is broken by the Yukawa couplings to the Higgs boson, and the resulting fermion masses and mixing angles show a pronounced hierarchy. In this work we connect the observed hierarchy to a sequence of intermediate effective theories, where the flavor symmetries are broken in a stepwise fashion by vacuum expectation values of suitably constructed spurion fields. We identify the possible scenarios in the quark sector and discuss some implications of this approach.
Sequential flavor symmetry breaking
Feldmann, Thorsten; Jung, Martin; Mannel, Thomas
2009-08-01
The gauge sector of the standard model exhibits a flavor symmetry that allows for independent unitary transformations of the fermion multiplets. In the standard model the flavor symmetry is broken by the Yukawa couplings to the Higgs boson, and the resulting fermion masses and mixing angles show a pronounced hierarchy. In this work we connect the observed hierarchy to a sequence of intermediate effective theories, where the flavor symmetries are broken in a stepwise fashion by vacuum expectation values of suitably constructed spurion fields. We identify the possible scenarios in the quark sector and discuss some implications of this approach.
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.
Is space-time symmetry a suitable generalization of parity-time symmetry?
International Nuclear Information System (INIS)
Amore, Paolo; Fernández, Francisco M.; Garcia, Javier
2014-01-01
We discuss space-time symmetric Hamiltonian operators of the form H=H 0 +igH ′ , where H 0 is Hermitian and g real. H 0 is invariant under the unitary operations of a point group G while H ′ is invariant under transformation by elements of a subgroup G ′ 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
Electroweak symmetry breaking: Higgs/whatever
International Nuclear Information System (INIS)
Chanowitz, M.S.
1989-01-01
In the first of these two lectures the Higgs mechanism is reviewed in its most general form, which does not necessarily require the existence of Higgs bosons. The general consequences of the hypothesis that electroweak symmetry breaking is due to the Higgs mechanism are deduced just from gauge invariance and unitarity. In the second lecture the general properties are illustrated with three specific models: the Weinberg-Salam model, its minimal supersymmetric extension, and technicolor. The second lecture concludes with a discussion of the experiment signals for strong WW scattering, whose presence or absence will allow us to determine whether the symmetry breaking sector lies above or below 1 TeV. 57 refs
Symmetries and exact solutions of the nondiagonal Einstein-Rosen metrics
International Nuclear Information System (INIS)
Goyal, N; Gupta, R K
2012-01-01
We seek exact solutions of the nondiagonal Einstein-Rosen metrics. The method of Lie symmetry of differential equations is utilized to obtain new exact solutions of Einstein vacuum equations obtained from the nondiagonal Einstein-Rosen metric. Four cases arise depending on the nature of the Lie symmetry generator. In all cases, we find reductions in terms of ordinary differential equations and exact solutions of the nonlinear system of partial differential equations (PDEs) are derived. For this purpose, first we check the Painlevé property and then corresponding to the nonlinear system of PDEs, symmetries and exact solutions are obtained.
Symmetries of the Euler compressible flow equations for general equation of state
Energy Technology Data Exchange (ETDEWEB)
Boyd, Zachary M. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Ramsey, Scott D. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Baty, Roy S. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2015-10-15
The Euler compressible flow equations exhibit different Lie symmetries depending on the equation of state (EOS) of the medium in which the flow occurs. This means that, in general, different types of similarity solution will be available in different flow media. We present a comprehensive classification of all EOS’s to which the Euler equations apply, based on the Lie symmetries admitted by the corresponding flow equations, restricting to the case of 1-D planar, cylindrical, or spherical geometry. The results are conveniently summarized in tables. This analysis also clarifies past work by Axford and Ovsiannikov on symmetry classification.
Symmetry generators in singular theories
International Nuclear Information System (INIS)
Lavrov, P.M.; Tyutin, I.V.
1989-01-01
It is proved that in the singular nondegenerate theories any symmetry of the lagrangian under non-point transformations of lagrangian variables with the open (in the general case) algebra in the hamiltonian approach generates corresponding transformations of canonical variables the generator of which is the Noether charge with respect to the Dirac brackets. On the surface of all constraints these transformations leave the hamiltonian invariant and the algebra of the Noether charges is closed. As a consequence it is shown that the nilpotent BRST charge operator always exists in gauge theories of the general form (if possible anomalies are not taken into account)
International Nuclear Information System (INIS)
Dragon, N.
1979-01-01
The possible use of trilinear algebras as symmetry algebras for para-Fermi fields is investigated. The shortcomings of the examples are argued to be a general feature of such generalized algebras. (author)
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.
Segmentation Using Symmetry Deviation
DEFF Research Database (Denmark)
Hollensen, Christian; Højgaard, L.; Specht, L.
2011-01-01
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...... hypopharyngeal cancer patients to find anatomical symmetry and evaluate it against the standard deviation of the normal patients to locate pathologic volumes. Combining the information with an absolute PET threshold of 3 Standard uptake value (SUV) a volume was automatically delineated. The overlap of automated....... The standard deviation of the anatomical symmetry, seen in figure for one patient along CT and PET, was extracted for normal patients and compared with the deviation from cancer patients giving a new way of determining cancer pathology location. Using the novel method an overlap concordance index...
Statistical symmetries in physics
International Nuclear Information System (INIS)
Green, H.S.; Adelaide Univ., SA
1994-01-01
Every law of physics is invariant under some group of transformations and is therefore the expression of some type of symmetry. Symmetries are classified as geometrical, dynamical or statistical. At the most fundamental level, statistical symmetries are expressed in the field theories of the elementary particles. This paper traces some of the developments from the discovery of Bose statistics, one of the two fundamental symmetries of physics. A series of generalizations of Bose statistics is described. A supersymmetric generalization accommodates fermions as well as bosons, and further generalizations, including parastatistics, modular statistics and graded statistics, accommodate particles with properties such as 'colour'. A factorization of elements of ggl(n b ,n f ) can be used to define truncated boson operators. A general construction is given for q-deformed boson operators, and explicit constructions of the same type are given for various 'deformed' algebras. A summary is given of some of the applications and potential applications. 39 refs., 2 figs
Wigner's Symmetry Representation Theorem
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 19; Issue 10. Wigner's Symmetry Representation Theorem: At the Heart of Quantum Field Theory! Aritra Kr Mukhopadhyay. General Article Volume 19 Issue 10 October 2014 pp 900-916 ...
Dynamical symmetries for fermions
International Nuclear Information System (INIS)
Guidry, M.
1989-01-01
An introduction is given to the Fermion Dynamical Symmetry Model (FDSM). The analytical symmetry limits of the model are then applied to the calculation of physical quantities such as ground-state masses and B(E 2 ) values in heavy nuclei. These comparisons with data provide strong support for a new principle of collective motion, the Dynamical Pauli Effect, and suggest that dynamical symmetries which properly account for the pauli principle are much more persistent in nuclear structure than the corresponding boson symmetries. Finally, we present an assessment of criticisms which have been voiced concerning the FDSM, and a discussion of new phenomena and ''exotic spectroscopy'' which may be suggested by the model. 14 refs., 8 figs., 4 tabs
Flavour from accidental symmetries
International Nuclear Information System (INIS)
Ferretti, Luca; King, Stephen F.; Romanino, Andrea
2006-01-01
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
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.)
International Nuclear Information System (INIS)
Blum, Alexander Simon
2009-01-01
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 4 , the other describing quarks and employing the symmetry D 14 . In the latter model it is the quark mixing matrix element V 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.)
The search for higher symmetry in string theory
Energy Technology Data Exchange (ETDEWEB)
Witten, E [Institute for Advanced Study, Princeton, NJ (USA)
1989-11-17
Some remarks are made about the nature and role of the search for higher symmetry in string theory. These symmetries are most likely to be uncovered in a mysterious 'unbroken phase', for which (2+1)-dimensional gravity provides an interesting and soluble model. New insights about conformal field theory, in which one gets 'out of flatland' to see a wider symmetry from a higher-dimensional vantage point, may offer clues to the unbroken phase of string theory. (author).
New infinite-dimensional hidden symmetries for heterotic string theory
International Nuclear Information System (INIS)
Gao Yajun
2007-01-01
The symmetry structures of two-dimensional heterotic string theory are studied further. A (2d+n)x(2d+n) matrix complex H-potential is constructed and the field equations are extended into a complex matrix formulation. A pair of Hauser-Ernst-type linear systems are established. Based on these linear systems, explicit formulations of new hidden symmetry transformations for the considered theory are given and then these symmetry transformations are verified to constitute infinite-dimensional Lie algebras: the semidirect product of the Kac-Moody o(d,d+n-circumflex) and Virasoro algebras (without center charges). These results demonstrate that the heterotic string theory under consideration possesses more and richer symmetry structures than previously expected
Supersymmetry and intermediate symmetry breaking in SO(10) superunification
International Nuclear Information System (INIS)
Asatryan, H.M.; Ioannisyan, A.N.
1985-01-01
A scheme of simultaneous breakdown of intermediate symmetry SO(10) → SU(3)sub(c) x U(1) x SU(2)sub(L) x SU(2)sub(R) and supersymmetry by means of a single scale parameter is suggested. This intermediate symmetry, which is preferable physically, owing to the broken supersymmetry has a minimum lying lower than SU(4) x SU(2)sub(L) x SU(2)sub(R). The intermediate symmetry is broken by the vacuum expectation value of the Higgs superfields. Owing to the quantum corrections the potential minimum turns out to correspond to breakdown of the intermediate symmetry up to the standard group SU(3)sub(c) x SU(2)sub(L) x U(1)sub(y). The value of the Weinberg angle is less than that in the supersymmetric SU(5) model and agrees with the experiment
PREFACE: Symmetries and Integrability of Difference Equations
Doliwa, Adam; Korhonen, Risto; Lafortune, Stéphane
2007-10-01
The notion of integrability was first introduced in the 19th century in the context of classical mechanics with the definition of Liouville integrability for Hamiltonian flows. Since then, several notions of integrability have been introduced for partial and ordinary differential equations. Closely related to integrability theory is the symmetry analysis of nonlinear evolution equations. Symmetry analysis takes advantage of the Lie group structure of a given equation to study its properties. Together, integrability theory and symmetry analysis provide the main method by which nonlinear evolution equations can be solved explicitly. Difference equations (DE), like differential equations, are important in numerous fields of science and have a wide variety of applications in such areas as mathematical physics, computer visualization, numerical analysis, mathematical biology, economics, combinatorics, and quantum field theory. It is thus crucial to develop tools to study and solve DEs. While the theory of symmetry and integrability for differential equations is now largely well-established, this is not yet the case for discrete equations. Although over recent years there has been significant progress in the development of a complete analytic theory of difference equations, further tools are still needed to fully understand, for instance, the symmetries, asymptotics and the singularity structure of difference equations. The series of SIDE meetings on Symmetries and Integrability of Difference Equations started in 1994. Its goal is to provide a platform for an international and interdisciplinary communication for researchers working in areas associated with integrable discrete systems, such as classical and quantum physics, computer science and numerical analysis, mathematical biology and economics, discrete geometry and combinatorics, theory of special functions, etc. The previous SIDE meetings took place in Estérel near Montréal, Canada (1994), at the University of
Deceit and dishonesty as practice: the comfort of lying.
Carter, Melody
2016-07-01
Lying and deceit are instruments of power, used by social actors in the pursuit of their practices as they seek to maintain social order. All social actors, nurses included, have deceit and dishonesty within their repertoire of practice. Much of this is benign, well intentioned and a function of being sociable and necessary in the pursuit of social order in the healthcare environment. Lying and deceit from a sociological point of view, is a reflection of the different modes of domination that exist within a social space. French philosopher Pierre Bourdieu theorized about the way that symbolic power works within social space. The social structures and the agency of individual actors moving within it are interrelated and interdependent. Bourdieu's ideas will be used to theorize about real clinical experiences where acts of deceit can be identified and a case example will be presented. Nurses are actors in the social space of clinical care, and their world is complex, challenging, and often fraught with the contradictory demands and choices that reflect and influence their behaviours. An exploration of lying and deceit in nursing as an instrument in the modes of domination that persist enables us to challenge some of the assumptions that are made about the motives that cause or tempt nurses to lie as well as to understand the way on which they are sometimes lied to, according to the acts of domination that exist in the field. Lying or acting dishonestly is a powerful act that is intent on retaining stability and social order and could be seen to be a justification of lying and deceit. However, we need to pause and consider, in whose interests are we striving to create social order? Is it in the end about the comfort of patients or for the comfort of professionals? © 2016 John Wiley & Sons Ltd.
On Deformations and Contractions of Lie Algebras
Directory of Open Access Journals (Sweden)
Marc de Montigny
2006-05-01
Full Text Available In this contributed presentation, we discuss and compare the mutually opposite procedures of deformations and contractions of Lie algebras. We suggest that with appropriate combinations of both procedures one may construct new Lie algebras. We first discuss low-dimensional Lie algebras and illustrate thereby that whereas for every contraction there exists a reverse deformation, the converse is not true in general. Also we note that some Lie algebras belonging to parameterized families are singled out by the irreversibility of deformations and contractions. After reminding that global deformations of the Witt, Virasoro, and affine Kac-Moody algebras allow one to retrieve Lie algebras of Krichever-Novikov type, we contract the latter to find new infinite dimensional Lie algebras.
Quantum Lie theory a multilinear approach
Kharchenko, Vladislav
2015-01-01
This is an introduction to the mathematics behind the phrase “quantum Lie algebra”. The numerous attempts over the last 15-20 years to define a quantum Lie algebra as an elegant algebraic object with a binary “quantum” Lie bracket have not been widely accepted. In this book, an alternative approach is developed that includes multivariable operations. Among the problems discussed are the following: a PBW-type theorem; quantum deformations of Kac--Moody algebras; generic and symmetric quantum Lie operations; the Nichols algebras; the Gurevich--Manin Lie algebras; and Shestakov--Umirbaev operations for the Lie theory of nonassociative products. Opening with an introduction for beginners and continuing as a textbook for graduate students in physics and mathematics, the book can also be used as a reference by more advanced readers. With the exception of the introductory chapter, the content of this monograph has not previously appeared in book form.
Freestall maintenance: effects on lying behavior of dairy cattle.
Drissler, M; Gaworski, M; Tucker, C B; Weary, D M
2005-07-01
In a series of 3 experiments, we documented how sand-bedding depth and distribution changed within freestalls after new bedding was added and the effect of these changes on lying behavior. In experiment 1, we measured changes in bedding depth over a 10-d period at 43 points in 24 freestalls. Change in depth of sand was the greatest the day after new sand was added and decreased over time. Over time, the stall surface became concave, and the deepest part of the stall was at the center. Based on the results of experiment 1, we measured changes in lying behavior when groups of cows had access to freestalls with sand bedding that was 0, 3.5, 5.2, or 6.2 cm at the deepest point, below the curb, while other dimensions remained fixed. We found that daily lying time was 1.15 h shorter in stalls with the lowest levels of bedding compared with stalls filled with bedding. Indeed, for every 1-cm decrease in bedding, cows spent 11 min less time lying down during each 24-h period. In a third experiment, we imposed 4 treatments that reflected the variation in sand depth within stalls: 0, 6.2, 9.9, and 13.7 cm below the curb. Again, lying times reduced with decreasing bedding, such that cows using the stalls with the least amount of bedding (13.7 cm below curb) spent 2.33 h less time per day lying down than when housed with access to freestalls filled with sand (0 cm below curb).
Hidden symmetry of the beam spread function resulting from the reciprocity theorem
International Nuclear Information System (INIS)
Dolin, Lev S.
2016-01-01
It is shown that the optical reciprocity theorem imposes certain constraints on the radiation field structure of a unidirectional point source (beam spread function (BSF)) in a turbid medium with spatially uniform optical properties. To satisfy the reciprocal relation, the BSF should have an additional symmetry property along with axial symmetry. This paper mathematically formulates the BSF symmetry condition that follows from the reciprocity theorem and discusses test results of some approximate analytical BSF models for their compliance with the symmetry requirement. A universal method for eliminating symmetry errors of approximate BSF models is proposed. - Highlights: • Symmetry properties of beam spread function (BSF) are considered. • In uniform turbid medium BSF has hidden symmetry property besides axial symmetry. • The examples of BSF models with and without the required symmetry are given. • A universal method for BSF symmetry error elimination is proposed.
Introduction "Workplace (a)symmetries: multimodal perspectives"
DEFF Research Database (Denmark)
Asmuss, Birte
studied in everyday and professional settings (Ariss, 2009; Glenn, 2010; Maynard, 1991; Roberts, 2000; Robinson, 2001). Numerous studies have pointed out that (a)symmetries in talk can be results of underlying interactional micro-practices like uneven turn distribution and question-answer formats...
Non-geometric fluxes and mixed-symmetry potentials
Bergshoeff, E.A.; Penas, V.A.; Riccioni, F.; Risoli, S.
2015-01-01
We discuss the relation between generalised fluxes and mixed-symmetry potentials. We refer to the fluxes that cannot be described even locally in the framework of supergravity as ‘non-geometric’. We first consider the NS fluxes, and point out that the non-geometric R flux is dual to a mixed-symmetry
Computations in finite-dimensional Lie algebras
Directory of Open Access Journals (Sweden)
A. M. Cohen
1997-12-01
Full Text Available This paper describes progress made in context with the construction of a general library of Lie algebra algorithms, called ELIAS (Eindhoven Lie Algebra System, within the computer algebra package GAP. A first sketch of the package can be found in Cohen and de Graaf[1]. Since then, in a collaborative effort with G. Ivanyos, the authors have continued to develop algorithms which were implemented in ELIAS by the second author. These activities are part of a bigger project, called ACELA and financed by STW, the Dutch Technology Foundation, which aims at an interactive book on Lie algebras (cf. Cohen and Meertens [2]. This paper gives a global description of the main ways in which to present Lie algebras on a computer. We focus on the transition from a Lie algebra abstractly given by an array of structure constants to a Lie algebra presented as a subalgebra of the Lie algebra of n×n matrices. We describe an algorithm typical of the structure analysis of a finite-dimensional Lie algebra: finding a Levi subalgebra of a Lie algebra.
Symmetry in quantum system theory: Rules for quantum architecture design
Energy Technology Data Exchange (ETDEWEB)
Schulte-Herbrueggen, Thomas; Sander, Uwe [Technical University of Munich, Garching (Germany). Dept. Chem.
2010-07-01
We investigate universality in the sense of controllability and observability, of multi-qubit systems in architectures of various symmetries of coupling type and topology. By determining the respective dynamic system Lie algebras, explicit reachability sets under symmetry constraints are provided. Thus for a given (possibly symmetric) experimental coupling architecture several decision problems can be solved in a unified way: (i) can a target Hamiltonian be simulated? (ii) can a target gate be synthesised? (iii) to which extent is the system observable by a given set of detection operators? and, as a special case of the latter, (iv) can an underlying system Hamiltonian be identified with a given set of detection operators? Finally, in turn, the absence of symmetry provides a convenient necessary condition for full controllability. Though often easier to assess than the well-established Lie-algebra rank condition, this is not sufficient unless the candidate dynamic simple Lie algebra can be pre-identified uniquely. Thus for architectures with various Ising and Heisenberg coupling types we give design rules sufficient to ensure full controllability. In view of follow-up studies, we relate the unification of necessary and sufficient conditions for universality to filtering simple Lie subalgebras of su(N) comprising classical and exceptional types.
Higher spins and Yangian symmetries
Energy Technology Data Exchange (ETDEWEB)
Gaberdiel, Matthias R. [Institut für Theoretische Physik, ETH Zurich, CH-8093 Zurich (Switzerland); Gopakumar, Rajesh [International Centre for Theoretical Sciences-TIFR, Survey No. 151, Shivakote, Hesaraghatta Hobli, Bengaluru North 560 089 (India); Li, Wei [CAS Key Laboratory of Theoretical Physics,Institute of Theoretical Physics, Chinese Academy of Sciences,100190 Beijing (China); Peng, Cheng [Department of Physics, Brown University, 182 Hope Street, Providence, RI 02912 (United States)
2017-04-26
The relation between the bosonic higher spin W{sub ∞}[λ] algebra, the affine Yangian of gl{sub 1}, and the SH{sup c} algebra is established in detail. For generic λ we find explicit expressions for the low-lying W{sub ∞}[λ] modes in terms of the affine Yangian generators, and deduce from this the precise identification between λ and the parameters of the affine Yangian. Furthermore, for the free field cases corresponding to λ=0 and λ=1 we give closed-form expressions for the affine Yangian generators in terms of the free fields. Interestingly, the relation between the W{sub ∞} modes and those of the affine Yangian is a non-local one, in general. We also establish the explicit dictionary between the affine Yangian and the SH{sup c} generators. Given that Yangian algebras are the hallmark of integrability, these identifications should pave the way towards uncovering the relation between the integrable and the higher spin symmetries.
Symmetry of priapulids (Priapulida). 2. Symmetry of larvae.
Adrianov, A V; Malakhov, V V
2001-02-01
Larvae of priapulids are characterized by radial symmetry evident from both external and internal characters of the introvert and lorica. The bilaterality appears as a result of a combination of several radial symmetries: pentaradial symmetry of the teeth, octaradial symmetry of the primary scalids, 25-radial symmetry of scalids, biradial symmetry of the neck, and biradial and decaradial symmetry of the trunk. Internal radiality is exhibited by musculature and the circumpharyngeal nerve ring. Internal bilaterality is evident from the position of the ventral nerve cord and excretory elements. Externally, the bilaterality is determined by the position of the anal tubulus and two shortened midventral rows of scalids bordering the ventral nerve cord. The lorical elements define the biradial symmetry that is missing in adult priapulids. The radial symmetry of larvae is a secondary appearance considered an evolutionary adaptation to a lifestyle within the three-dimensional environment of the benthic sediment. Copyright 2001 Wiley-Liss, Inc.
International Nuclear Information System (INIS)
Prykarpatsky, A.K.; Blackmore, D.L.; Bogolubov, N.N. Jr.
2007-05-01
The infinite-dimensional operator Lie algebras of the related integrable nonlocal differential-difference dynamical systems are treated as their hidden symmetries. As a result of their dimerization the Lax type representations for both local differential-difference equations and nonlocal ones are obtained. An alternative approach to the Lie-algebraic interpretation of the integrable local differential-difference systems is also proposed. The Hamiltonian representation for a hierarchy of Lax type equations on a dual space to the centrally extended Lie algebra of integro-differential operators with matrix-valued coefficients coupled with suitable eigenfunctions and adjoint eigenfunctions evolutions of associated spectral problems is obtained by means of a specially constructed Baecklund transformation. The Hamiltonian description for the corresponding set of additional symmetry hierarchies is represented. The relation of these hierarchies with Lax type integrable (3+1)-dimensional nonlinear dynamical systems and their triple Lax type linearizations is analyzed. The Lie-algebraic structures, related with centrally extended current operator Lie algebras are discussed with respect to constructing new nonlinear integrable dynamical systems on functional manifolds and super-manifolds. Special Poisson structures and related with them factorized integrable operator dynamical systems having interesting applications in modern mathematical physics, quantum computing mathematics and other fields are constructed. The previous purely computational results are explained within the approach developed. (author)
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...
Schwichtenberg, Jakob
2018-01-01
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. Thanks to the input of readers from around the world, this second edition has been purged of typographical errors and also contains several revised sections with improved explanations. .
On the characterization of infinitesimal symmetries of the relativistic phase space
International Nuclear Information System (INIS)
Janyška, Josef; Vitolo, Raffaele
2012-01-01
The phase space of relativistic particle mechanics is defined as the first jet space of motions regarded as time-like one-dimensional submanifolds of spacetime. A Lorentzian metric and an electromagnetic 2-form define naturally a generalized contact structure on the odd-dimensional phase space. In the paper, infinitesimal symmetries of the phase structures are characterized. More precisely, it is proved that all phase infinitesimal symmetries are special Hamiltonian lifts of distinguished conserved quantities on the phase space. It is proved that generators of infinitesimal symmetries constitute a Lie algebra with respect to a special bracket. A momentum map for groups of symmetries of the geometric structures is provided. (paper)
Low-lying baryon spectrum with two dynamical twisted mass fermions
Energy Technology Data Exchange (ETDEWEB)
Alexandrou, C. [Cyprus Univ., Nicosia (Cyprus). Dept. of Physics; Computation-based Science and Technology Research Center, Cyprus Institute, Nicosia (Cyprus); Baron, R.; Guichon, P. [CEA-Saclay, IRFU/Service de Physique Nucleaire, Gif-sur-Yvette (France); Carbonell, J.; Drach, V. [UJF/CNRS/IN2P3, Grenoble (France). Lab. de Physique Subatomique et Cosmologie; Jansen, K. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Korzec, T. [Cyprus Univ., Nicosia (Cyprus). Dept. of Physics; Pene, O. [Paris-11 Univ., 91 - Orsay (France). Lab. de Physique Theorique
2009-10-15
The masses of the low lying baryons are evaluated using two degenerate flavors of twisted mass sea quarks corresponding to pseudo scalar masses in the range of about 270 MeV to 500 MeV. The strange valence quark mass is tuned to reproduce the mass of the kaon in the physical limit. The tree-level Symanzik improved gauge action is employed. We use lattices of spatial size 2.1 fm and 2.7 fm at two values of the lattice spacing with r{sub 0}/a=5.22(2) and r{sub 0}/a=6.61(3). We check for both finite volume and cut-off effects on the baryon masses. We performed a detailed study of the chiral extrapolation of the octet and decuplet masses using SU(2) {chi}PT. The lattice spacings determined using the nucleon mass at the physical point are consistent with the values extracted using the pion decay constant. We examine the issue of isospin symmetry breaking for the octet and decuplet baryons and its dependence on the lattice spacing. We show that in the continuum limit isospin breaking is consistent with zero, as expected. The baryon masses that we find after taking the continuum limit and extrapolating to the physical limit are in good agreement with experiment. (orig.)
Emergent symmetries in the canonical tensor model
Obster, Dennis; Sasakura, Naoki
2018-04-01
The canonical tensor model (CTM) is a tensor model proposing a classically and quantum mechanically consistent description of gravity, formulated as a first-class constraint system with structural similarities to the ADM formalism of general relativity. The classical CTM produces a general relativistic system in a formal continuum limit, the emergence of which should be explained by the quantum CTM. In this paper we study the symmetry properties of a wave function that exactly solves the quantum constraints of the CTM. We have found that it has strong peaks at configurations invariant under some Lie groups, as predicted by a mechanism described in our previous paper. A surprising result is the preference for configurations invariant not only under Lie groups with positive definite signature, but also with Lorentzian signature. Such symmetries could characterize the global structures of spacetimes, and our results are encouraging towards showing spacetime emergence in the CTM. To verify the asymptotic convergence of the wave function we have also analyzed the asymptotic behavior, which for the most part seems to be well under control.
Lie group classification and exact solutions of the generalized Kompaneets equations
Directory of Open Access Journals (Sweden)
Oleksii Patsiuk
2015-04-01
Full Text Available We study generalized Kompaneets equations (GKEs with one functional parameter, and using the Lie-Ovsiannikov algorithm, we carried out the group classification. It is shown that the kernel algebra of the full groups of the GKEs is the one-dimensional Lie algebra. Using the direct method, we find the equivalence group. We obtain six non-equivalent (up to transformations from the equivalence group GKEs that allow wider invariance algebras than the kernel one. We find a number of exact solutions of the non-linear GKE which has the maximal symmetry properties.
Morozov, Oleg I.
2018-06-01
The important unsolved problem in theory of integrable systems is to find conditions guaranteeing existence of a Lax representation for a given PDE. The exotic cohomology of the symmetry algebras opens a way to formulate such conditions in internal terms of the PDE s under the study. In this paper we consider certain examples of infinite-dimensional Lie algebras with nontrivial second exotic cohomology groups and show that the Maurer-Cartan forms of the associated extensions of these Lie algebras generate Lax representations for integrable systems, both known and new ones.
Invariants and labels for Lie-Poisson Systems
International Nuclear Information System (INIS)
Thiffeault, J.L.; Morrison, P.J.
1998-04-01
Reduction is a process that uses symmetry to lower the order of a Hamiltonian system. The new variables in the reduced picture are often not canonical: there are no clear variables representing positions and momenta, and the Poisson bracket obtained is not of the canonical type. Specifically, we give two examples that give rise to brackets of the noncanonical Lie-Poisson form: the rigid body and the two-dimensional ideal fluid. From these simple cases, we then use the semidirect product extension of algebras to describe more complex physical systems. The Casimir invariants in these systems are examined, and some are shown to be linked to the recovery of information about the configuration of the system. We discuss a case in which the extension is not a semidirect product, namely compressible reduced MHD, and find for this case that the Casimir invariants lend partial information about the configuration of the system
Minimally doubled fermions and spontaneous chiral symmetry breaking
Directory of Open Access Journals (Sweden)
Osmanaj (Zeqirllari Rudina
2018-01-01
Full Text Available Chiral symmetry breaking in massless QCD is a very important feature in the current understanding of low energy physics. Low - lying Dirac modes are suitable to help us understand the spontaneous chiral symmetry breaking, since the formation of a non zero chiral condensate is an effect of their accumulation near zero. The Banks – Casher relation links the spectral density of the Dirac operator to the condensate with an identity that can be read in both directions. In this work we propose a spectral method to achieve a reliable determination of the density of eigenvalues of Dirac operator near zero using the Gauss – Lanczos quadrature. In order to understand better the dynamical chiral symmetry breaking and use the method we propose, we have chosen to work with minimally doubled fermions. These kind of fermions have been proposed as a strictly local discretization of the QCD fermions action, which preserves chiral symmetry at finite cut-off. Being chiral fermions, is easier to work with them and their low - lying Dirac modes and to understand the dynamical spontaneous chiral symmetry breaking.
Minimally doubled fermions and spontaneous chiral symmetry breaking
Osmanaj (Zeqirllari), Rudina; Hyka (Xhako), Dafina
2018-03-01
Chiral symmetry breaking in massless QCD is a very important feature in the current understanding of low energy physics. Low - lying Dirac modes are suitable to help us understand the spontaneous chiral symmetry breaking, since the formation of a non zero chiral condensate is an effect of their accumulation near zero. The Banks - Casher relation links the spectral density of the Dirac operator to the condensate with an identity that can be read in both directions. In this work we propose a spectral method to achieve a reliable determination of the density of eigenvalues of Dirac operator near zero using the Gauss - Lanczos quadrature. In order to understand better the dynamical chiral symmetry breaking and use the method we propose, we have chosen to work with minimally doubled fermions. These kind of fermions have been proposed as a strictly local discretization of the QCD fermions action, which preserves chiral symmetry at finite cut-off. Being chiral fermions, is easier to work with them and their low - lying Dirac modes and to understand the dynamical spontaneous chiral symmetry breaking.
Soliton surfaces associated with generalized symmetries of integrable equations
International Nuclear Information System (INIS)
Grundland, A M; Post, S
2011-01-01
In this paper, based on the Fokas et al approach (Fokas and Gel'fand 1996 Commun. Math. Phys. 177 203-20; Fokas et al 2000 Sel. Math. 6 347-75), we provide a symmetry characterization of continuous deformations of soliton surfaces immersed in a Lie algebra using the formalism of generalized vector fields, their prolongation structure and links with the Frechet derivatives. We express the necessary and sufficient condition for the existence of such surfaces in terms of the invariance criterion for generalized symmetries and identify additional sufficient conditions which admit an explicit integration of the immersion functions of 2D surfaces in Lie algebras. We discuss in detail the su(N)-valued immersion functions generated by conformal symmetries of the CP N-1 sigma model defined on either the Minkowski or Euclidean space. We further show that the sufficient conditions for explicit integration of such immersion functions impose additional restrictions on the admissible conformal symmetries of the model defined on Minkowski space. On the other hand, the sufficient conditions are identically satisfied for arbitrary conformal symmetries of finite action solutions of the CP N-1 sigma model defined on Euclidean space.
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
International Nuclear Information System (INIS)
Chimento, Luis P.
2002-01-01
We find the group of symmetry transformations under which the Einstein equations for the spatially flat Friedmann-Robertson-Walker universe are form invariant. They relate the energy density and the pressure of the fluid to the expansion rate. We show that inflation can be obtained from nonaccelerated scenarios by a symmetry transformation. We derive the transformation rule for the spectrum and spectral index of the curvature perturbations. Finally, the group is extended to investigate inflation in the anisotropic Bianchi type-I spacetime and the brane-world cosmology
R-symmetries from the orbifolded heterotic string
International Nuclear Information System (INIS)
Schmitz, Matthias
2014-08-01
We examine the geometric origin of discrete R-symmetries in heterotic orbifold compactifications. By analysing the symmetries of the worldsheet instanton solutions and the underlying geometry, we obtain a scheme that allows us to systematically explore the R-symmetries arising in these compactifications. Applying this scheme to a classification of orbifold geometries, we are able to find all R-symmetries of heterotic orbifolds with Abelian point groups. We show that in the vast majority of cases, the R-symmetries found satisfy anomaly universality constraints, as required in heterotic orbifolds. Then we examine the implications of the presence of these R-symmetries on a class of phenomenologically attractive orbifold compactifications known as the heterotic mini-landscape. We use the technique of Hilbert bases in order to analyse the properties of a vacuum configuration. We find that phenomenologically viable models remain and the main attractive features of the mini-landscape are unaltered.
Devious Lies: Adventures in Freelance Science Outreach
Fatland, D. R.
2003-12-01
Observations are given from two freelance science outreach projects undertaken by the author: Tutoring at-risk secondary students and teaching astronomy to 5th-7th graders in a camp retreat environment. Two recurring thematic challenges in these experiences are considered: First the 'Misperception Problem', the institutionalized chasm between the process of doing science and K-12 science education (wherein science is often portrayed as something distant and inaccessible, while ironically children are necessarily excellent scientists). And second the 'Engagement Problem', engaging a student's attention and energy by matching teaching material and--more importantly--teaching techniques to the student's state of development. The objective of this work is twofold: To learn how to address these two challenges and to empower the students in a manner independent of the scientific content of any particular subject. An underlying hypothesis is that confidence to problem solve (a desirable life-skill) can be made more accessible through a combination of problem solving by the student and seeing how others have solved seemingly impossible problems. This hypothesis (or agenda) compels an emphasis on critical thinking and raises the dilemma of reconciling non-directed teaching with very pointed conclusions about the verity of pseudo-science and ideas prevalent about science in popular culture. An interesting pedagogical found-object in this regard is the useful 'devious lie' which can encourage a student to question the assumption that the teacher (and by extension any professed expert) has the right answers.
Quantum integrable systems related to lie algebras
International Nuclear Information System (INIS)
Olshanetsky, M.A.; Perelomov, A.M.
1983-01-01
Some quantum integrable finite-dimensional systems related to Lie algebras are considered. This review continues the previous review of the same authors (1981) devoted to the classical aspects of these systems. The dynamics of some of these systems is closely related to free motion in symmetric spaces. Using this connection with the theory of symmetric spaces some results such as the forms of spectra, wave functions, S-matrices, quantum integrals of motion are derived. In specific cases the considered systems describe the one-dimensional n-body systems interacting pairwise via potentials g 2 v(q) of the following 5 types: vsub(I)(q)=q - 2 , vsub(II)(q)=sinh - 2 q, vsub(III)(q)=sin - 2 q, vsub(IV)(q)=P(q), vsub(V)(q)=q - 2 +#betta# 2 q 2 . Here P(q) is the Weierstrass function, so that the first three cases are merely subcases on the fourth. The system characterized by the Toda nearest-neighbour potential exp(qsub(j)-qsub(j+1)) is moreover considered. This review presents from a general and universal point of view results obtained mainly over the past fifteen years. Besides, it contains some new results both of physical and mathematical interest. (orig.)
Invariant renormalization method for nonlinear realizations of dynamical symmetries
International Nuclear Information System (INIS)
Kazakov, D.I.; Pervushin, V.N.; Pushkin, S.V.
1977-01-01
The structure of ultraviolet divergences is investigated for the field theoretical models with nonlinear realization of the arbitrary semisimple Lie group, with spontaneously broken symmetry of vacuum. An invariant formulation of the background field method of renormalization is proposed which gives the manifest invariant counterterms off mass shell. A simple algorithm for construction of counterterms is developed. It is based on invariants of the group of dynamical symmetry in terms of the Cartan forms. The results of one-loop and two-loop calculations are reported
The structure of complex Lie groups
Lee, Dong Hoon
2001-01-01
Complex Lie groups have often been used as auxiliaries in the study of real Lie groups in areas such as differential geometry and representation theory. To date, however, no book has fully explored and developed their structural aspects.The Structure of Complex Lie Groups addresses this need. Self-contained, it begins with general concepts introduced via an almost complex structure on a real Lie group. It then moves to the theory of representative functions of Lie groups- used as a primary tool in subsequent chapters-and discusses the extension problem of representations that is essential for studying the structure of complex Lie groups. This is followed by a discourse on complex analytic groups that carry the structure of affine algebraic groups compatible with their analytic group structure. The author then uses the results of his earlier discussions to determine the observability of subgroups of complex Lie groups.The differences between complex algebraic groups and complex Lie groups are sometimes subtle ...
Cartan calculus on quantum Lie algebras
International Nuclear Information System (INIS)
Schupp, P.; Watts, P.; Zumino, B.
1993-01-01
A generalization of the differential geometry of forms and vector fields to the case of quantum Lie algebras is given. In an abstract formulation that incorporates many existing examples of differential geometry on quantum spaces we combine an exterior derivative, inner derivations, Lie derivatives, forms and functions au into one big algebra, the ''Cartan Calculus.''
Classification and identification of Lie algebras
Snobl, Libor
2014-01-01
The purpose of this book is to serve as a tool for researchers and practitioners who apply Lie algebras and Lie groups to solve problems arising in science and engineering. The authors address the problem of expressing a Lie algebra obtained in some arbitrary basis in a more suitable basis in which all essential features of the Lie algebra are directly visible. This includes algorithms accomplishing decomposition into a direct sum, identification of the radical and the Levi decomposition, and the computation of the nilradical and of the Casimir invariants. Examples are given for each algorithm. For low-dimensional Lie algebras this makes it possible to identify the given Lie algebra completely. The authors provide a representative list of all Lie algebras of dimension less or equal to 6 together with their important properties, including their Casimir invariants. The list is ordered in a way to make identification easy, using only basis independent properties of the Lie algebras. They also describe certain cl...
Testosterone Administration Reduces Lying in Men
Wibral, M.; Dohmen, T.J.; Klingmüller, Dietrich; Weber, Bernd; Falk, Armin
2012-01-01
Lying is a pervasive phenomenon with important social and economic implications. However, despite substantial interest in the prevalence and determinants of lying, little is known about its biological foundations. Here we study a potential hormonal influence, focusing on the steroid hormone
Elementary construction of graded lie groups
International Nuclear Information System (INIS)
Scheunert, M.; Rittenberg, V.
1977-06-01
We show how the definitions of the classical Lie groups have to be modified in the case where Grassmann variables are present. In particular, we construct the general linear, the special linear and the orthosymplectic graded Lie groups. Special attention is paid to the question of how to formulate an adequate 'unitarity condition'. (orig.) [de
Graded-Lie-algebra cohomology and supergravity
International Nuclear Information System (INIS)
D'Auria, R.; Fre, P.; Regge, T.
1980-01-01
Detailed explanations of the cohomology invoked in the group-manifold approach to supergravity is given. The Chevalley cohomology theory of Lie algebras is extended to graded Lie algebras. The scheme of geometrical theories is enlarged so to include cosmological terms and higher powers of the curvature. (author)
Continuum analogues of contragredient Lie algebras
International Nuclear Information System (INIS)
Saveliev, M.V.; Vershik, A.M.
1989-03-01
We present an axiomatic formulation of a new class of infinite-dimensional Lie algebras - the generalizations of Z-graded Lie algebras with, generally speaking, an infinite-dimensional Cartan subalgebra and a contiguous set of roots. We call such algebras ''continuum Lie algebras''. The simple Lie algebras of constant growth are encapsulated in our formulation. We pay particular attention to the case when the local algebra is parametrized by a commutative algebra while the Cartan operator (the generalization of the Cartan matrix) is a linear operator. Special examples of these algebras are the Kac-Moody algebras, algebras of Poisson brackets, algebras of vector fields on a manifold, current algebras, and algebras with differential or integro-differential Cartan operator. The nonlinear dynamical systems associated with the continuum contragredient Lie algebras are also considered. (author). 9 refs
Traces of chiral symmetry on light planes
International Nuclear Information System (INIS)
Sazdjian, Hagop.
1975-01-01
The possibility of a description of the hadronic world by field theories defined on light planes and formulated in terms of three interacting quark field variables has been investigated. The framework of models where the chiral symmetry breaking is produced by the only mechanical masses of quarks has been considered. The hypothesis that the light plane charges generate in the real world approximate symmetries of one particle states has also been emitted. The projection of the algebraic structure of the observables in the space of physical states have yielded various relations in terms of the masses and couplings of the low lying mesons. They seem to be in agreement with experimental data, and suggest the consistency of the adopted model to describe symmetry breaking phenomena. The quark mechanical masses m(u) approximately 30MeV and m(s) approximately 200MeV have also been estimated. The smallness of these masses in respect to those of hadrons seems to indicate that they do not constitute the only mass scale of the hadronic world, but that there should exist another scale parameter, independent of the quark mechanical masses, and symmetric of SU(3) [fr
Introduction to Chiral Symmetry
Energy Technology Data Exchange (ETDEWEB)
Koch, Volker [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
2017-05-09
These lectures are an attempt to a pedagogical introduction into the elementary concepts of chiral symmetry in nuclear physics. We will also discuss some effective chiral models such as the linear and nonlinear sigma model as well as the essential ideas of chiral perturbation theory. We will present some applications to the physics of ultrarelativistic heavy ion collisionsd.
Jinzenji, Masao
2018-01-01
This book furnishes a brief introduction to classical mirror symmetry, a term that denotes the process of computing Gromov–Witten invariants of a Calabi–Yau threefold by using the Picard–Fuchs differential equation of period integrals of its mirror Calabi–Yau threefold. The book concentrates on the best-known example, the quintic hypersurface in 4-dimensional projective space, and its mirror manifold. First, there is a brief review of the process of discovery of mirror symmetry and the striking result proposed in the celebrated paper by Candelas and his collaborators. Next, some elementary results of complex manifolds and Chern classes needed for study of mirror symmetry are explained. Then the topological sigma models, the A-model and the B-model, are introduced. The classical mirror symmetry hypothesis is explained as the equivalence between the correlation function of the A-model of a quintic hyper-surface and that of the B-model of its mirror manifold. On the B-model side, the process of construct...
Approximate symmetries of Hamiltonians
Chubb, Christopher T.; Flammia, Steven T.
2017-08-01
We explore the relationship between approximate symmetries of a gapped Hamiltonian and the structure of its ground space. We start by considering approximate symmetry operators, defined as unitary operators whose commutators with the Hamiltonian have norms that are sufficiently small. We show that when approximate symmetry operators can be restricted to the ground space while approximately preserving certain mutual commutation relations. We generalize the Stone-von Neumann theorem to matrices that approximately satisfy the canonical (Heisenberg-Weyl-type) commutation relations and use this to show that approximate symmetry operators can certify the degeneracy of the ground space even though they only approximately form a group. Importantly, the notions of "approximate" and "small" are all independent of the dimension of the ambient Hilbert space and depend only on the degeneracy in the ground space. Our analysis additionally holds for any gapped band of sufficiently small width in the excited spectrum of the Hamiltonian, and we discuss applications of these ideas to topological quantum phases of matter and topological quantum error correcting codes. Finally, in our analysis, we also provide an exponential improvement upon bounds concerning the existence of shared approximate eigenvectors of approximately commuting operators under an added normality constraint, which may be of independent interest.
Molecular symmetry and spectroscopy
Bunker, Philip; Jensen, Per
2006-01-01
The first edition, by P.R. Bunker, published in 1979, remains the sole textbook that explains the use of the molecular symmetry group in understanding high resolution molecular spectra. Since 1979 there has been considerable progress in the field and a second edition is required; the original author has been joined in its writing by Per Jensen. The Material of the first edition has been reorganized and much has been added. The molecular symmetry group is now introduced early on, and the explanation of how to determine nuclear spin statistical weights has been consolidated in one chapter, after groups, symmetry groups, character tables and the Hamiltonian have been introduced. A description of the symmetry in the three-dimensional rotation group K(spatial), irreducible spherical tensor operators, and vector coupling coefficients is now included. The chapters on energy levels and selection rules contain a great deal of material that was not in the first edition (much of it was undiscovered in 1979), concerning ...
Introduction to chiral symmetry
International Nuclear Information System (INIS)
Koch, V.
1996-01-01
These lectures are an attempt to a pedagogical introduction into the elementary concepts of chiral symmetry in nuclear physics. Effective chiral models such as the linear and nonlinear sigma model will be discussed as well as the essential ideas of chiral perturbation theory. Some applications to the physics of ultrarelativistic heavy ion collisions will be presented
Pels, D.L.
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
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...
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 4; Issue 10. Groups and Symmetry: A Guide to Discovering Mathematics. Geetha Venkataraman. Book Review Volume 4 Issue 10 October 1999 pp 91-92. Fulltext. Click here to view fulltext PDF. Permanent link:
International Nuclear Information System (INIS)
Sezgin, E.
1991-08-01
We review the structure of W ∞ algebras, their super and topological extensions, and their contractions down to (super) w ∞ . Emphasis is put on the field theoretic realizations of these algebras. We also review the structure of w ∞ and W ∞ gravities and comment on various applications of W ∞ symmetry. (author). 42 refs
International Nuclear Information System (INIS)
Hojman, Sergio A.
1996-01-01
The purpose of these lectures is to present some of the ways in which non-Noetherian symmetries are used in contemporary mathematical physics. These include, among others, obtaining conservation laws for dynamical systems, solving non-linear problems, getting alternative Lagrangians for systems of differential equations and constructing symplectic structures and Hamiltonians for dynamical systems starting from scratch
Detection symmetry and asymmetry
du Buf, J.M.H.
1991-01-01
Experiments were performed on the detection symmetry and asymmetry of incremental and decremental disks, as a function of both disk diameter and duration. It was found that, for a background luminance of 300cd.m-2, thresholds of dynamic (briefly presented) foveal disks are symmetrical for all
International Nuclear Information System (INIS)
Stern, J.
2000-01-01
The problem of a uniform description of symmetries, their dynamic disturbing and the structure of the vacuum is discussed. The role which problems of this kind played in searching for and understanding the Standard Model of elementary particles from the 1960s till now is also highlighted. (Z.J.)
Fields, symmetries, and quarks
International Nuclear Information System (INIS)
Mosel, U.
1989-01-01
'Fields, symmetries, and quarks' covers elements of quantum field theory, symmetries, gauge field theories and phenomenological descriptions of hadrons, with special emphasis on topics relevant to nuclear physics. It is aimed at nuclear physicists in general and at scientists who need a working knowledge of field theory, symmetry principles of elementary particles and their interactions and the quark structure of hadrons. The book starts out with an elementary introduction into classical field theory and its quantization. As gauge field theories require a working knowledge of global symmetries in field theories this topic is then discussed in detail. The following part is concerned with the general structure of gauge field theories and contains a thorough discussion of the still less widely known features of Non-Abelian gauge field theories. Quantum Chromodynamics (QCD), which is important for the understanding of hadronic matter, is discussed in the next section together with the quark compositions of hadrons. The last two chapters give a detailed discussion of phenomenological bag-models. The MIT bag is discussed, so that all theoretical calculations can be followed step by step. Since in all other bag-models the calculational methods and steps are essentially identical, this chapter should enable the reader to actually perform such calculations unaided. A last chapter finally discusses the topological bag-models which have become quite popular over the last few years. (orig.)
Symmetry of priapulids (Priapulida). 1. Symmetry of adults.
Adrianov, A V; Malakhov, V V
2001-02-01
Priapulids possess a radial symmetry that is remarkably reflected in both external morphology and internal anatomy. It results in the appearance of 25-radial (a number divisible by five) symmetry summarized as a combination of nonaradial, octaradial, and octaradial (9+8+8) symmetries of scalids. The radial symmetry is a secondary appearance considered as an evolutionary adaptation to a lifestyle within the three-dimensional environment of bottom sediment. The eight anteriormost, or primary, scalids retain their particular position because of their innervation directly from the circumpharyngeal brain. As a result of a combination of the octaradial symmetry of primary scalids, pentaradial symmetry of teeth, and the 25-radial symmetry of scalids, the initial bilateral symmetry remains characterized by the single sagittal plane. Copyright 2001 Wiley-Liss, Inc.
Computational Power of Symmetry-Protected Topological Phases.
Stephen, David T; Wang, Dong-Sheng; Prakash, Abhishodh; Wei, Tzu-Chieh; Raussendorf, Robert
2017-07-07
We consider ground states of quantum spin chains with symmetry-protected topological (SPT) order as resources for measurement-based quantum computation (MBQC). We show that, for a wide range of SPT phases, the computational power of ground states is uniform throughout each phase. This computational power, defined as the Lie group of executable gates in MBQC, is determined by the same algebraic information that labels the SPT phase itself. We prove that these Lie groups always contain a full set of single-qubit gates, thereby affirming the long-standing conjecture that general SPT phases can serve as computationally useful phases of matter.
Symmetry and bifurcations of momentum mappings
Energy Technology Data Exchange (ETDEWEB)
Arms, J.M.; Marsden, J.E.; Moncrief, V.
1981-01-01
The zero set of a momentum mapping is shown to have a singularity at each point with symmetry. The zero set is diffeomorphic to the product of a manifold and the zero set of a homogeneous quadratic function. The proof uses the Kuranishi theory of deformations. Among the applications, it is shown that the set of all solutions of the Yang-Mills equations on a Lorentz manifold has a singularity at any solution with symmetry, in the sense of a pure gauge symmetry. Similarly, the set of solutions of Einstein's equations has a singularity at any solution that has spacelike Killing fields, provided the spacetime has a compact Cauchy surface.
Low lying magnetic dipole strength distribution in 176Hf
International Nuclear Information System (INIS)
Kuliev, A. A.; Ertugral, F.; Yakut, H.; Bektasoglu, M.; Guliyev, E.
2006-01-01
In this study the scissors mode 1 + states are systematically investigated within the rotational invariant Quasiparticle Random Phase Approximation (QRPA) for 1 76Hf isotopes. We consider the 1 + vibrations generated by the isovector spin-spin interactions and the isoscalar (h 0 ) and isovector (h 1 ) quadrupole type separable forces restoring the broken symmetry by a deformed mean field. It has been shown that restoration of the broken rotational symmetry of the Hamiltonian essentially decreases the B(M1) value of the low lying 1 + states and increases the collectivization of the scissors mode excitations in the spectroscopic energy region. Agreement between the calculated mean excitation energies as well as the summed B(M1) value of the scissors mode excitations and the available experimental data of 1 76Hf is rather good. For instance, distributions of the calculated B(M1) transition strengths in the 1 76 Hf isotopes with respect to K π =1 + excitations is represented in Figure. Thus, we see that the models which use the Hamiltonian with broken rotational symmetry strongly overestimate the M1 strength at low energy. These results indicate an importance of the models which are free from the low-energy spurious states. The marked differences between the results for 1 + states, calculated in rotational invariant (RI) and non-rotational invariant (NRI) model indicate the importance of the approaches which are free from spurious low-energy solutions. A separation of the rotational state from the 1 + states changes somewhat the distribution of the B(M1) strength in the spectroscopic energy region and increases the fragmentation of the scissors mode 1 + excitations in agreement with the experimental data
Exceptional quantum subgroups for the rank two Lie algebras B2 and G2
Coquereaux, R.; Tahri, E.H.
2010-01-01
Exceptional modular invariants for the Lie algebras B2 (at levels 2,3,7,12) and G2 (at levels 3,4) can be obtained from conformal embeddings. We determine the associated alge bras of quantum symmetries and discover or recover, as a by-product, the graphs describing exceptional quantum subgroups of type B2 or G2 which encode their module structure over the associated fusion category. Global dimensions are given.
Lie Group Classification of a Generalized Lane-Emden Type System in Two Dimensions
Directory of Open Access Journals (Sweden)
Motlatsi Molati
2012-01-01
Full Text Available The aim of this work is to perform a complete Lie symmetry classification of a generalized Lane-Emden type system in two dimensions which models many physical phenomena in biological and physical sciences. The classical approach of group classification is employed for classification. We show that several cases arise in classifying the arbitrary parameters, the forms of which include amongst others the power law nonlinearity, and exponential and quadratic forms.
Spinor Structure and Internal Symmetries
Varlamov, V. V.
2015-10-01
Spinor structure and internal symmetries are considered within one theoretical framework based on the generalized spin and abstract Hilbert space. Complex momentum is understood as a generating kernel of the underlying spinor structure. It is shown that tensor products of biquaternion algebras are associated with the each irreducible representation of the Lorentz group. Space-time discrete symmetries P, T and their combination PT are generated by the fundamental automorphisms of this algebraic background (Clifford algebras). Charge conjugation C is presented by a pseudoautomorphism of the complex Clifford algebra. This description of the operation C allows one to distinguish charged and neutral particles including particle-antiparticle interchange and truly neutral particles. Spin and charge multiplets, based on the interlocking representations of the Lorentz group, are introduced. A central point of the work is a correspondence between Wigner definition of elementary particle as an irreducible representation of the Poincaré group and SU(3)-description (quark scheme) of the particle as a vector of the supermultiplet (irreducible representation of SU(3)). This correspondence is realized on the ground of a spin-charge Hilbert space. Basic hadron supermultiplets of SU(3)-theory (baryon octet and two meson octets) are studied in this framework. It is shown that quark phenomenologies are naturally incorporated into presented scheme. The relationship between mass and spin is established. The introduced spin-mass formula and its combination with Gell-Mann-Okubo mass formula allows one to take a new look at the problem of mass spectrum of elementary particles.
Dual symmetry in gauge theories
International Nuclear Information System (INIS)
Koshkarov, A.L.
1997-01-01
Continuous dual symmetry in electrodynamics, Yang-Mills theory and gravitation is investigated. Dual invariant which leads to badly nonlinear motion equations is chosen as a Lagrangian of the pure classical dual nonlinear electrodynamics. In a natural manner some dual angle which is determined by the electromagnetic strengths at the point of the time-space appears in the model. Motion equations may well be interpreted as the equations of the standard Maxwell theory with source. Alternative interpretation is the quasi-Maxwell linear theory with magnetic charge. Analogous approach is possible in the Yang-Mills theory. In this case the dual-invariant non-Abelian theory motion equations possess the same instanton solutions as the conventional Yang-Mills equations have. An Abelian two-parameter dual group is found to exist in gravitation. Irreducible representations have been obtained: the curvature tensor was expanded into the sum of twice anti-self-dual and self-dual parts. Gravitational instantons are defined as (real )solutions to the usual duality equations. Central symmetry solutions to these equations are obtained. The twice anti-self-dual part of the curvature tensor may be used for introduction of new gravitational equations generalizing Einstein''s equations. However, the theory obtained reduces to the conformal-flat Nordstroem theory
Topological Poisson Sigma models on Poisson-Lie groups
International Nuclear Information System (INIS)
Calvo, Ivan; Falceto, Fernando; Garcia-Alvarez, David
2003-01-01
We solve the topological Poisson Sigma model for a Poisson-Lie group G and its dual G*. We show that the gauge symmetry for each model is given by its dual group that acts by dressing transformations on the target. The resolution of both models in the open geometry reveals that there exists a map from the reduced phase of each model (P and P*) to the main symplectic leaf of the Heisenberg double (D 0 ) such that the symplectic forms on P, P* are obtained as the pull-back by those maps of the symplectic structure on D 0 . This uncovers a duality between P and P* under the exchange of bulk degrees of freedom of one model with boundary degrees of freedom of the other one. We finally solve the Poisson Sigma model for the Poisson structure on G given by a pair of r-matrices that generalizes the Poisson-Lie case. The Hamiltonian analysis of the theory requires the introduction of a deformation of the Heisenberg double. (author)
Integrable finite-dimensional systems related to Lie algebras
International Nuclear Information System (INIS)
Olshanetsky, M.A.; Perelomov, A.M.
1979-01-01
Some solvable finite-dimensional classical and quantum systems related to the Lie algebras are considered. The dynamics of these systems is closely related to free motion on symmetric spaces. In specific cases the systems considered describe the one-dimensional n-body problem recently considered by many authors. The review represents from general and universal point of view the results obtained during the last few years. Besides, it contains some results both of physical and mathematical type
Dynamical symmetries of the shell model
International Nuclear Information System (INIS)
Van Isacker, P.
2000-01-01
The applications of spectrum generating algebras and of dynamical symmetries in the nuclear shell model are many and varied. They stretch back to Wigner's early work on the supermultiplet model and encompass important landmarks in our understanding of the structure of the atomic nucleus such as Racah's SU(2) pairing model and Elliot's SU(3) rotational model. One of the aims of this contribution has been to show the historical importance of the idea of dynamical symmetry in nuclear physics. Another has been to indicate that, in spite of being old, this idea continues to inspire developments that are at the forefront of today's research in nuclear physics. It has been argued in this contribution that the main driving features of nuclear structure can be represented algebraically but at the same time the limitations of the symmetry approach must be recognised. It should be clear that such approach can only account for gross properties and that any detailed description requires more involved numerical calculations of which we have seen many fine examples during this symposium. In this way symmetry techniques can be used as an appropriate starting point for detailed calculations. A noteworthy example of this approach is the pseudo-SU(3) model which starting from its initial symmetry Ansatz has grown into an adequate and powerful description of the nucleus in terms of a truncated shell model. (author)
Symmetries in physics and harmonics
International Nuclear Information System (INIS)
Kolk, D.
2006-01-01
In this book the symmetries of elementary particles are described in relation to the rules of harmonics in music. The selection rules are described in connections with harmonic intervals. Also symmetry breaking is considered in this framework. (HSI)
Scaling symmetries, conservation laws and action principles in one-dimensional gas dynamics
International Nuclear Information System (INIS)
Webb, G M; Zank, G P
2009-01-01
Scaling symmetries of the planar, one-dimensional gas dynamic equations with adiabatic index γ are used to obtain Lagrangian and Eulerian conservation laws associated with the symmetries. The known Eulerian symmetry operators for the scaling symmetries are converted to the Lagrangian form, in which the Eulerian spatial position of the fluid element is given in terms of the Lagrangian fluid labels. Conditions for a linear combination of the three scaling symmetries to be a divergence or variational symmetry of the action are established. The corresponding Lagrangian and Eulerian form of the conservation laws are determined by application of Noether's theorem. A nonlocal conservation law associated with the scaling symmetries is obtained by applying a nonlocal symmetry operator to the scaling symmetry-conserved vector. An action principle incorporating known conservation laws using Lagrangian constraints is developed. Noether's theorem for the constrained action principle gives the same formulas for the conserved vector as the classical Noether theorem, except that the Lie symmetry vector field now includes the effects of nonlocal potentials. Noether's theorem for the constrained action principle is used to obtain nonlocal conservation laws. The scaling symmetry conservation laws only apply for special forms of the entropy of the gas.
Dynamical symmetries of semi-linear Schrodinger and diffusion equations
International Nuclear Information System (INIS)
Stoimenov, Stoimen; Henkel, Malte
2005-01-01
Conditional and Lie symmetries of semi-linear 1D Schrodinger and diffusion equations are studied if the mass (or the diffusion constant) is considered as an additional variable. In this way, dynamical symmetries of semi-linear Schrodinger equations become related to the parabolic and almost-parabolic subalgebras of a three-dimensional conformal Lie algebra (conf 3 ) C . We consider non-hermitian representations and also include a dimensionful coupling constant of the non-linearity. The corresponding representations of the parabolic and almost-parabolic subalgebras of (conf 3 ) C are classified and the complete list of conditionally invariant semi-linear Schrodinger equations is obtained. Possible applications to the dynamical scaling behaviour of phase-ordering kinetics are discussed
Nucci, M. C.; Leach, P. G. L.
2007-09-01
We apply the techniques of Lie's symmetry analysis to a caricature of the simplified multistrain model of Castillo-Chavez and Feng [C. Castillo-Chavez, Z. Feng, To treat or not to treat: The case of tuberculosis, J. Math. Biol. 35 (1997) 629-656] for the transmission of tuberculosis and the coupled two-stream vector-based model of Feng and Velasco-Hernandez [Z. Feng, J.X. Velasco-Hernandez, Competitive exclusion in a vector-host model for the dengue fever, J. Math. Biol. 35 (1997) 523-544] to identify the combinations of parameters which lead to the existence of nontrivial symmetries. In particular we identify those combinations which lead to the possibility of the linearization of the system and provide the corresponding solutions. Many instances of additional symmetry are analyzed.
Introduction to the theory of Lie groups
Godement, Roger
2017-01-01
This textbook covers the general theory of Lie groups. By first considering the case of linear groups (following von Neumann's method) before proceeding to the general case, the reader is naturally introduced to Lie theory. Written by a master of the subject and influential member of the Bourbaki group, the French edition of this textbook has been used by several generations of students. This translation preserves the distinctive style and lively exposition of the original. Requiring only basics of topology and algebra, this book offers an engaging introduction to Lie groups for graduate students and a valuable resource for researchers.
Vertex ring-indexed Lie algebras
International Nuclear Information System (INIS)
Fairlie, David; Zachos, Cosmas
2005-01-01
Infinite-dimensional Lie algebras are introduced, which are only partially graded, and are specified by indices lying on cyclotomic rings. They may be thought of as generalizations of the Onsager algebra, but unlike it, or its sl(n) generalizations, they are not subalgebras of the loop algebras associated with sl(n). In a particular interesting case associated with sl(3), their indices lie on the Eisenstein integer triangular lattice, and these algebras are expected to underlie vertex operator combinations in CFT, brane physics, and graphite monolayers
Representations of some quantum tori Lie subalgebras
International Nuclear Information System (INIS)
Jiang, Jingjing; Wang, Song
2013-01-01
In this paper, we define the q-analog Virasoro-like Lie subalgebras in x ∞ =a ∞ (b ∞ , c ∞ , d ∞ ). The embedding formulas into x ∞ are introduced. Irreducible highest weight representations of A(tilde sign) q , B(tilde sign) q , and C(tilde sign) q -series of the q-analog Virasoro-like Lie algebras in terms of vertex operators are constructed. We also construct the polynomial representations of the A(tilde sign) q , B(tilde sign) q , C(tilde sign) q , and D(tilde sign) q -series of the q-analog Virasoro-like Lie algebras.
Quartic trace identity for exceptional Lie algebras
International Nuclear Information System (INIS)
Okubo, S.
1979-01-01
Let X be a representation matrix of generic element x of a simple Lie algebra in generic irreducible representation ]lambda] of the Lie algebra. Then, for all exceptional Lie algebras as well as A 1 and A 2 , we can prove the validity of a quartic trace identity Tr(X 4 ) =K (lambda)[Tr(X 2 )] 2 , where the constant K (lambda) depends only upon the irreducible representation ]lambda], and its explicit form is calculated. Some applications of second and fourth order indices have also been discussed
Unified Symmetry of Hamilton Systems
International Nuclear Information System (INIS)
Xu Xuejun; Qin Maochang; Mei Fengxiang
2005-01-01
The definition and the criterion of a unified symmetry for a Hamilton system are presented. The sufficient condition under which the Noether symmetry is a unified symmetry for the system is given. A new conserved quantity, as well as the Noether conserved quantity and the Hojman conserved quantity, deduced from the unified symmetry, is obtained. An example is finally given to illustrate the application of the results.
Quantum symmetries in particle interactions
International Nuclear Information System (INIS)
Shirkov, D.V.
1983-01-01
The concept of a quantum symmetry is introduced as a symmetry in the formulation of which quantum representations and specific quantum notions are used essentially. Three quantum symmetry principles are discussed: the principle of renormalizability (possibly super-renormalizability), the principle of local gauge symmetry, and the principle of supersymmetry. It is shown that these principles play a deterministic role in the development of quantum field theory. Historically their use has led to ever stronger restrictions on the interaction mechanism of quantum fields
Symmetry and topology in evolution
International Nuclear Information System (INIS)
Lukacs, B.; Berczi, S.; Molnar, I.; Paal, G.
1991-10-01
This volume contains papers of an interdisciplinary symposium on evolution. The aim of this symposium, held in Budapest, Hungary, 28-29 May 1991, was to clear the role of symmetry and topology at different levels of the evolutionary processes. 21 papers were presented, their topics included evolution of the Universe, symmetry of elementary particles, asymmetry of the Earth, symmetry and asymmetry of biomolecules, symmetry and topology of lining objects, human asymmetry etc. (R.P.)
Jurco, Branislav
2011-01-01
Let g be a simplicial Lie algebra with Moore complex Ng of length k. Let G be the simplicial Lie group integrating g, which is simply connected in each simplicial level. We use the 1-jet of the classifying space of G to construct, starting from g, a Lie k-algebra L. The so constructed Lie k-algebra L is actually a differential graded Lie algebra. The differential and the brackets are explicitly described in terms (of a part) of the corresponding k-hypercrossed complex structure of Ng. The res...
Lie-Nambu and Lie-Poisson structures in linear and nonlinear quantum mechanics
International Nuclear Information System (INIS)
Czachor, M.
1996-01-01
Space of density matrices in quantum mechanics can be regarded as a Poisson manifold with the dynamics given by certain Lie-Poisson bracket corresponding to an infinite dimensional Lie algebra. The metric structure associated with this Lie algebra is given by a metric tensor which is not equivalent to the Cartan-Killing metric. The Lie-Poisson bracket can be written in a form involving a generalized (Lie-)Nambu bracket. This bracket can be used to generate a generalized, nonlinear and completely integrable dynamics of density matrices. (author)
International Nuclear Information System (INIS)
Sheftel', M.B.
1997-01-01
The basics of modern group analysis of different equations are presented. The group analysis produces in a natural way the variables, which are most suitable for a problem of question, and also the associated differential-geometric structures, such as pseudo Riemann geometry, connections, Hamiltonian and Lagrangian formalism
P-Adic analysis and the transfinite E8 exceptional Lie symmetry group unification
Energy Technology Data Exchange (ETDEWEB)
El Naschie, M.S. [King Abdullah Institute for Nano and Advanced Technology, KSU, Riyadh (Saudi Arabia)], E-mail: Chaossf@aol.com
2008-11-15
In P-Adic analysis like in a fractal Cantorian space there is no absolute scale. P-Adic analysis with its prime numbers base is the mathematical quarks of the exceptional E8 and E-infinity. The P-Adic space permits the use of Weyl original spacetime gauge theory which is the rationale behind E-infinity.
P-Adic analysis and the transfinite E8 exceptional Lie symmetry group unification
International Nuclear Information System (INIS)
El Naschie, M.S.
2008-01-01
In P-Adic analysis like in a fractal Cantorian space there is no absolute scale. P-Adic analysis with its prime numbers base is the mathematical quarks of the exceptional E8 and E-infinity. The P-Adic space permits the use of Weyl original spacetime gauge theory which is the rationale behind E-infinity
Similarity and symmetry methods applications in elasticity and mechanics of materials
Mladenov, Ivaïlo
2014-01-01
The principle aim of the book is to present a self-contained, modern account of similarity and symmetry methods, which are important mathematical tools for both physicists, engineers and applied mathematicians. The idea is to provide a balanced presentation of the mathematical techniques and applications of symmetry methods in mathematics, physics and engineering. That is why it includes recent developments and many examples in finding systematically conservation laws, local and nonlocal symmetries for ordinary and partial differential equations. The role of continuous symmetries in classical and quantum field theories is exposed at a technical level accessible even for non specialists. The importance of symmetries in continuum mechanics and mechanics of materials is highlighted through recent developments, such as the construction of constitutive models for various materials combining Lie symmetries with experimental data. As a whole this book is a unique collection of contributions from experts in the field...
Charge independence and charge symmetry
Energy Technology Data Exchange (ETDEWEB)
Miller, G A [Washington Univ., Seattle, WA (United States). Dept. of Physics; van Oers, W T.H. [Manitoba Univ., Winnipeg, MB (Canada). Dept. of Physics; [TRIUMF, Vancouver, BC (Canada)
1994-09-01
Charge independence and charge symmetry are approximate symmetries of nature, violated by the perturbing effects of the mass difference between up and down quarks and by electromagnetic interactions. The observations of the symmetry breaking effects in nuclear and particle physics and the implications of those effects are reviewed. (author). 145 refs., 3 tabs., 11 figs.
Charge independence and charge symmetry
International Nuclear Information System (INIS)
Miller, G.A.
1994-09-01
Charge independence and charge symmetry are approximate symmetries of nature, violated by the perturbing effects of the mass difference between up and down quarks and by electromagnetic interactions. The observations of the symmetry breaking effects in nuclear and particle physics and the implications of those effects are reviewed. (author). 145 refs., 3 tabs., 11 figs
Symmetry energy in nuclear surface
International Nuclear Information System (INIS)
Danielewicz, P.; Lee, Jenny
2009-01-01
Interplay between the dependence of symmetry energy on density and the variation of nucleonic densities across nuclear surface is discussed. That interplay gives rise to the mass dependence of the symmetry coefficient in an energy formula. Charge symmetry of the nuclear interactions allows to introduce isoscalar and isovector densities that are approximately independent of the magnitude of neutron-proton asymmetry. (author)
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.
Group analysis and renormgroup symmetries
International Nuclear Information System (INIS)
Kovalev, V.F.; Pustovalov, V.V.; Shirkov, D.V.
1996-01-01
An original regular approach to constructing special type symmetries for boundary-value problems, namely renormgroup symmetries, is presented. Different methods of calculating these symmetries based on modern group analysis are described. An application of the approach to boundary value problems is demonstrated with the help of a simple mathematical model. 35 refs
On the algebraic realization of SU(4) symmetry
International Nuclear Information System (INIS)
Asatryan, G.M.; Zaslavsky, A.N.
1976-01-01
A possibility of nonlinear realization of the symmetry with linearization on the SU(4)xYxC group is discussed. Algebraic properties of SU(4) are restored from the Weinberg condition: amplitudes of goldstone scattering on particles should have a reasonable (as in the Regge theory) asymptotic behaviour. In this case the breaking appears to be minimal. Large values of psi meson masses lead to high-lying charmed trajectories in the SU(4) algebraic realization
Canonical forms of tensor representations and spontaneous symmetry breaking
International Nuclear Information System (INIS)
Cummins, C.J.
1986-01-01
An algorithm for constructing canonical forms for any tensor representation of the classical compact Lie groups is given. This method is used to find a complete list of the symmetry breaking patterns produced by Higgs fields in the third-rank antisymmetric representations of U(n), SU(n) and SO(n) for n<=7. A simple canonical form is also given for kth-rank symmetric tensor representations. (author)
DEFF Research Database (Denmark)
Agarwal, Pankaj K.; Arge, Lars Allan; Erickson, Jeff
2003-01-01
We propose three indexing schemes for storing a set S of N points in the plane, each moving along a linear trajectory, so that any query of the following form can be answered quickly: Given a rectangle R and a real value t, report all K points of S that lie inside R at time t. We first present an...
Reformulation of the symmetries of first-order general relativity
Montesinos, Merced; González, Diego; Celada, Mariano; Díaz, Bogar
2017-10-01
We report a new internal gauge symmetry of the n-dimensional Palatini action with cosmological term (n>3 ) that is the generalization of three-dimensional local translations. This symmetry is obtained through the direct application of the converse of Noether’s second theorem on the theory under consideration. We show that diffeomorphisms can be expressed as linear combinations of it and local Lorentz transformations with field-dependent parameters up to terms involving the variational derivatives of the action. As a result, the new internal symmetry together with local Lorentz transformations can be adopted as the fundamental gauge symmetries of general relativity. Although their gauge algebra is open in general, it allows us to recover, without resorting to the equations of motion, the very well-known Lie algebra satisfied by translations and Lorentz transformations in three dimensions. We also report the analog of the new gauge symmetry for the Holst action with cosmological term, finding that it explicitly depends on the Immirzi parameter. The same result concerning its relation to diffeomorphisms and the open character of the gauge algebra also hold in this case. Finally, we consider the non-minimal coupling of a scalar field to gravity in n dimensions and establish that the new gauge symmetry is affected by this matter field. Our results indicate that general relativity in dimension greater than three can be thought of as a gauge theory.
Energy Technology Data Exchange (ETDEWEB)
Chomaz, Philippe [Grand Accelerateur National d`Ions Lourds (GANIL), 14 - Caen (France)
1998-12-31
In the world of infinitely small, the world of atoms, nuclei and particles, the quantum mechanics enforces its laws. The discovery of Quanta, this unbelievable castration of the Possible in grains of matter and radiation, in discrete energy levels compels us of thinking the Single to comprehend the Universal. Quantum Numbers, magic Numbers and Numbers sign the wave. The matter is vibration. To describe the music of the world one needs keys, measures, notes, rules and partition: one needs quantum mechanics. The particles reduce themselves not in material points as the scholars of the past centuries thought, but they must be conceived throughout the space, in the accomplishment of shapes of volumes. When Einstein asked himself whether God plays dice, there was no doubt among its contemporaries that if He exists He is a geometer. In a Nature reduced to Geometry, the symmetries assume their role in servicing the Harmony. The symmetries allow ordering the energy levels to make them understandable. They impose there geometrical rules to the matter waves, giving them properties which sometimes astonish us. Hidden symmetries, internal symmetries and newly conceived symmetries have to be adopted subsequently to the observation of some order in this world of Quanta. In turn, the symmetries provide new observables which open new spaces of observation 17 refs., 16 figs.
Neutrino mixing: from the broken μ-τ symmetry to the broken Friedberg–Lee symmetry
International Nuclear Information System (INIS)
Xing, Zhizhong
2007-01-01
I argue that the observed flavor structures of leptons and quarks might imply the existence of certain flavor symmetries. The latter should be a good starting point to build realistic models towards deeper understanding of the fermion mass spectra and flavor mixing patterns. The μ-τ permutation symmetry serves for such an example to interpret the almost maximal atmospheric neutrino mixing angle (θ 23 ~ 45°) and the strongly suppressed CHOOZ neutrino mixing angle (θ 13 < 10°). In this talk I like to highlight a new kind of flavor symmetry, the Friedberg–Lee symmetry, for the effective Majorana neutrino mass operator. Luo and I have shown that this symmetry can be broken in an oblique way, such that the lightest neutrino remains massless but an experimentally-favored neutrino mixing pattern is achievable. We get a novel prediction for θ 13 in the CP-conserving case: sinθ 13 = tanθ 12 |(1 - tanθ 23 )/(1 + tanθ 23 )|. Our scenario can simply be generalized to accommodate CP violation and be combined with the seesaw mechanism. Finally I stress the importance of probing possible effects of μ-τ symmetry breaking either in terrestrial neutrino oscillation experiments or with ultrahigh-energy cosmic neutrino telescopes. (author)
When is a lie acceptable? Work and private life lying acceptance depends on its beneficiary.
Cantarero, Katarzyna; Szarota, Piotr; Stamkou, Eftychia; Navas, Marisol; Dominguez Espinosa, Alejandra Del Carmen
2018-01-01
In this article we show that when analyzing attitude towards lying in a cross-cultural setting, both the beneficiary of the lie (self vs other) and the context (private life vs. professional domain) should be considered. In a study conducted in Estonia, Ireland, Mexico, The Netherlands, Poland, Spain, and Sweden (N = 1345), in which participants evaluated stories presenting various types of lies, we found usefulness of relying on the dimensions. Results showed that in the joint sample the most acceptable were other-oriented lies concerning private life, then other-oriented lies in the professional domain, followed by egoistic lies in the professional domain; and the least acceptance was shown for egoistic lies regarding one's private life. We found a negative correlation between acceptance of a behavior and the evaluation of its deceitfulness.
Dark discrete gauge symmetries
International Nuclear Information System (INIS)
Batell, Brian
2011-01-01
We investigate scenarios in which dark matter is stabilized by an Abelian Z N discrete gauge symmetry. Models are surveyed according to symmetries and matter content. Multicomponent dark matter arises when N is not prime and Z N contains one or more subgroups. The dark sector interacts with the visible sector through the renormalizable kinetic mixing and Higgs portal operators, and we highlight the basic phenomenology in these scenarios. In particular, multiple species of dark matter can lead to an unconventional nuclear recoil spectrum in direct detection experiments, while the presence of new light states in the dark sector can dramatically affect the decays of the Higgs at the Tevatron and LHC, thus providing a window into the gauge origin of the stability of dark matter.
Symmetries and microscopic physics
International Nuclear Information System (INIS)
Blaizot, J.P.
1997-01-01
This book is based on a course of lectures devoted to the applications of group theory to quantum physics. The purpose is to give students a precise idea of general principles involving the concept of symmetry and to present practical methods used to calculate physical properties derived from symmetries. The first chapter is an introduction to the main results of group theory, 2 chapters highlight principles and methods concerning geometrical transformations in the space of states, state degeneracy and perturbation theory. The last 4 chapters investigate the applications of these methods to atom physics, nuclear structure and elementary particles. A chapter is devoted to the atom of hydrogen and another to the isospin. Numerous exercises and problems, some with their corrections, are proposed. (A.C.)
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.
Strong Electroweak Symmetry Breaking
Grinstein, Benjamin
2011-01-01
Models of spontaneous breaking of electroweak symmetry by a strong interaction do not have fine tuning/hierarchy problem. They are conceptually elegant and use the only mechanism of spontaneous breaking of a gauge symmetry that is known to occur in nature. The simplest model, minimal technicolor with extended technicolor interactions, is appealing because one can calculate by scaling up from QCD. But it is ruled out on many counts: inappropriately low quark and lepton masses (or excessive FCNC), bad electroweak data fits, light scalar and vector states, etc. However, nature may not choose the minimal model and then we are stuck: except possibly through lattice simulations, we are unable to compute and test the models. In the LHC era it therefore makes sense to abandon specific models (of strong EW breaking) and concentrate on generic features that may indicate discovery. The Technicolor Straw Man is not a model but a parametrized search strategy inspired by a remarkable generic feature of walking technicolor,...
Symmetry rules. How science and nature are founded on symmetry
Energy Technology Data Exchange (ETDEWEB)
Rosen, J.
2008-07-01
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. (orig.)
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.
A broken symmetry ontology: Quantum mechanics as a broken symmetry
International Nuclear Information System (INIS)
Buschmann, J.E.
1988-01-01
The author proposes a new broken symmetry ontology to be used to analyze the quantum domain. This ontology is motivated and grounded in a critical epistemological analysis, and an analysis of the basic role of symmetry in physics. Concurrently, he is led to consider nonheterogeneous systems, whose logical state space contains equivalence relations not associated with the causal relation. This allows him to find a generalized principle of symmetry and a generalized symmetry-conservation formalisms. In particular, he clarifies the role of Noether's theorem in field theory. He shows how a broken symmetry ontology already operates in a description of the weak interactions. Finally, by showing how a broken symmetry ontology operates in the quantum domain, he accounts for the interpretational problem and the essential incompleteness of quantum mechanics. He proposes that the broken symmetry underlying this ontological domain is broken dilation invariance
Lie-superalgebraical aspects of quantum statistics
International Nuclear Information System (INIS)
Palev, T.D.
1978-01-01
The Lie-superalgebraical properties of the ordinary quantum statistics are discussed with the aim of possible generalization in quantum theory and in theoretical physics. It is indicated that the algebra generated by n pairs of Fermi or paraFermi operators is isomorphic to the classical simple Lie algebra Bsub(n) of the SO(2n+1) orthogonal group, whereas n pairs of Bose or paraBose operators generate the simple orthosympletic superalgebra B(O,n). The transition to infinite number of creation and annihilation operators (n → infinity) does not change a superalgebraic structure. Hence, ordinary Bose and Fermi quantization can be considered as quantization over definite irreducible representations of two simple Lie superalgebras. The idea is given of how one can introduce creation and annihilation operators that satisfy the second quantization postulates and generate other simple Lie superalgebras
Multiplication: From Thales to Lie1
Indian Academy of Sciences (India)
Addition. To describe the geometric constructions of addition, as ..... general, we could apply the implicit function theorem of calculus to solve locally the defining ... and whose multiplication and inverse are analytic maps, is called a Lie group.
International Nuclear Information System (INIS)
Bunakov, V.E.; Ivanov, I.B.
1999-01-01
Connections between the symmetries of Hamiltonian systems in classical and quantum mechanics, on one hand, and their regularity or chaoticity, on the other hand, are considered. The quantum-chaoticity criterion that was proposed previously and which was borrowed from the theory of compound-nucleus resonances is used to analyze the quantum diamagnetic Kepler problem - that is, the motion of a spinless charged particle in a Coulomb and a uniform magnetic field
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.
International Nuclear Information System (INIS)
Herrero, O F
2010-01-01
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.
New examples of continuum graded Lie algebras
International Nuclear Information System (INIS)
Savel'ev, M.V.
1989-01-01
Several new examples of continuum graded Lie algebras which provide an additional elucidation of these algebras are given. Here, in particular, the Kac-Moody algebras, the algebra S 0 Diff T 2 of infinitesimal area-preserving diffeomorphisms of the torus T 2 , the Fairlie, Fletcher and Zachos sine-algebras, etc., are described as special cases of the cross product Lie algebras. 8 refs
Using Noether symmetries to specify f(R) gravity
International Nuclear Information System (INIS)
Paliathanasis, Andronikos
2013-01-01
A detailed study of the modified gravity, f(R) models is performed, using the fact that the Noether point symmetries of these models are geometric symmetries of the mini su-perspace of the theory. It is shown that the requirement that the field equations admit Noether point symmetries selects definite models in a self-consistent way. As an application in Cosmology we consider the Friedman -Robertson-Walker spacetime and show that the only cosmological model which is integrable via Noether point symmetries is the (R b − 2Λ) c model, which generalizes the Lambda Cosmology. Furthermore using the corresponding Noether integrals we compute the analytic form of the main cosmological functions
Continuous symmetry from Euclid to Klein
Barker, William
2007-01-01
The fundamental idea of geometry is that of symmetry. With that principle as the starting point, Barker and Howe begin an insightful and rewarding study of Euclidean geometry. The primary focus of the book is on transformations of the plane. The transformational point of view provides both a path for deeper understanding of traditional synthetic geometry and tools for providing proofs that spring from a consistent point of view. As a result, proofs become more comprehensible, as techniques can be used and reused in similar settings. The approach to the material is very concrete, with complete
Symmetry methods for option pricing
Davison, A. H.; Mamba, S.
2017-06-01
We obtain a solution of the Black-Scholes equation with a non-smooth boundary condition using symmetry methods. The Black-Scholes equation along with its boundary condition are first transformed into the one dimensional heat equation and an initial condition respectively. We then find an appropriate general symmetry generator of the heat equation using symmetries and the fundamental solution of the heat equation. The symmetry generator is chosen such that the boundary condition is left invariant; the symmetry can be used to solve the heat equation and hence the Black-Scholes equation.
Introduction to symmetry and supersymmetry in quantum field theory
International Nuclear Information System (INIS)
Lopuszanski, J.
1988-01-01
This is a set of lecture notes given by the author at the Universities of Gottingen and Wroclaw. The text presents the axiomatic approach to field theory and studies in depth the concepts of symmetry and supersymmetry and their associated generators, currents and charges. It is intended as a one- semester course for graduate students in the field of mathematical physics and high energy physics. Contents: Introduction; Example of a Classical and Quantum Scalar Free Field Theory; Scene and Subject of the Drama. Axiom 1 and 2; Subject of the Drama; Principle of Relativity. Causality. Axiom 3, 4 and 5; Irreducibility of the Field Algebra and Scattering Theory. Axiom 6. Axiom O; Preliminaries about Physical Symmetries; Currents and Charges; Global Symmetries and Supersymmetries of the S - Matrix; Representations of the Super-Lie Algebra; The Case of Massless Particles; Fermionic Charges; Concluding Remarks
Soliton surfaces and generalized symmetries of integrable systems
International Nuclear Information System (INIS)
Grundland, A M; Riglioni, D; Post, S
2014-01-01
In this paper, we discuss some specific features of symmetries of integrable systems which can be used to construct the Fokas–Gel’fand formula for the immersion of 2D-soliton surfaces, associated with such systems, in Lie algebras. We establish a sufficient condition for the applicability of this formula. This condition requires the existence of two vector fields which generate a common symmetry of the initial system and its corresponding linear spectral problem. This means that these two fields have to be group-related and we determine an explicit form of this relation. It provides a criterion for the selection of symmetries suitable for use in the Fokas–Gel’fand formula. We include some examples illustrating its application. (paper)
Effective field theory of emergent symmetry breaking in deformed atomic nuclei
International Nuclear Information System (INIS)
Papenbrock, T; Weidenmüller, H A
2015-01-01
Spontaneous symmetry breaking in non-relativistic quantum systems has previously been addressed in the framework of effective field theory. Low-lying excitations are constructed from Nambu–Goldstone modes using symmetry arguments only. We extend that approach to finite systems. The approach is very general. To be specific, however, we consider atomic nuclei with intrinsically deformed ground states. The emergent symmetry breaking in such systems requires the introduction of additional degrees of freedom on top of the Nambu–Goldstone modes. Symmetry arguments suffice to construct the low-lying states of the system. In deformed nuclei these are vibrational modes each of which serves as band head of a rotational band. (paper)
New and old symmetries of the Maxwell and Dirac equations
International Nuclear Information System (INIS)
Fushchich, V.I.; Nikitin, A.G.
1983-01-01
The symmetry properties of Maxwell's equations for the electromagnetic field and also of the Dirac and Kemmer-Duffin-Petiau equations are analyzed. In the framework of a ''non-Lie'' approach it is shown that, besides the well-known invariance with respect to the conformal group and the Heaviside-Larmor-Rainich transformations, Maxwell's equations have an additional symmetry with respect to the group U(2)xU(2) and with respect to the 23-dimensional Lie algebra A 23 . The transformations of the additional symmetry are given by nonlocal (integro-differential) operators. The symmetry of the Dirac equation in the class of differential and integro-differential transformations is investigated. It is shown that this equation is invariant with respect to an 18-parameter group, which includes the Poincare group as a subgroup. A 28-parameter invariance group of the Kemmer-Duffin-Petiau equation is found. Finite transformations of the conformal group for a massless field with arbitrary spin are obtained. The explicit form of conformal transformations for the electromagnetic field and also for the Dirac and Weyl fields is given
Random-phase approximation and broken symmetry
International Nuclear Information System (INIS)
Davis, E.D.; Heiss, W.D.
1986-01-01
The validity of the random-phase approximation (RPA) in broken-symmetry bases is tested in an appropriate many-body system for which exact solutions are available. Initially the regions of stability of the self-consistent quasiparticle bases in this system are established and depicted in a 'phase' diagram. It is found that only stable bases can be used in an RPA calculation. This is particularly true for those RPA modes which are not associated with the onset of instability of the basis; it is seen that these modes do not describe any excited state when the basis is unstable, although from a formal point of view they remain acceptable. The RPA does well in a stable broken-symmetry basis provided one is not too close to a point where a phase transition occurs. This is true for both energies and matrix elements. (author)
To see symmetry in a forest of trees
International Nuclear Information System (INIS)
Chan, Chuan-Tsung; Kawamoto, Shoichi; Tomino, Dan
2014-01-01
The exact symmetry identities among four-point tree-level amplitudes of bosonic open string theory as derived by G.W. Moore are re-examined. The main focuses of this work are: (1) Explicit construction of kinematic configurations and a new polarization basis for the scattering processes. These setups simplify greatly the functional forms of the exact symmetry identities, and help us to extract easily high-energy limits of stringy amplitudes appearing in the exact identities. (2) Connection and comparison between D.J. Gross's high-energy stringy symmetry and the exact symmetry identities as derived by G.W. Moore. (3) Observation of symmetry patterns of stringy amplitudes with respect to the order of energy dependence in scattering amplitudes
Extended Galilean symmetries of non-relativistic strings
Energy Technology Data Exchange (ETDEWEB)
Batlle, Carles [Departament de Matemàtiques and IOC, Universitat Politècnica de Catalunya, EPSEVG,Av. V. Balaguer 1, E-08808 Vilanova i la Geltrú (Spain); Gomis, Joaquim; Not, Daniel [Departament de Física Quàntica i Astrofísica and Institut de Ciències del Cosmos (ICCUB),Universitat de Barcelona,Martí i Franquès 1, E-08028 Barcelona (Spain)
2017-02-09
We consider two non-relativistic strings and their Galilean symmetries. These strings are obtained as the two possible non-relativistic (NR) limits of a relativistic string. One of them is non-vibrating and represents a continuum of non-relativistic massless particles, and the other one is a non-relativistic vibrating string. For both cases we write the generator of the most general point transformation and impose the condition of Noether symmetry. As a result we obtain two sets of non-relativistic Killing equations for the vector fields that generate the symmetry transformations. Solving these equations shows that NR strings exhibit two extended, infinite dimensional space-time symmetries which contain, as a subset, the Galilean symmetries. For each case, we compute the associated conserved charges and discuss the existence of non-central extensions.
Normalization in Lie algebras via mould calculus and applications
Paul, Thierry; Sauzin, David
2017-11-01
We establish Écalle's mould calculus in an abstract Lie-theoretic setting and use it to solve a normalization problem, which covers several formal normal form problems in the theory of dynamical systems. The mould formalism allows us to reduce the Lie-theoretic problem to a mould equation, the solutions of which are remarkably explicit and can be fully described by means of a gauge transformation group. The dynamical applications include the construction of Poincaré-Dulac formal normal forms for a vector field around an equilibrium point, a formal infinite-order multiphase averaging procedure for vector fields with fast angular variables (Hamiltonian or not), or the construction of Birkhoff normal forms both in classical and quantum situations. As a by-product we obtain, in the case of harmonic oscillators, the convergence of the quantum Birkhoff form to the classical one, without any Diophantine hypothesis on the frequencies of the unperturbed Hamiltonians.
Enhanced α-Transfer population of the 2ms+ mixed-symmetry state in 52Ti
Ali, Fuad A.; Muecher, Dennis; Bildstein, Vinzenz; Greaves, Beau; Kilic, Ali. I.; Holt, Jason D.; Berner, Christian; Gernhaeuser, R.; Nowak, K.; Hellgartner, S.; Lutter, R.; Reichert, S.
2017-09-01
The residual nucleon-nucleon interaction plays a crucial role in nuclear structure physics. In spherical even-even nuclei the quadrupole interaction leads to so called proton-neutron mixed symmetry states, which are sensitive to the underlying subshell structure. We present new data using the MINIBALL germanium array. States in 52Ti were populated via the α-transfer reaction 48Ca(12C,8Be)52Ti using a 48Ca beam from the Maier-Leibnitz-Laboratory in Munich. In the frame work of IBM-2, Alonso et al. have shown that the population of the 2ms+ state is strictly forbidden for the alpha transfer from a doubly magic nucleus. In contrast, we measured a large relative cross section into the 22+ mixed-symmetry state in 52Ti relative to the 21+ state of 31.1(20) %. This value exceeds earlier measurements in the 140Ba nucleus, representing the case of a particular strong population of the 2ms,SUP>+ state. This points towards effects of core polarizations of 48Ca in the low-lying structure of 52Ti. We have performed ab-initio shell model calculations to understand the origin of the discovered discrepancies. Permanent Address: Department of Physics, College of Education, University of Sulaimani, P. O. Box 334, Sulaimani, Kurdistan Region, Iraq.
Test of the fermion dynamical symmetry model microscopy in the sd shell
International Nuclear Information System (INIS)
Halse, P.
1987-01-01
The recently formulated fermion dynamical symmetry model treats low-lying collective levels as states classified in a pseudo-orbit pseudo-spin (k-i) basis having either k = 1 and zero i seniority, or i = (3/2) and zero k seniority. The validity of this suggestion, which has not previously been subjected to a microscopic examination, is determined for even-even nuclei in the sd shell, for which the model is phenomenologically successful, by comparing these states with the eigenfunctions of a realistic Hamiltonian. Most low-lying levels are almost orthogonal to the fermion dynamical symmetry model zero seniority subspaces
Symmetry Breaking in a random passive scalar
Kilic, Zeliha; McLaughlin, Richard; Camassa, Roberto
2017-11-01
We consider the evolution of a decaying passive scalar in the presence of a gaussian white noise fluctuating shear flow. We focus on deterministic initial data and establish the short, intermediate, and long time symmetry properties of the evolving point wise probability measure for the random passive scalar. Analytical results are compared directly to Monte Carlo simulations. Time permitting we will compare the predictions to experimental observations.
Analytic progress on exact lattice chiral symmetry
International Nuclear Information System (INIS)
Kikukawa, Y.
2002-01-01
Theoretical issues of exact chiral symmetry on the lattice are discussed and related recent works are reviewed. For chiral theories, the construction with exact gauge invariance is reconsidered from the point of view of domain wall fermion. The issue in the construction of electroweak theory is also discussed. For vector-like theories, we discuss unitarity (positivity), Hamiltonian approach, and several generalizations of the Ginsparg-Wilson relation (algebraic and odd-dimensional)
Conformal internal symmetry of 2d σ-models coupled to gravity and a dilaton
International Nuclear Information System (INIS)
Julia, B.; Nicolai, H.
1996-08-01
General relativity reduced to two dimensions possesses a large group of symmetries that exchange classical solutions. The associated Lie algebra is known to contain the affine Kac-Moody algebra A 1 (1) and half of a real Witt algebra. In this paper we exhibit the full symmetry under the semi-direct product of Lie(A 1 (1) ) by the Witt algebra Lie(W). Furthermore we exhibit the corresponding hidden gauge symmetries. We show that the theory can be understood in terms of an infinite dimensional potential space involving all degrees of freedom: The dilaton as well as matter and gravitation. In the dilaton sector the linear system that extends the previously known Lax pair has the form of a twisted self-duality constraint that is the analog of the self-duality constraint arising in extended supergravities in higher spacetime dimensions. Our results furnish a group theoretical explanation for the simultaneous occurrence of two spectral parameters, a constant one (=y) and a variable one (=t). They hold for all 2d non-linear σ-models that are obtained by dimensional reduction of G/H models in three dimensions coupled to pure gravity. In that case the Lie algebra is Lie(W∝G (1) ); this symmetry acts on a set of off shell fields (in a fixed gauge) and preserves the equations of motion. (orig.)
Lectures on homology with internal symmetries
International Nuclear Information System (INIS)
Solovyov, Yu.
1993-09-01
Homology with internal symmetries is a natural generalization of cyclic homology introduced, independently, by Connes and Tsygan, which has turned out to be a very useful tool in a number of problems of algebra, geometry topology, analysis and mathematical physics. It suffices to say cycling homology and cohomology are successfully applied in the index theory of elliptic operators on foliations, in the description of the homotopy type of pseudoisotopy spaces, in the theory of characteristic classes in algebraic K-theory. They are also applied in noncommutative differential geometry and in the cohomology of Lie algebras, the branches of mathematics which brought them to life in the first place. Essentially, we consider dihedral homology, which was successfully applied for the description of the homology type of groups of homeomorphisms and diffeomorphisms of simply connected manifolds. (author). 27 refs
Testosterone administration reduces lying in men.
Directory of Open Access Journals (Sweden)
Matthias Wibral
Full Text Available Lying is a pervasive phenomenon with important social and economic implications. However, despite substantial interest in the prevalence and determinants of lying, little is known about its biological foundations. Here we study a potential hormonal influence, focusing on the steroid hormone testosterone, which has been shown to play an important role in social behavior. In a double-blind placebo-controlled study, 91 healthy men (24.32±2.73 years received a transdermal administration of 50 mg of testosterone (n=46 or a placebo (n=45. Subsequently, subjects participated in a simple task, in which their payoff depended on the self-reported outcome of a die-roll. Subjects could increase their payoff by lying without fear of being caught. Our results show that testosterone administration substantially decreases lying in men. Self-serving lying occurred in both groups, however, reported payoffs were significantly lower in the testosterone group (p<0.01. Our results contribute to the recent debate on the effect of testosterone on prosocial behavior and its underlying channels.
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.
Energy Technology Data Exchange (ETDEWEB)
Hill, Christopher T.
2018-03-19
We review and expand upon recent work demonstrating that Weyl invariant theories can be broken "inertially," which does not depend upon a potential. This can be understood in a general way by the "current algebra" of these theories, independently of specific Lagrangians. Maintaining the exact Weyl invariance in a renormalized quantum theory can be accomplished by renormalization conditions that refer back to the VEV's of fields in the action. We illustrate the computation of a Weyl invariant Coleman-Weinberg potential that breaks a U(1) symmetry together,with scale invariance.
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...... 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...
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
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
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...
Sugawara operators for classical Lie algebras
Molev, Alexander
2018-01-01
The celebrated Schur-Weyl duality gives rise to effective ways of constructing invariant polynomials on the classical Lie algebras. The emergence of the theory of quantum groups in the 1980s brought up special matrix techniques which allowed one to extend these constructions beyond polynomial invariants and produce new families of Casimir elements for finite-dimensional Lie algebras. Sugawara operators are analogs of Casimir elements for the affine Kac-Moody algebras. The goal of this book is to describe algebraic structures associated with the affine Lie algebras, including affine vertex algebras, Yangians, and classical \\mathcal{W}-algebras, which have numerous ties with many areas of mathematics and mathematical physics, including modular forms, conformal field theory, and soliton equations. An affine version of the matrix technique is developed and used to explain the elegant constructions of Sugawara operators, which appeared in the last decade. An affine analogue of the Harish-Chandra isomorphism connec...
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.
Lie-algebraic classification of effective theories with enhanced soft limits
Bogers, Mark P.; Brauner, Tomáš
2018-05-01
A great deal of effort has recently been invested in developing methods of calculating scattering amplitudes that bypass the traditional construction based on Lagrangians and Feynman rules. Motivated by this progress, we investigate the long-wavelength behavior of scattering amplitudes of massless scalar particles: Nambu-Goldstone (NG) bosons. The low-energy dynamics of NG bosons is governed by the underlying spontaneously broken symmetry, which likewise allows one to bypass the Lagrangian and connect the scaling of the scattering amplitudes directly to the Lie algebra of the symmetry generators. We focus on theories with enhanced soft limits, where the scattering amplitudes scale with a higher power of momentum than expected based on the mere existence of Adler's zero. Our approach is complementary to that developed recently in ref. [1], and in the first step we reproduce their result. That is, as far as Lorentz-invariant theories with a single physical NG boson are concerned, we find no other nontrivial theories featuring enhanced soft limits beyond the already well-known ones: the Galileon and the Dirac-Born-Infeld (DBI) scalar. Next, we show that in a certain sense, these theories do not admit a nontrivial generalization to non-Abelian internal symmetries. Namely, for compact internal symmetry groups, all NG bosons featuring enhanced soft limits necessarily belong to the center of the group. For noncompact symmetry groups such as the ISO( n) group featured by some multi-Galileon theories, these NG bosons then necessarily belong to an Abelian normal subgroup. The Lie-algebraic consistency constraints admit two infinite classes of solutions, generalizing the known multi-Galileon and multi-flavor DBI theories.
Classical extended conformal symmetries
International Nuclear Information System (INIS)
Viswanathan, R.
1990-02-01
Extensions of the Virasoro algebra are constructed as Poisson brackets of higher spin fields which appear as coefficient fields in certain covariant derivative operators of order N. These differential operators are constructed so as to be covariant under reparametrizations on fields of definite conformal dimension. Factorization of such an N-th order operator in terms of first order operators, together with the inclusion of a spin one U(1) current, is shown to lead to a two-parameter W-algebra. One of these parameters plays the role of interpolating between W-algebras based on different Lie algebras of the same rank. (author). 11 refs
Symmetries and integrability of a fourth-order Euler-Bernoulli beam equation
International Nuclear Information System (INIS)
Bokhari, Ashfaque H.; Zaman, F. D.; Mahomed, F. M.
2010-01-01
The complete symmetry group classification of the fourth-order Euler-Bernoulli ordinary differential equation, where the elastic modulus and the area moment of inertia are constants and the applied load is a function of the normal displacement, is obtained. We perform the Lie and Noether symmetry analysis of this problem. In the Lie analysis, the principal Lie algebra which is one dimensional extends in four cases, viz. the linear, exponential, general power law, and a negative fractional power law. It is further shown that two cases arise in the Noether classification with respect to the standard Lagrangian. That is, the linear case for which the Noether algebra dimension is one less than the Lie algebra dimension as well as the negative fractional power law. In the latter case the Noether algebra is three dimensional and is isomorphic to the Lie algebra which is sl(2,R). This exceptional case, although admitting the nonsolvable algebra sl(2,R), remarkably allows for a two-parameter family of exact solutions via the Noether integrals. The Lie reduction gives a second-order ordinary differential equation which has nonlocal symmetry.
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).
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.
Casimir elements of epsilon Lie algebras
International Nuclear Information System (INIS)
Scheunert, M.
1982-10-01
The classical framework for investigating the Casimir elements of a Lie algebra is generalized to the case of an epsilon Lie algebra L. We construct the standard L-module isomorphism of the epsilon-symmetric algebra of L onto its enveloping algebra and we introduce the Harish-Chandra homomorphism. In case the generators of L can be written in a canonical two-index form, we construct the associated standard sequence of Casimir elements and derive a formula for their eigenvalues in an arbitrary highest weight module. (orig.)