Noether gauge symmetry approach in quintom cosmology
Aslam, Adnan; Momeni, Davood; Myrzakulov, Ratbay; Rashid, Muneer Ahmad; Raza, Muhammad
2013-01-01
In literature usual point like symmetries of the Lagrangian have been introduced to study the symmetries and the structure of the fields. This kind of Noether symmetry is a subclass of a more general family of symmetries, called Noether Gauge Symmetries (NGS). Motivated by this mathematical tool, in this article, we discuss the generalized Noether symmetry of Quintom model of dark energy, which is a two component fluid model of quintessence and phantom fields. Our model is a generalization of the Noether symmetries of a single and multiple components which have been investigated in detail before. We found the general form of the quintom potential in which the whole dynamical system has a point like symmetry. We investigated different possible solutions of the system for diverse family of gauge function. Specially, we discovered two family of potentials, one corresponds to a free quintessence (phantom) and the second is in the form of quadratic interaction between two components. These two families of potentia...
Noether Gauge Symmetry Approach in f(R) Gravity
Hussain, Ibrar; Mahomed, F M
2011-01-01
We discuss the f(R) gravity model in which the origin of dark energy is identified as a modification of gravity. The Noether symmetry with gauge term is investigated for the f(R) cosmological model. By utilization of the Noether Gauge Symmetry (NGS) approach, we obtain two exact forms f(R) for which such symmetries exist. Further it is shown that these forms of f(R) are stable.
Noether symmetry approach in f(R)-tachyon model
Energy Technology Data Exchange (ETDEWEB)
Jamil, Mubasher, E-mail: mjamil@camp.nust.edu.pk [Center for Advanced Mathematics and Physics (CAMP), National University of Sciences and Technology (NUST), H-12, Islamabad (Pakistan); Mahomed, F.M., E-mail: Fazal.Mahomed@wits.ac.za [Centre for Differential Equations, Continuum Mechanics and Applications, School of Computational and Applied Mathematics, University of the Witwatersrand, Wits 2050 (South Africa); Momeni, D., E-mail: d.momeni@yahoo.com [Department of Physics, Faculty of Sciences, Tarbiat Moa' llem University, Tehran (Iran, Islamic Republic of)
2011-08-26
In this Letter by utilizing the Noether symmetry approach in cosmology, we attempt to find the tachyon potential via the application of this kind of symmetry to a flat Friedmann-Robertson-Walker (FRW) metric. We reduce the system of equations to simpler ones and obtain the general class of the tachyon's potential function and f(R) functions. We have found that the Noether symmetric model results in a power law f(R) and an inverse fourth power potential for the tachyonic field. Further we investigate numerically the cosmological evolution of our model and show explicitly the behavior of the equation of state crossing the cosmological constant boundary.
Noether Symmetry Approach for Dirac-Born-Infeld Cosmology
Capozziello, Salvatore; Myrzakulov, Ratbay
2014-01-01
We consider the Noether Symmetry Approach for a cosmological model derived from a tachyon scalar field $T$ with a Dirac-Born-Infeld Lagrangian and a potential $V(T)$. Furthermore, we assume a coupled canonical scalar field $\\phi$ with an arbitrary interaction potential $B(T,\\phi)$. Exact solutions are derived consistent with the accelerated behavior of cosmic fluid.
Noether Symmetry Approach in Gauss-Bonnet Cosmology
Capozziello, Salvatore; Odintsov, Sergei D
2014-01-01
We discuss the Noether Symmetry Approach in the framework of Gauss-Bonnet cosmology showing that the functional form of the $F(R, {\\cal G})$ function, where $R$ is the Ricci scalar and ${\\cal G}$ is the Gauss-Bonnet topological invariant, can be determined by the presence of symmetries. Besides, the method allows to find out exact solutions due to the reduction of cosmological dynamical system and the presence of conserved quantities. Some specific cosmological models are worked out
Noether Symmetry Approach for teleparallel-curvature cosmology
Capozziello, Salvatore; Myrzakulov, Ratbay
2014-01-01
We consider curvature-teleparallel $F(R,T)$ gravity, where the gravitational Lagrangian density is given by an arbitrary function of the Ricci scalar $R$ and the torsion scalar $T$. Using the Noether Symmetry Approach, we show that the functional form of the $F(R, T)$ function, can be determined by the presence of symmetries . Furthermore, we obtain exact solutions through to the presence of conserved quantities and the reduction of cosmological dynamical system. Example of particular cosmological models are considered.
Noether symmetry approach in f(G,T) gravity
Shamir, M. Farasat; Ahmad, Mushtaq
2017-01-01
We explore the recently introduced modified Gauss-Bonnet gravity (Sharif and Ikram in Eur Phys J C 76:640, 2016), f(G,T) pragmatic with G, the Gauss-Bonnet term, and T, the trace of the energy-momentum tensor. Noether symmetry approach has been used to develop some cosmologically viable f(G,T) gravity models. The Noether equations of modified gravity are reported for flat FRW universe. Two specific models have been studied to determine the conserved quantities and exact solutions. In particular, the well known deSitter solution is reconstructed for some specific choice of f(G,T) gravity model.
Noether Symmetry Approach in $f(\\mathcal{G},T)$ Gravity
Shamir, M Farasat
2016-01-01
We explore the recently introduced modified Gauss-Bonnet gravity, $f(\\mathcal{G},T)$ pragmatic with $\\mathcal{G}$, the Gauss-Bonnet term, and ${T}$, the trace of the energy-momentum tensor. Noether symmetry approach has been used to develop some cosmologically viable $f(\\mathcal{G},T)$ gravity models. The Noether equations of modified gravity are reported for flat FRW universe. Two specific models have been studied to determine the conserved quantities and exact solutions. In particular, the well known deSitter solution is reconstructed for some specific choice of $f(\\mathcal{G},T)$ gravity model.
Noether symmetry approach in f(G,T) gravity
Energy Technology Data Exchange (ETDEWEB)
Shamir, M.F.; Ahmad, Mushtaq [National University of Computer and Emerging Sciences, Lahore Campus (Pakistan)
2017-01-15
We explore the recently introduced modified Gauss-Bonnet gravity (Sharif and Ikram in Eur Phys J C 76:640, 2016), f(G,T) pragmatic with G, the Gauss-Bonnet term, and T, the trace of the energy-momentum tensor. Noether symmetry approach has been used to develop some cosmologically viable f(G,T) gravity models. The Noether equations of modified gravity are reported for flat FRW universe. Two specific models have been studied to determine the conserved quantities and exact solutions. In particular, the well known deSitter solution is reconstructed for some specific choice of f(G,T) gravity model. (orig.)
Noether symmetry approach in f( T, B) teleparallel cosmology
Bahamonde, Sebastian; Capozziello, Salvatore
2017-02-01
We consider the cosmology derived from f( T, B) gravity where T is the torsion scalar and B=2/epartial _{μ }(e T^{μ }) a boundary term. In particular we discuss how it is possible to recover, under the same standard, the teleparallel f( T) gravity, the curvature f( R) gravity, and the teleparallel-curvature f( R, T) gravity, which are particular cases of f( T, B). We adopt the Noether Symmetry Approach to study the related dynamical systems and to find cosmological solutions.
Noether symmetry approach in f(T, B) teleparallel cosmology
Energy Technology Data Exchange (ETDEWEB)
Bahamonde, Sebastian [University College London, Department of Mathematics, London (United Kingdom); Capozziello, Salvatore [Universita di Napoli ' ' Federico II' ' , Dipartimento di Fisica, Naples (Italy); Gran Sasso Science Institute, L' Aquila (Italy); Compl. Univ. di Monte S. Angelo, Naples (Italy); INFN, Napoli (Italy)
2017-02-15
We consider the cosmology derived from f(T, B) gravity where T is the torsion scalar and B = (2)/(e)∂{sub μ}(eT{sup μ}) a boundary term. In particular we discuss how it is possible to recover, under the same standard, the teleparallel f(T) gravity, the curvature f(R) gravity, and the teleparallel-curvature f(R, T) gravity, which are particular cases of f(T, B). We adopt the Noether Symmetry Approach to study the related dynamical systems and to find cosmological solutions. (orig.)
Cosmological models with spinor and scalar fields by Noether symmetry approach
Kremer, Gilberto M
2013-01-01
General cosmological models with spinor and scalar fields playing the role of gravitational sources are analyzed. The Noether symmetry approach is taken as a criterion to constrain the undefined potentials and couplings of the generic actions. For all the found Noether symmetries the corresponding dynamical systems can be analytically integrated. The obtained cosmological solutions describe the early and late Universe as expected by basing on the known eras of the Universe.
Energy Technology Data Exchange (ETDEWEB)
Tajahmad, Behzad [University of Tabriz, Faculty of Physics, Tabriz (Iran, Islamic Republic of)
2017-04-15
In this paper, we present the Noether symmetries of flat FRW spacetime in the context of a new action in teleparallel gravity which we construct based on the f(R) version. This modified action contains a coupling between the scalar field potential and magnetism. Also, we introduce an innovative approach, the beyond Noether symmetry (B.N.S.) approach, for exact solutions which carry more conserved currents than the Noether approach. By data analysis of the exact solutions, obtained from the Noether approach, late-time acceleration and phase crossing are realized, and some deep connections with observational data such as the age of the universe, the present value of the scale factor as well as the state and deceleration parameters are observed. In the B.N.S. approach, we consider the dark energy dominated era. (orig.)
A scalar field dark energy model: Noether symmetry approach
Dutta, Sourav; Panja, Madan Mohan; Chakraborty, Subenoy
2016-04-01
Scalar field dark energy cosmology has been investigated in the present paper in the frame work of Einstein gravity. In the context of Friedmann-Lemaitre-Robertson-Walker space time minimally coupled scalar field with self interacting potential and non-interacting perfect fluid with barotropic equation of state (dark matter) is chosen as the matter context. By imposing Noether symmetry on the Lagrangian of the system the symmetry vector is obtained and the self interacting potential for the scalar field is determined. Then we choose a point transformation (a, φ )→ (u, v) such that one of the transformation variable (say u) is cyclic for the Lagrangian. Subsequently, using conserved charge (corresponding to the cyclic co-ordinate) and the constant of motion, solutions are obtained. Finally, the cosmological implication of the solutions in the perspective of recent observation has been examined.
O'Hanlon actions by Noether symmetry
Darabi, F.
2015-01-01
By using the conformal symmetry between Brans-Dicke action with $\\omega=-\\frac{3}{2}$ and O'Hanlon action, we seek the O'Hanlon actions in Einstein frame respecting the Noether symmetry. Since the Noether symmetry is preserved under conformal transformations, the existence of Noether symmetry in the Brans-Dicke action asserts the Noether symmetry in O'Hanlon action in Einstein frame. Therefore, the potentials respecting Noether symmetry in Brans-Dicke action give the corresponding potentials ...
f(R) cosmology by Noether's symmetry
Capozziello, Salvatore
2008-01-01
A general approach to find out exact cosmological solutions in f(R)-gravity is discussed. Instead of taking into account phenomenological models, we assume, as a physical criterium, the existence of Noether symmetries in the cosmological f(R) Lagrangian. As a result, the presence of such symmetries selects viable models and allow to solve the equations of motion. We discuss also the case in which no Noether charge is present but general criteria can be used to achieve solutions.
Noether symmetry approach in f(T, B) teleparallel cosmology.
Bahamonde, Sebastian; Capozziello, Salvatore
2017-01-01
We consider the cosmology derived from f(T, B) gravity where T is the torsion scalar and [Formula: see text] a boundary term. In particular we discuss how it is possible to recover, under the same standard, the teleparallel f(T) gravity, the curvature f(R) gravity, and the teleparallel-curvature f(R, T) gravity, which are particular cases of f(T, B). We adopt the Noether Symmetry Approach to study the related dynamical systems and to find cosmological solutions.
Zhang, Sun
2015-01-01
In this paper, based on the works of Capozziello et al., we have studied the Noether symmetry approach in the cosmological model with scalar and gauge fields proposed recently by Soda et al. The correct Noether symmetries and related Lie algebra are given according to the minisuperspace quantum cosmological model. The Wheeler-De Witt (WDW) equation is presented after quantization and the classical trajectories are then obtained in the semi-classical limit. The oscillating features of the wave function in the cosmic evolution recover the so-called Hartle criterion, and the selection rule in minisuperspace quantum cosmology is strengthened. Then we have realized now the proposition that Noether symmetries select classical universes.
ON THE NOETHER SYMMETRY AND LIE SYMMETRY OF MECHANICAL SYSTEMS
Institute of Scientific and Technical Information of China (English)
梅凤翔; 郑改华
2002-01-01
The Noether symmetry is an invariance of Hamilton action under infinitesimal transformations of time and the coordinates. The Lie symmetry is an invariance of the differential equations of motion under the transformations. In this paper, the relation between these two symmetries is proved definitely and firstly for mechanical systems. The results indicate that all the Noether symmetries are Lie symmetries for Lagrangian systems meanwhile a Noether symmetry is a Lie symmetry for the general holonomic or nonholonomic systems provided that some conditions hold.
de Souza, Rudinei C; Kremer, Gilberto M
2013-01-01
We analyse a scalar field non-minimally coupled to gravity in the context of a Universe described by the flat Friedmann-Robertson-Walker (F-R-W) metric. The adopted model comprises a Universe filled by the scalar field and standard matter (dark and baryonic). The corresponding field equations are obtained through the Palatini formalism. From the action of the model in the flat F-R-W space-time, a point-like Lagrangian of first order is obtained and the Noether symmetry approach is applied to restrict the forms of the a priori undefined coupling and potential of the scalar field. We show that the massive scalar field is associated with a Noether symmetry of the model. Analytical cosmological solutions for this case are found and their respective importance for the description of the dark energy are discussed.
Non-minimally coupled tachyon field with Noether symmetry under the Palatini approach
Collodel, Lucas G.; Kremer, Gilberto M.
2015-03-01
A model for a homogeneous, isotropic, flat Universe composed by dark energy and matter is investigated. Dark energy is considered to behave as a tachyon field, which is non-minimally coupled to gravity. The connection is treated as metric independent when varying the action, providing an extra term to the Lagrangian density. The self-interaction potential and coupling are naturally found by imposing a Noether symmetry to the system. We analyze the evolution of the density parameters and we compare the results obtained for the deceleration parameter, luminosity distance and Hubble parameter with those found in literature from observational data.
Non-minimally coupled tachyon field with Noether symmetry under the Palatini approach
Collodel, Lucas Gardai
2014-01-01
A model for a homogeneous, isotropic, flat Universe composed by dark energy and matter is investigated. Dark energy is considered to behave as a tachyon field, which is non-minimally coupled to gravity. The connection is treated as metric independent when varying the action, providing an extra term to the Lagrangian density. The self-interaction potential and coupling are naturally found by imposing a Noether symmetry to the system. We analyze the evolution of the density parameters and we compare the results obtained for the deceleration parameter, luminosity distance and Hubble parameter with those found in literature from observational data.
Classification of Cosmic Scale Factor via Noether Gauge Symmetries
Jhangeer, Adil; Naz, Tayyaba; Iftikhar, Nazish
2015-01-01
In this paper, a complete classification of Friedmann-Robertson-Walker (FRW) spacetime by using approximate Noether approach is presented. Considered spacetime is discussed for three different types of universe i.e. flat, open and closed. Different forms of cosmic scale factor $a$ with respect to the nature of the universe, which posses the nontrivial Noether gauge symmetries (NGS) are reported. The perturbed Lagrangian corresponding to FRW metric in the Noether equation is used to get Noether operators. For different types of universe minimal and maximal set of Noether operators are reported. A list of Noether operators are also computed which is not only independent from the choice of the cosmic scale factor but also the choice type of universe. Further, corresponding energy type first integral of motions are also calculated.
Institute of Scientific and Technical Information of China (English)
ZHANG Ming-Jiang; FANG Jian-Hui; LU Kai; ZHANG Ke-Jun; LI Yan
2009-01-01
The perturbation to Noether symmetry and Noether adiabatic invariants of general discrete holonomic systems are studied.First,the discrete Noether exact invariant induced directly from the Noether symmetry of the system without perturbation is given.Secondly,the concept of discrete high-order adiabatic invariant is presented,the criterion of the perturbation to Noether symmetry is established,and the discrete Noether adiabatic invariant induced directly from the perturbation to Noether symmetry is obtained.Lastly,an example is discussed to illustrate the application of the results.
String duality transformations in $f(R)$ gravity from Noether symmetry approach
Capozziello, Salvatore; Vernieri, Daniele
2015-01-01
We select $f(R)$ gravity models that undergo scale factor duality transformations. As a starting point, we consider the tree-level effective gravitational action of bosonic String Theory coupled with the dilaton field. This theory inherits the Busher's duality of its parent String Theory. Using conformal transformations of the metric tensor, it is possible to map the effective one-loop bosonic string theory of gravity into $f(R)$ gravity, relating the dilaton field to the Ricci scalar curvature. Furthermore, the duality can be framed under the standard of Noether symmetries and exact cosmological solutions are derived. Using suitable changes of variables, the string-based $f(R)$ Lagrangians are shown in cases where the duality transformation becomes a parity inversion.
Institute of Scientific and Technical Information of China (English)
XIE Yin-Li; YANG Xin-Fang; JIA Li-Qun
2011-01-01
Noether symmetry of Nielsen equation and Noether conserved quantity deduced directly from Noether symmetry for dynamical systems of the relative motion are studied.The definition and criteria of Noether symmetry of a Nielsen equation under the infinitesimal transformations of groups are given.Expression of Noether conserved quantity deduced directly from Noether symmetry of Nielsen equation for the system are obtained.Finally, an example is given to illustrate the application of the results.PACS numbers: 11.30.-j, 45.20.Jj, 02.20.Sv
Noether symmetries and duality transformations in cosmology
Paliathanasis, Andronikos
2016-01-01
We discuss the relation between local transformations generated by Noether (point) symmetries and discrete transformations for a class of minisuperspace cosmological models. Moreover as far as concerns the scale-factor duality of the dilaton field, we show that it is related to the existence of a Noether symmetry for the field equations. In particular, the same point symmetry exists for the Brans-Dicke- scalar field with linear potential for $\\omega_{BD}=1$ . Furthermore, in the context of the O'Hanlon theory for $f\\left( R\\right) $-gravity, it is possible to show how a duality transformation in the minisuperspace can be used to relate different gravitational models.
Noether symmetries and duality transformations in cosmology
Paliathanasis, Andronikos; Capozziello, Salvatore
2016-09-01
We discuss the relation between Noether (point) symmetries and discrete symmetries for a class of minisuperspace cosmological models. We show that when a Noether symmetry exists for the gravitational Lagrangian, then there exists a coordinate system in which a reversal symmetry exists. Moreover, as far as concerns, the scale-factor duality symmetry of the dilaton field, we show that it is related to the existence of a Noether symmetry for the field equations, and the reversal symmetry in the normal coordinates of the symmetry vector becomes scale-factor duality symmetry in the original coordinates. In particular, the same point symmetry as also the same reversal symmetry exists for the Brans-Dicke scalar field with linear potential while now the discrete symmetry in the original coordinates of the system depends on the Brans-Dicke parameter and it is a scale-factor duality when ωBD = 1. Furthermore, in the context of the O’Hanlon theory for f(R)-gravity, it is possible to show how a duality transformation in the minisuperspace can be used to relate different gravitational models.
Noether gauge symmetry classes for pp-wave spacetimes
Camci, U
2016-01-01
The Noether gauge symmetries of geodesic Lagrangian for the pp-wave spacetimes are determined in each of the Noether gauge symmetry classes of the pp-wave spacetimes. It is shown that a type N pp-wave spacetime can admit at most three Noether gauge symmetry, and furthermore the number of Noether gauge symmetries turn out to be four, five, six, seven and eight. We found that all conformally flat plane wave spacetimes admit the maximal, i.e. ten, Noether gauge symmetry. Also it is found that if the pp-wave spacetime is non-conformally flat plane wave, then the number of Noether gauge symmetry is nine or ten. By means of the obtained Noether constants the search of the exact solutions of the geodesic equations for the pp-wave spacetimes is considered and we found new exact solutions of the geodesic equations in some special Noether gauge symmetry classes.
Approximate Noether gauge symmetries of the Bardeen model
Energy Technology Data Exchange (ETDEWEB)
Camci, U. [Akdeniz University, Department of Physics, Faculty of Science, Antalya (Turkey)
2014-12-01
We investigate the approximate Noether gauge symmetries of the geodesic Lagrangian for the Bardeen spacetime model. This is accommodated by a set of new approximate Noether gauge symmetry relations for the perturbed geodesic Lagrangian in the spacetime. A detailed analysis of the spacetime of the Bardeen model up to third-order approximate Noether gauge symmetries is presented. (orig.)
Noether theorem for {mu}-symmetries
Energy Technology Data Exchange (ETDEWEB)
Cicogna, Giampaolo [Dipartimento di Fisica, Universita di Pisa and INFN, Sezione di Pisa, Largo B Pontecorvo 3, 50127 Pisa (Italy); Gaeta, Giuseppe [Dipartimento di Matematica, Universita di Milano, via Saldini 50, 20133 Milano (Italy)
2007-09-28
We give a version of Noether theorem adapted to the framework of {mu}-symmetries; this extends to such case recent work by Muriel, Romero and Olver in the framework of {lambda}-symmetries, and connects {mu}-symmetries of a Lagrangian to a suitably modified conservation law. In some cases this '{mu}-conservation law' actually reduces to a standard one; we also note a relation between {mu}-symmetries and conditional invariants. We also consider the case where the variational principle is itself formulated as requiring vanishing variation under {mu}-prolonged variation fields, leading to modified Euler-Lagrange equations. In this setting, {mu}-symmetries of the Lagrangian correspond to standard conservation laws as in the standard Noether theorem. We finally propose some applications and examples.
Institute of Scientific and Technical Information of China (English)
WANG Peng
2011-01-01
Perturbation to Noether symmetry of discrete mechanico-electrical systems on an uniform lattice is investigated.First, Noether theorem of a system is presented. Secondly, the criterion of perturbation to Noether symmetry of the system is given. Based on the definition of adiabatic invariants, Noether adiabatic invariants of the system are obtained. Finally, An example is given to support these results.%@@ Perturbation to Noether symmetry of discrete mechanico-electrical systems on an uniform lattice is investigated.First, Noether theorem of a system is presented.Secondly , the criterion of perturbation to Noether symmetry of the system is given.Based on the definition of adiabatic invariants, Noether adiabatic invariants of the system are obtained .Finally, An example is given to support these results.
Complete classification of spherically symmetric static spacetimes via Noether symmetries
Ali, Farhad; Ali, Sajid
2013-01-01
In this paper we give a complete classification of spherically symmetric static space-times by their Noether symmetries. The determining equations for Noether symmetries are obtained by using the usual Lagrangian of a general spherically symmetric static spacetime which are integrated for each case. In particular we observe that spherically symmetric static spacetimes are categorized into six distinct classes corresponding to Noether algebra of dimensions 5, 6, 7, 9, 11 and 17. Using Noether`s theorem we also write down the first integrals for each class of such spacetimes corresponding to their Noether symmetries.
Noether-Lie Symmetry of Generalized Classical Mechanical Systems
Institute of Scientific and Technical Information of China (English)
JIA Wen-Zhi; ZHANG Xiao-Ni; WANG Shun-Jin; FANG Jian-Hui; WANG Peng; DING Ning
2008-01-01
In this paper, the Noether-Lie symmetry and conserved quantities of generalized classical mechanical system are studied. The definition and the criterion of the Noether Lie symmetry for the system under the general infinitesimal transformations of groups are given. The Noether conserved quantity and the Hojman conserved quantity deduced from the Noether-Lie symmetry are obtained. An example is given to illustrate the application of the results.
Noether-Mei Symmetry of Mechanical System in Phase Space
Institute of Scientific and Technical Information of China (English)
FANG Jian-Hui; WANG Peng; DING Ning
2006-01-01
In this paper, a new kind of symmetry and its conserved quantities of a mechanical system in phase space are studied. The definition of this new symmetry, i.e., a Noether-Mei symmetry, is presented, and the criterion of this symmetry is also given. The Noether conserved quantity and the Mei conserved quantity deduced from the Noether-Mei symmetry of the system are obtained. Finally, two examples are given to illustrate the application of the results.
Noether Symmetries Of A Modified Model In Teleparallel Gravity
Tajahmad, Behzad
2016-01-01
In this paper, we have presented the Noether symmetries of flat FRW spacetime in the context of a new action in Teleparallel Gravity which we construct it based on f(R) version. This modified action contains a coupling between scalar field potential and magnetism. Also, we introduce an innovative approach (B.N.S. Approach) for exact solutions which carry more conserved currents than Noether approach. By data analysis the exact solutions, obtained from Noether approach, late time acceleration and phase crossing are realized, and some deep connections with observational data such as age of universe, the present amount of scale factor, state and deceleration parameters are observed. In B.N.S. approach, we have considered dark energy dominated era.
Institute of Scientific and Technical Information of China (English)
LUO Shao-Kai; JIA Li-Qun; CAI Jian-Le
2005-01-01
For the holonomic nonconservative system, by using the Noether symmetry, a non-Noether conserved quantity is obtained directly under general infinitesimal transformations of groups in which time is variable. At first,the Noether symmetry, Lie symmetry, and Noether conserved quantity are given. Secondly, the condition under which the Noether symmetry is a Lie symmetry under general infinitesimal transformations is obtained. Finally, a set of nonNoether conserved quantities of the system are given by the Noether symmetry, and an example is given to illustrate the application of the results.
Scalar-Tensor Teleparallel Wormholes by Noether Symmetries
Bahamonde, Sebastian; Capozziello, Salvatore; Jamil, Mubasher
2016-01-01
A gravitational theory of a scalar field non-minimally coupled with torsion and boundary term is considered with the aim to construct Lorentzian wormholes. Geometrical parameters including shape and redshift functions are obtained for these solutions. We adopt the formalism of Noether Gauge Symmetry Approach in order to find symmetries, Lie brackets and invariants (conserved quantities). Furthermore by imposing specific forms of potential function, we are able to calculate metric coefficients and discuss their geometrical behavior.
Scalar-tensor teleparallel wormholes by Noether symmetries
Bahamonde, Sebastian; Camci, Ugur; Capozziello, Salvatore; Jamil, Mubasher
2016-10-01
A gravitational theory of a scalar field nonminimally coupled with torsion and a boundary term is considered with the aim to construct Lorentzian wormholes. Geometrical parameters including shape and redshift functions are obtained for these solutions. We adopt the formalism of the Noether gauge symmetry approach in order to find symmetries, Lie brackets and invariants (conserved quantities). Furthermore by imposing specific forms of potential function, we are able to calculate metric coefficients and discuss their geometrical behavior.
Noether symmetry in f(R) cosmology
Vakili, Babak
2008-01-01
The Noether symmetry of a generic $f(R)$ cosmological model is investigated by utilizing the behavior of the corresponding Lagrangian under the infinitesimal generators of the desired symmetry. We explicitly calculate the form of $f(R)$ for which such symmetries exist. It is shown that the resulting form of $f(R)$ yields a power law expansion for the cosmological scale factor. We also obtain the effective equation of state parameter for the corresponding cosmology and show that our model can provide a gravitational alternative to the quintessence.
Institute of Scientific and Technical Information of China (English)
Luo Shao-Kai
2007-01-01
For a relativistic holonomic nonconservative system, by using the Noether symmetry, a new non-Noether conserved quantity is given under general infinitesimal transformations of groups. On the basis of the theory of invariance of differential equations of motion under general infinitesimal transformations, we construct the relativistic Noether symmetry, Lie symmetry and the condition under which the Noether symmetry is a Lie symmetry under general infinitesimal transformations. By using the Noether symmetry, a new relativistic non-Noether conserved quantity is given which only depends on the variables t, qs and (q)s. An example is given to illustrate the application of the results.
A complex Noether approach for variational partial differential equations
Naz, R.; Mahomed, F. M.
2015-10-01
Scalar complex partial differential equations which admit variational formulations are studied. Such a complex partial differential equation, via a complex dependent variable, splits into a system of two real partial differential equations. The decomposition of the Lagrangian of the complex partial differential equation in the real domain is shown to yield two real Lagrangians for the split system. The complex Maxwellian distribution, transonic gas flow, Maxwellian tails, dissipative wave and Klein-Gordon equations are considered. The Noether symmetries and gauge terms of the split system that correspond to both the Lagrangians are constructed by the Noether approach. In the case of coupled split systems, the same Noether symmetries are obtained. The Noether symmetries for the uncoupled split systems are different. The conserved vectors of the split system which correspond to both the Lagrangians are compared to the split conserved vectors of the complex partial differential equation for the examples. The split conserved vectors of the complex partial differential equation are the same as the conserved vectors of the split system of real partial differential equations in the case of coupled systems. Moreover a Noether-like theorem for the split system is proved which provides the Noether-like conserved quantities of the split system from knowledge of the Noether-like operators. An interesting result on the split characteristics and the conservation laws is shown as well. The Noether symmetries and gauge terms of the Lagrangian of the split system with the split Noether-like operators and gauge terms of the Lagrangian of the given complex partial differential equation are compared. Folklore suggests that the split Noether-like operators of a Lagrangian of a complex Euler-Lagrange partial differential equation are symmetries of the Lagrangian of the split system of real partial differential equations. This is not the case. They are proved to be the same if the
Noether symmetries in Gauss-Bonnet-teleparallel cosmology
Energy Technology Data Exchange (ETDEWEB)
Capozziello, Salvatore [Universita' di Napoli' ' Federico II' ' , Complesso Universitario di Monte S. Angelo, Dipartimento di Fisica ' ' E. Pancini' ' , Napoli (Italy); INFN Sezione di Napoli, Complesso Universitario di Monte S. Angelo, Napoli (Italy); Gran Sasso Science Institute (INFN), L' Aquila (Italy); Tomsk State Pedagogical University, Tomsk (Russian Federation); De Laurentis, Mariafelicia [INFN Sezione di Napoli, Complesso Universitario di Monte S. Angelo, Napoli (Italy); Tomsk State Pedagogical University, Tomsk (Russian Federation); Goethe University, Institute for Theoretical Physics, Frankfurt (Germany); Laboratory of Theoretical Cosmology, Tomsk State University of Control Systems and Radioelectronics (TUSUR), Tomsk (Russian Federation); Dialektopoulos, Konstantinos F. [Universita' di Napoli' ' Federico II' ' , Complesso Universitario di Monte S. Angelo, Dipartimento di Fisica ' ' E. Pancini' ' , Napoli (Italy); INFN Sezione di Napoli, Complesso Universitario di Monte S. Angelo, Napoli (Italy)
2016-11-15
A generalized teleparallel cosmological model, f(T{sub G},T), containing the torsion scalar T and the teleparallel counterpart of the Gauss-Bonnet topological invariant T{sub G}, is studied in the framework of the Noether symmetry approach. As f(G, R) gravity, where G is the Gauss-Bonnet topological invariant and R is the Ricci curvature scalar, exhausts all the curvature information that one can construct from the Riemann tensor, in the same way, f(T{sub G},T) contains all the possible information directly related to the torsion tensor. In this paper, we discuss how the Noether symmetry approach allows one to fix the form of the function f(T{sub G},T) and to derive exact cosmological solutions. (orig.)
Noether symmetries in Gauss-Bonnet-teleparallel cosmology.
Capozziello, Salvatore; De Laurentis, Mariafelicia; Dialektopoulos, Konstantinos F
2016-01-01
A generalized teleparallel cosmological model, [Formula: see text], containing the torsion scalar T and the teleparallel counterpart of the Gauss-Bonnet topological invariant [Formula: see text], is studied in the framework of the Noether symmetry approach. As [Formula: see text] gravity, where [Formula: see text] is the Gauss-Bonnet topological invariant and R is the Ricci curvature scalar, exhausts all the curvature information that one can construct from the Riemann tensor, in the same way, [Formula: see text] contains all the possible information directly related to the torsion tensor. In this paper, we discuss how the Noether symmetry approach allows one to fix the form of the function [Formula: see text] and to derive exact cosmological solutions.
Noether symmetries in Gauss-Bonnet-teleparallel cosmology
Capozziello, Salvatore; De Laurentis, Mariafelicia; Dialektopoulos, Konstantinos F.
2016-11-01
A generalized teleparallel cosmological model, f(T_{G},T), containing the torsion scalar T and the teleparallel counterpart of the Gauss-Bonnet topological invariant T_{{G}}, is studied in the framework of the Noether symmetry approach. As f({G}, R) gravity, where {G} is the Gauss-Bonnet topological invariant and R is the Ricci curvature scalar, exhausts all the curvature information that one can construct from the Riemann tensor, in the same way, f(T_{G},T) contains all the possible information directly related to the torsion tensor. In this paper, we discuss how the Noether symmetry approach allows one to fix the form of the function f(T_{G},T) and to derive exact cosmological solutions.
Noether Symmetries in Gauss-Bonnet-teleparallel cosmology
Capozziello, Salvatore; Dialektopoulos, Konstantinos F
2016-01-01
A generalized teleparallel cosmological model, $f(T_\\mathcal{G},T)$, containing the torsion scalar $T$ and the teleparallel counterpart of the Gauss-Bonnet topological invariant $T_{\\mathcal{G}}$, is studied in the framework of the Noether Symmetry Approach. As $f(\\mathcal{G}, R)$ gravity, where $\\mathcal{G}$ is the Gauss-Bonnet topological invariant and $R$ is the Ricci curvature scalar, exhausts all the curvature information that one can construct from the Riemann tensor, in the same way, $f(T_\\mathcal{G},T)$ contains all the possible information directly related to the torsion tensor. In this paper, we discuss how the Noether Symmetry Approach allows to fix the form of the function $f(T_\\mathcal{G},T)$ and to derive exact cosmological solutions.
Noether symmetries in extended gravity quantum cosmology
Capozziello, Salvatore
2013-01-01
We summarize the use of Noether symmetries in Minisuperspace Quantum Cosmology. In particular, we consider minisuperspace models, showing that the existence of conserved quantities gives selection rules that allow to recover classical behaviors in cosmic evolution according to the so called Hartle criterion. Such a criterion selects correlated regions in the configuration space of dynamical variables whose meaning is related to the emergence of classical observable universes. Some minisuperspace models are worked out starting from Extended Gravity, in particular coming from scalar tensor, f(R) and f(T) theories. Exact cosmological solutions are derived.
Motion on constant curvature spaces and quantization using Noether symmetries.
Bracken, Paul
2014-12-01
A general approach is presented for quantizing a metric nonlinear system on a manifold of constant curvature. It makes use of a curvature dependent procedure which relies on determining Noether symmetries from the metric. The curvature of the space functions as a constant parameter. For a specific metric which defines the manifold, Lie differentiation of the metric gives these symmetries. A metric is used such that the resulting Schrödinger equation can be solved in terms of hypergeometric functions. This permits the investigation of both the energy spectrum and wave functions exactly for this system.
Noether symmetries of discrete mechanico-electrical systems
Institute of Scientific and Technical Information of China (English)
Fu Jing-Li; Chen Ben-Yong; Xie Feng-Ping
2008-01-01
This paper focuses on studying Noether symmetries and conservation laws of the discrete mechanico-electrical systems with the nonconservative and the dissipative forces. Based on the invariance of discrete Hamilton action of the systems under the infinitesimal transformation with respect to the generalized coordinates, the generalized electrical quantities and time, it presents the discrete analogue of variational principle, the discrete analogue of Lagrange-Maxwell equations, the discrete analogue of Noether theorems for Lagrange Maxwell and Lagrange mechanico-electrical systems.Also, the discrete Noether operator identity and the discrete Noether-type conservation laws are obtained for these systems. An actual example is given to illustrate these results.
Perturbation to Noether Symmetries and Adiabatic Invariants for Birkhoffian Systems
Directory of Open Access Journals (Sweden)
Yi Zhang
2015-01-01
Full Text Available Based on El-Nabulsi dynamical model for a non-conservative system, the problem of perturbation to Noether symmetries and adiabatic invariants of a Birkhoffian system under the action of a small disturbance is proposed and studied. Firstly, the El-Nabulsi-Pfaff variational problem from extended exponentially fractional integral is presented and the El-Nabulsi-Birkhoff equations are established. Secondly, the definitions and the criterions criteria of the Noether symmetric transformations and quasisymmetric transformations of the Birkhoffian system are given, and the Noether theorems of the system are established, which reveal the inner relationship between the Noether symmetries and the conserved quantities. Thirdly, the perturbation of Noether symmetries under a small disturbance is studied, and corresponding adiabatic invariants are obtained. As special cases, the deductions in nonconservative Hamiltonian system and nonconservative Lagrangian system and standard Birkhoffian system are given. At the end of the paper, the case known as Hojman-Urrutia problem is discussed to investigate the Noether symmetries and the adiabatic invariants, the perturbation to Noether symmetries and the adiabatic invariants under El-Nabulsi dynamical model.
Noether symmetry and Lie symmetry of discrete holonomic systems with dependent coordinates
Institute of Scientific and Technical Information of China (English)
Shi Shen-Yang; Huang Xiao-Hong
2008-01-01
The Noether symmetry,the Lie symmetry and the conserved quantity of discrete holonomic systems with dependent coordinates are investigated in this paper.The Noether symmetry provides a discrete Noether identity and a conserved qu中antity of the system.The invariance of discrete motion equations under infinitesimal transformation groups is defined as the Lie symmetry,and the condition of obtaining the Noether conserved quantity from the Lie symmetry is also presented.An example is discussed to show the applications of the results.
EMDEN-FOWLER TYPE SYSTEM: NOETHER SYMMETRIES AND FIRST INTEGRALS
Institute of Scientific and Technical Information of China (English)
B.Muatjetjeja; C.M.Khalique
2012-01-01
We classify a generalized coupled singular Emden-Fowler type system ü +a(t)vn =0,(v) + b(t)um =0 with respect to the standard first-order Lagrangian according to the Noether point symmetries which it admits.First integrals of the various cases which admit Noether point symmetries are then obtained.This system was discussed in the literature from the view-point of existence and uniqueness of positive solutions.
Non-Noether symmetries and conserved quantities of the Lagrange mechano-electrical systems
Institute of Scientific and Technical Information of China (English)
Fu Jing-Li; Chen Li-Qun; Liu Rong-Wan
2004-01-01
This paper focuses on studying non-Noether symmetries and conserved quantities of Lagrange mechano-electrical dynamical systems. Based on the relationships between the motion and Lagrangian, we present conservation laws on non-Noether symmetries for Lagrange mechano-electrical dynamical systems. A criterion is obtained on which non-Noether symmetry leads to Noether symmetry of the systems. The work also gives connections between the nonNoether symmetries and Lie point symmetries, and further obtains Lie invariants to form a complete set of non-Noether conserved quantity. Finally, an example is discussed to illustrate these results.
Mei Symmetry and Noether Symmetry of the Relativistic Variable Mass System
Institute of Scientific and Technical Information of China (English)
FANG Jian-Hui
2004-01-01
The definition and criterion of the Mei symmetry of a relativistic variable mass system are given. The relation between the Mei symmetry and the Noether symmetry of the system is found under infinitesimal transformations of groups. The conserved quantities to which the Mei symmetry and Noether symmetry of the system lead are obtained.An example is given to illustrate the application of the result.
Scalar-tensor cosmology with R^{-1} curvature correction by Noether Symmetry
Motavali, H; Jog, M Rowshan Almeh
2008-01-01
We discuss scalar-tensor cosmology with an extra $R^{-1}$ correction by the Noether Symmetry Approach. The existence of such a symmetry selects the forms of the coupling $\\omega(\\phi)$, of the potential $V(\\phi)$ and allows to obtain physically interesting exact cosmological solutions.
Hamiltonian dynamics and Noether symmetries in Extended Gravity Cosmology
Capozziello, Salvatore; Odintsov, Sergei D
2012-01-01
We discuss the Hamiltonian dynamics for cosmologies coming from Extended Theories of Gravity. In particular, minisuperspace models are taken into account searching for Noether symmetries. The existence of conserved quantities gives selection rule to recover classical behaviors in cosmic evolution according to the so called Hartle criterion, that allows to select correlated regions in the configuration space of dynamical variables. We show that such a statement works for general classes of Extended Theories of Gravity and is conformally preserved. Furthermore, the presence of Noether symmetries allows a straightforward classification of singularities that represent the points where the symmetry is broken. Examples of nonminimally coupled and higher-order models are discussed.
Some exact anisotropic solutions via Noether symmetry in f(R) gravity
Energy Technology Data Exchange (ETDEWEB)
Sharif, M., E-mail: msharif.math@pu.edu.pk; Nawazish, I., E-mail: iqranawazish07@gmail.com [University of the Punjab, Department of Mathematics (Pakistan)
2015-01-15
We attempt to find exact solutions of the Bianchi I model in f(R) gravity using the Noether symmetry approach. For this purpose, we take a perfect fluid and formulate conserved quantities for the power-law f(R) model. We discuss some cosmological parameters for the resulting solution which are responsible for expanding behavior of the universe. We also explore Noether gauge symmetry and the corresponding conserved quantity. It is concluded that symmetry generators as well as conserved quantities exist in all cases and the behavior of cosmological parameters shows consistency with recent observational data.
Noether's theorem and Lie symmetries for time-dependent Hamilton-Lagrange systems.
Struckmeier, Jürgen; Riedel, Claus
2002-12-01
Noether and Lie symmetry analyses based on point transformations that depend on time and spatial coordinates will be reviewed for a general class of time-dependent Hamiltonian systems. The resulting symmetries are expressed in the form of generators whose time-dependent coefficients follow as solutions of sets of ordinary differential ("auxiliary") equations. The interrelation between the Noether and Lie sets of auxiliary equations will be elucidated. The auxiliary equations of the Noether approach will be shown to admit invariants for a much broader class of potentials, compared to earlier studies. As an example, we work out the Noether and Lie symmetries for the time-dependent Kepler system. The Runge-Lenz vector of the time-independent Kepler system will be shown to emerge as a Noether invariant if we adequately interpret the pertaining auxiliary equation. Furthermore, additional nonlocal invariants and symmetries of the Kepler system will be isolated by identifying further solutions of the auxiliary equations that depend on the explicitly known solution path of the equations of motion. Showing that the invariants remain unchanged under the action of different symmetry operators, we demonstrate that a unique correlation between a symmetry transformation and an invariant does not exist.
Indian Academy of Sciences (India)
R Naz; F M Mahomed
2014-07-01
The Lie and Noether point symmetry analyses of a th-order system of complex ordinary differential equations (ODEs) with dependent variables are performed. The decomposition of complex symmetries of the given system of complex ODEs yields Lie- and Noether-like operators. The system of complex ODEs can be split into 2 coupled real partial differential equations (PDEs) and 2 Cauchy–Riemann (CR) equations. The classical approach is invoked to compute the symmetries of the 4 real PDEs and these are compared with the decomposed Lie- and Noetherlike operators of the system of complex ODEs. It is shown that, in general, the Lie- and Noether-like operators of the system of complex ODEs and the symmetries of the decomposed system of real PDEs are not the same. A similar analysis is carried out for restricted systems of complex ODEs that split into 2 coupled real ODEs. We summarize our findings on restricted complex ODEs in two propositions.
Noether symmetry analysis of anisotropic universe in modified gravity
Shamir, M. Farasat; Kanwal, Fiza
2017-05-01
In this paper we study the anisotropic universe using Noether symmetries in modified gravity. In particular, we choose a locally rotationally symmetric Bianchi type-I universe for the analysis in f(R,G) gravity, where R is the Ricci scalar and G is the Gauss-Bonnet invariant. Firstly, a model f(R,G)=f_0R^l+f_1G^n is proposed and the corresponding Noether symmetries are investigated. We have also recovered the Noether symmetries for f( R) and f(G) theories of gravity. Secondly, some important cosmological solutions are reconstructed. Exponential and power-law solutions are reported for a well-known f(R,G) model, i.e., f(R,G)=f_0R^nG^{1-n}. Especially, Kasner's solution is recovered and it is anticipated that the familiar de Sitter spacetime giving Λ CDM cosmology may be reconstructed for some suitable value of n.
Institute of Scientific and Technical Information of China (English)
Zheng Shi-Wang; Tang Yi-Fa; Fu Jing-Li
2006-01-01
Non-Noether symmetries and conservative quantities of nonholonomic nonconservative dynamical systems are investigated in this paper. Based on the relationships among motion, nonconservative forces, nonholonomic constrained forces and Lagrangian, non-Noether symmetries and Lutzky conservative quantities are presented for nonholonomic nonconservative dynamical systems. The relation between non-Noether symmetry and Noether symmetry is discussed and it is further shown that non-Noether conservative quantities can be obtained by a complete set of Noether invariants. Finally, an example is given to illustrate these results.
Weak Noether symmetry for nonholonomic systems of non-Chetaev type
Institute of Scientific and Technical Information of China (English)
Xie Jia-Fang; Gang Tie-Qiang; Mei Feng-Xiang
2008-01-01
Baaed on the weak Noether symmetry proposed by Mei F X,this paper discusses the weak Noether symmetry for nonholonomic system of non-Chetaev type,and presents expressions of three kinds of conserved quantities by weak Noether symmetry.Finally,the application of this new results is showed by a practical example.
Institute of Scientific and Technical Information of China (English)
Zhang Yi
2009-01-01
This paper is devoted to studying the conformal invariance and Noether symmetry and Lie symmetry of a holonomic mechanical system in event space. The definition of the conformal invariance and the corresponding conformal factors of the holonomic system in event space are given. By investigating the relation between the conformal invariance and the Noether symmetry and the Lie symmetry, expressions of conformal factors of the system under these circumstances are obtained, and the Noether conserved quantity and the Hojman conserved quantity directly derived from the conformal invariance are given. Two examples are given to illustrate the application of the results.
Camci, U; Oz, I Basaran
2016-01-01
The Noether symmetry approach is useful tool to restrict the arbitrariness in a gravity theory when the equations of motion are underdetermined due to the high number of functions to be determined in the ansatz. We consider two scalar-coupled theories of gravity, one motivated by induced gravity, the other more standard; in Bianchi I, Bianchi III and Kantowski-Sachs cosmological models. For these models, we present a full set of Noether gauge symmetries, which are more general than those obtained by the strict Noether symmetry approach in our recent work. Some exact solutions are derived using the first integrals corresponding to the obtained Noether gauge symmetries.
de Souza, Rudinei C
2013-01-01
The aim of the present work is to investigate a non-minimally coupled scalar field model through the Noether symmetry approach. The radiation, matter and cosmological constant eras are analyzed. By means of a change of coordinates in the configuration space generated by the Noether symmetry, the field equations can be reduced to a single equation which is of the form of the Friedmann equation for the $\\Lambda$CDM model. In this way, it is formally shown that the dynamical system can furnish solutions with the same form as those of the $\\Lambda$CDM model, although the theory here considered is physically different from the former. The conserved quantity associated with the Noether symmetry can be related to the kinetic term of the scalar field and could constrain the possible deviations of the model from the $\\Lambda$CDM picture.
Conformal invariance, Noether symmetry, Lie symmetry and conserved quantities of Hamilton systems
Institute of Scientific and Technical Information of China (English)
Chen Rong; Xu Xue-Jun
2012-01-01
In this paper,the relation of the conformal invariance,the Noether symmetry,and the Lie symmetry for the Hamilton system is discussed in detail. The definition of the conformal invariance for Hamilton systems is given.The relation between the conformal invariance and the Noether symmetry is discussed,the conformal factors of the determining expressions are found by using the Noether symmetry,and the Noether conserved quantity resulted from the conformal invariance is obtained.The relation between the conformal invariance and the Lie symmetry is discussed,the conformal factors are found by using the Lie symmetry,and the Hojman conserved quantity resulted from the conformal invariance of the system is obtained.Two examples are given to illustrate the application of the results.
Generalized (2+1) dimensional black hole by Noether symmetry
Energy Technology Data Exchange (ETDEWEB)
Darabi, F. [Center for Excellence in Astronomy and Astrophysics of IRAN (CEAAI-RIAAM), Maragha (Iran, Islamic Republic of); Azarbaijan Shahid Madani University, Department of Physics, Tabriz (Iran, Islamic Republic of); Atazadeh, K.; Rezaei-Aghdam, A. [Azarbaijan Shahid Madani University, Department of Physics, Tabriz (Iran, Islamic Republic of)
2013-12-15
We use the Noether symmetry approach to find f(R) theory of (2+1) dimensional gravity and (2+1) dimensional black hole solution consistent with this f(R) gravity and the associated symmetry. We obtain f(R)=D{sub 1} R(n/n+1)(R/K){sup 1/n} + D{sub 2}R + D{sub 3}, where the constant term D{sub 3} plays no dynamical role. Then, we find general spherically symmetric solution for this f(R) gravity which is potentially capable of being as a black hole. Moreover, in the special case D{sub 1} = 0, D{sub 2} = 1, namely f(R) = R + D{sub 3}, we obtain a generalized BTZ black hole which, other than common conserved charges m and J, contains a new conserved charge Q. It is shown that this conserved charge corresponds to the freedom in the choice of the constant term D{sub 3} and represents symmetry of the action under the transformation R {yields}R' = R + D{sub 3} along the killing vector {partial_derivative}{sub R}. The ordinary BTZ black hole is obtained as the special case where D{sub 3} is fixed to be proportional to the infinitesimal cosmological constant and consequently the symmetry is broken via Q=0. We study the thermodynamics of the generalized BTZ black hole and show that its entropy can be described by the Cardy-Verlinde formula. (orig.)
Institute of Scientific and Technical Information of China (English)
ZHANG Ming-Jiang; FANG Jian-Hui; LU Kai
2009-01-01
Based on the concept of adiabatic invariant, the perturbation to Noether-Mei symmetry and adiabatic invariants for nonholonomic mechanical systems in phase space are studied. The definition of the perturbation to Noether-Mei symmetry for the system is presented, and the criterion of the perturbation to Noether-Mei symmetry is given. Meanwhile, the Noether adiabatic invariants and the Mei adiabatic invariants for the perturbed system are obtained.
Noether-Lie symmetry and conserved quantities of mechanical system in phase space
Institute of Scientific and Technical Information of China (English)
Fang Jian-Hui; Liao Yong-Pan; Ding Ning; Wang Peng
2006-01-01
In this paper, a new kind of symmetry and its conserved quantities of a mechanical system in phase space are studied. The definition of this new symmetry, i.e. a Noether-Lie symmetry, is presented, and the criterion of this symmetry is also given. The Noether conserved quantity and the generalized Hojman conserved quantity of the NoetherLie symmetry of the system are obtained. The Noether-Lie symmetry contains the Nocthcr symmetry and the Lie symmetry, and has more generalized significance.
Directory of Open Access Journals (Sweden)
Gülden Gün
2013-01-01
Full Text Available We analyze Noether and -symmetries of the path equation describing the minimum drag work. First, the partial Lagrangian for the governing equation is constructed, and then the determining equations are obtained based on the partial Lagrangian approach. For specific altitude functions, Noether symmetry classification is carried out and the first integrals, conservation laws and group invariant solutions are obtained and classified. Then, secondly, by using the mathematical relationship with Lie point symmetries we investigate -symmetry properties and the corresponding reduction forms, integrating factors, and first integrals for specific altitude functions of the governing equation. Furthermore, we apply the Jacobi last multiplier method as a different approach to determine the new forms of -symmetries. Finally, we compare the results obtained from different classifications.
Noether Symmetries of the Area-Minimizing Lagrangian
Directory of Open Access Journals (Sweden)
Adnan Aslam
2012-01-01
Full Text Available It is shown that the Lie algebra of Noether symmetries for the Lagrangian minimizing an (n-1-area enclosing a constant n-volume in a Euclidean space is so(n⊕sℝn and in a space of constant curvature the Lie algebra is so(n. Furthermore, if the space has one section of constant curvature of dimension n1, another of n2, and so on to nk and one of zero curvature of dimension m, with n≥∑j=1knj+m (as some of the sections may have no symmetry, then the Lie algebra of Noether symmetries is ⊕j=1kso(nj+1⊕(so(m⊕sℝm.
Noether symmetry for non-minimally coupled fermion fields
de Souza, Rudinei C
2008-01-01
A cosmological model where a fermion field is non-minimally coupled with the gravitational field is studied. By applying Noether symmetry the possible functions for the potential density of the fermion field and for the coupling are determined. Cosmological solutions are found showing that the non-minimally coupled fermion field behaves as an inflaton describing an accelerated inflationary scenario, whereas the minimally coupled fermion field describes a decelerated period being identified as dark matter.
Noether Symmetries Quantization and Superintegrability of Biological Models
Directory of Open Access Journals (Sweden)
Maria Clara Nucci
2016-12-01
Full Text Available It is shown that quantization and superintegrability are not concepts that are inherent to classical Physics alone. Indeed, one may quantize and also detect superintegrability of biological models by means of Noether symmetries. We exemplify the method by using a mathematical model that was proposed by Basener and Ross (2005, and that describes the dynamics of growth and sudden decrease in the population of Easter Island.
Generalized Noether symmetry in f(T) gravity
Energy Technology Data Exchange (ETDEWEB)
Mohseni Sadjadi, H., E-mail: mohsenisad@ut.ac.ir [Department of Physics, University of Tehran, P.O.B. 14395-547, Tehran 14399-55961 (Iran, Islamic Republic of)
2012-12-05
We consider modified teleparallel gravity (f(T) gravity), as a framework to explain the present accelerated expansion of the universe. The matter component is assumed to be cold dark matter. To find the explicit form of the function f, we utilize generalized Noether theorem and use generalized vector fields as variational symmetries of the corresponding Lagrangian. We study the cosmological consequences of the obtained results.
Generalized Noether symmetry in f(T) gravity
Sadjadi, H Mohseni
2012-01-01
We consider modified teleparallel gravity, (f(T) gravity), as a framework to explain the present accelerated expansion of the universe. The matter component is assumed to be cold dark matter. To find the explicit form of the function $f$, we utilize generalized Noether theorem and use generalized vector fields as a variational symmetries of the corresponding Lagrangian. We study the cosmological consequences of the obtained results.
Noether symmetry analysis of anisotropic universe in modified gravity
Energy Technology Data Exchange (ETDEWEB)
Shamir, M.F.; Kanwal, Fiza [National University of Computer and Emerging Sciences, Department of Sciences and Humanities, Lahore (Pakistan)
2017-05-15
In this paper we study the anisotropic universe using Noether symmetries in modified gravity. In particular, we choose a locally rotationally symmetric Bianchi type-I universe for the analysis in f(R, G) gravity, where R is the Ricci scalar and G is the Gauss-Bonnet invariant. Firstly, a model f(R, G) = f{sub 0}R{sup l} + f{sub 1}G{sup n} is proposed and the corresponding Noether symmetries are investigated. We have also recovered the Noether symmetries for f(R) and f(G) theories of gravity. Secondly, some important cosmological solutions are reconstructed. Exponential and power-law solutions are reported for a well-known f(R, G) model, i.e., f(R, G) = f{sub 0}R{sup n}G{sup 1-n}. Especially, Kasner's solution is recovered and it is anticipated that the familiar de Sitter spacetime giving ΛCDM cosmology may be reconstructed for some suitable value of n. (orig.)
Institute of Scientific and Technical Information of China (English)
ZHANG Xiao-Ni; FANG Jian-Hui; PANG Ting; LIN Peng
2009-01-01
For a nonholonomic mechanical system, the generalized Mei conserved quantity and the new generalized Hojman conserved quantity deduced from Noether symmetry of the system are studied.The criterion equation of the Noether symmetry for the system is got.The conditions under which the Noether symmetry can lead to the two new conserved quantities are presented and the forms of the conserved quantities are obtained.Finally, an example is given to illustrate the application of the results.
Noether symmetries in the phase space
Díaz, Bogar; Galindo-Linares, Elizabeth; Ramírez-Romero, Cupatitzio; Silva-Ortigoza, Gilberto; Suárez-Xique, Román; Torres del Castillo, Gerardo F.; Velázquez, Mercedes
2014-09-01
The constants of motion of a mechanical system with a finite number of degrees of freedom are related to the variational symmetries of a Lagrangian constructed from the Hamiltonian of the original system. The configuration space for this Lagrangian is the phase space of the original system. The symmetries considered in this manner include transformations of the time and may not be canonical in the standard sense.
Noether symmetries in the phase space
Directory of Open Access Journals (Sweden)
Bogar Díaz
2014-09-01
Full Text Available The constants of motion of a mechanical system with a finite number of degrees of freedom are related to the variational symmetries of a Lagrangian constructed from the Hamiltonian of the original system. The configuration space for this Lagrangian is the phase space of the original system. The symmetries considered in this manner include transformations of the time and may not be canonical in the standard sense.
Nucci, M. C.
2014-03-01
If tn are the heights of the Riemann zeros 1/2 + itn, an old idea, attributed to Hilbert and Polya [6], stated that the Riemann hypothesis would be proved if the tn could be shown to be eigenvalues of a self-adjoint operator. In 1986 Berry [1] conjectured that tn could instead be the eigenvalues of a deterministic quantum system with a chaotic classical counterpart and in 1999 Berry and Keating [3] proposed the Hamiltonian H = xp, with x and p the position and momentum of a one-dimensional particle, respectively. This was proven not to be the correct Hamiltonian since it yields a continuum spectrum [23] and therefore a more general Hamiltonian H = w(x)(p + l2p/p) was proposed [25], [4], [24] and different expressions of the function w(x) were considered [25], [24], [16] although none of them yielding exactly tn. We show that the quantization by means of Lie and Noether symmetries [18], [19], [20], [7] of the Lagrangian equation corresponding to the Hamiltonian H yields straightforwardly the Schrödinger equation and clearly explains why either the continuum or the discrete spectrum is obtained. Therefore we infer that suitable Lie and Noether symmetries of the classical Lagrangian corresponding to H should be searched in order to alleviate one of Berry's quantum obsessions [2].
Quantum tunneling from generalized (2+1) dimensional black holes having Noether symmetry
Energy Technology Data Exchange (ETDEWEB)
Darabi, F. [Azarbaijan Shahid Madani University, Department of Physics, Tabriz (Iran, Islamic Republic of); Research Institute for Astronomy and Astrophysics of Maragha (RIAAM), Maragha (Iran, Islamic Republic of); Atazadeh, K.; Rezaei-Aghdam, A. [Azarbaijan Shahid Madani University, Department of Physics, Tabriz (Iran, Islamic Republic of)
2014-07-15
We have studied the Hawking radiation from generalized rotating and static (2+1)-dimensional BTZ black holes. In this regard, we have benefited from the quantum tunneling approach with WKB approximation and obtained the tunneling rate of outgoing scalar and spinor particles across the horizons. We have also obtained the Hawking temperature at the horizons corresponding to the emission of these particles. It is shown that the tunneling rate and Hawking temperature of generalized (2+1)-dimensional BTZ black holes are different from ordinary (2+1)-dimensional BTZ black holes due to the Noether symmetry. In other words, the Noether symmetry can change the tunneling rate and Hawking temperature of the BTZ black holes. This symmetry may cause the BTZ black holes to avoid evaporation and its breakdown may start the evaporation. (orig.)
Institute of Scientific and Technical Information of China (English)
Fu Jing-Li; Nie Ning-Ming; Huang Jian-Fei; Jiménez Salvador; Tang Yi-Fa; Vázquez Luis; Zhao Wei-Jia
2009-01-01
This paper presents a method to find Noether-type conserved quantities and Lie point symmetries for discrete mechanico-electrical dynamical systems, which leave invariant the set of solutions of the corresponding difference scheme.This approach makes it possible to devise techniques for solving the Lagrange-Maxwell equations in differences which correspond to mechanico-electrical systems, by adapting existing differential equations. In particular, it obtains a new systematic method to determine both the one-parameter Lie groups and the discrete Noether conserved quantities of Lie point symmetries for mechanico-electrical systems. As an application, it obtains the Lie point symmetries and the conserved quantities for the difference equation of a model that represents a capacitor microphone.
General scalar-tensor cosmology: analytical solutions via noether symmetry
Energy Technology Data Exchange (ETDEWEB)
Massaeli, Erfan; Motaharfar, Meysam; Sepangi, Hamid Reza [Shahid Beheshti University, Department of Physics, Tehran (Iran, Islamic Republic of)
2017-02-15
We analyze the cosmology of a general scalar-tensor theory which encompasses generalized Brans-Dicke theory, Gauss-Bonnet gravity, non-minimal derivative gravity, generalized Galilean gravity and also the general k-essence type models. Instead of taking into account phenomenological considerations we adopt a Noether symmetry approach, as a physical criterion, to single out the form of undetermined functions in the action. These specified functions symmetrize equations of motion in the simplest possible form which result in exact solutions. Demanding de Sitter, power-law and bouncing universe solutions in the absence and presence of matter density leads to exploring new as well as well-investigated models. We show that there are models for which the dynamics of the system allows a transition from a decelerating phase (matter dominated era) to an accelerating phase (dark energy epoch) and could also lead to general Brans-Dicke with string correction without a self-interaction potential. Furthermore, we classify the models based on a phantom or quintessence dark energy point of view. Finally, we obtain the condition for stability of a de Sitter solution for which the solution is an attractor of the system. (orig.)
General Scalar-Tensor cosmology: Analytical solutions via Noether symmetry
Masaeli, Erfan; Sepangi, Hamid Reza
2016-01-01
We analyze the cosmology of a general Scalar-Tensor theory which encompasses generalized Brans-Dicke theory, Gauss-Bonnet gravity, non-minimal derivative gravity, generalized Galileon gravity and also the general k-essence type models. Instead of taking into account phenomenological considerations we adopt a Noether symmetry approach, as a physical criterion, to single out the form of undetermined functions in the action. These specified functions symmetrize equations of motion in the simplest possible form which result in exact solutions. Demanding de Sitter, power-law and bouncing universe solutions in the absence and presence of matter density leads to exploring new as well as well-investigated models. We show that there are models for which dynamics of the system allow transition from a decelerating phase (matter dominated era) to an accelerating phase (dark energy epoch) and could also lead to general Brans-Dicke with string correction without a self-interaction potential. Furthermore, we classify the mo...
General scalar-tensor cosmology: analytical solutions via noether symmetry
Massaeli, Erfan; Motaharfar, Meysam; Sepangi, Hamid Reza
2017-02-01
We analyze the cosmology of a general scalar-tensor theory which encompasses generalized Brans-Dicke theory, Gauss-Bonnet gravity, non-minimal derivative gravity, generalized Galilean gravity and also the general k-essence type models. Instead of taking into account phenomenological considerations we adopt a Noether symmetry approach, as a physical criterion, to single out the form of undetermined functions in the action. These specified functions symmetrize equations of motion in the simplest possible form which result in exact solutions. Demanding de Sitter, power-law and bouncing universe solutions in the absence and presence of matter density leads to exploring new as well as well-investigated models. We show that there are models for which the dynamics of the system allows a transition from a decelerating phase (matter dominated era) to an accelerating phase (dark energy epoch) and could also lead to general Brans-Dicke with string correction without a self-interaction potential. Furthermore, we classify the models based on a phantom or quintessence dark energy point of view. Finally, we obtain the condition for stability of a de Sitter solution for which the solution is an attractor of the system.
Kepler方程的Noether-Lie对称性与守恒量%Noether-Lie Symmetry and Conserved Quantities of the Kepler Equation
Institute of Scientific and Technical Information of China (English)
殷保祥; 刘晓巍; 李元成; 徐超; 宋子龙
2012-01-01
The Noether-Lie symmetry and conserved quantities of the Kepler equation are studied. The Kepler equation, we obtain the Noether symmetry and the Lie symmetry for the equation and the conserved quantities deduced from them, then the definition and criterion for Noether-Lie symmetry of the Kepler equation are derived. Lastly,the Noether conserved quantity and the Hojman conserved quantity are deduced from the Noether-Lie symmetry.%研究Kepler方程的对称性与守恒量。给出Kepler方程的Noether-Lie对称性的定义和判据,以及由Noether-Lie对称性导出Noether守恒量和Hojman守恒量。
Institute of Scientific and Technical Information of China (English)
刘晓巍; 李元成
2011-01-01
The Noether-Lie symmetry and conserved quantities of the Rosenberg problem are studied. From the study of the Rosenberg problem,the Noether symmetry and the Lie symmetry for the equation are obtained, thereby the conserved quantities are deduced. Then the definition and the criterion for Noether-Lie symmetry of the Rosenberg problem are derived. Finally,the Noether conserved quantity and the Hojman conserved quantity are deduced from the Noether-Lie symmetry%研究Rosenberg问题的对称性与守恒量．给出Rosenberg问题的Noether-Lie对称性的定义和判据，以及由Noether-Lie对称性导出Noether守恒量和Hojman守恒量．
Invariant solutions and Noether symmetries in Hybrid Gravity
Borowiec, Andrzej; De Laurentis, Mariafelicia; Lobo, Francisco S N; Paliathanasis, Andronikos; Paolella, Mariacristina; Wojnar, Aneta
2014-01-01
Symmetries play a crucial role in physics and, in particular, the Noether symmetries are a useful tool both to select models motivated at a fundamental level, and to find exact solutions for specific Lagrangians. In this work, we consider the application of point symmetries in the recently proposed metric-Palatini Hybrid Gravity in order to select the $f({\\cal R})$ functional form and to find analytical solutions for the field equations and for the related Wheeler-DeWitt (WDW) equation. We show that, in order to find out integrable $f({\\cal R})$ models, conformal transformations in the Lagrangians are extremely useful. In this context, we explore two conformal transformations of the forms $d\\tau=N(a) dt$ and $d\\tau=N(\\phi) dt$. For the former conformal transformation, we found two cases of $f({\\cal R})$ functions where the field equations admit Noether symmetries. In the second case, the Lagrangian reduces to a Brans-Dicke-like theory with a general coupling function. For each case, it is possible to transfor...
Noether Symmetry of an Anisotropic Universe in a Modified Teleparallel Gravity
Tajahmad, Behzad
2016-01-01
In this paper, we have presented the Noether symmetries of locally rotationally symmetric Bianchi type I (LRS BI), anisotropic model, in the context of the teleparallel gravity. We have studied a certain modified teleparallel theory based on action that, in particular, contains a coupling between the scalar field and field strength (magnetism part). We derive the symmetry generators and show that, by means of cyclic variables approach, we can not reach at solutions for field equations. Hence by the use of B.N.S. approach we have solve the equations which carries Noether currents as well. The main goal of the paper is to give an interpretation laying at the last half of the age of universe that is accelerating. By data analysis of the obtained results, we have showed a compatible results with observational data.
Hojman conserved quantity deduced by weak Noether symmetry for Lagrange systems
Institute of Scientific and Technical Information of China (English)
Xie Jia-Fang; Gang Tie-Qiang; Mei Feng-Xiang
2008-01-01
This paper studies the Hojman conserved quantity,a non-Noether conserved quantity,deduced by special weak Noether symmetry for Lagrange systems.Under special infinitesimal transformations in which the time is not variable,its criterion is given and a method of how to seek the Hojman conserved quantity is presented.A Hojman conserved quantity can be found by using the special weak Noether symmetry.
Noether symmetry in $F(T)$ gravity with $f$-essence
Myrzakulov, Kairat; Myrzakulov, Ratbay
2016-01-01
In $F(T)$ gravity theory, a Friedman-Robertson-Walker cosmological model with $f$-essence where fermion field is non-minimally coupled with the gravitational field is studied. Using the Noether symmetry approach the possible forms of $F(T)$ gravity and the non-canonical fermionic lagrangian $K$ are determined. Cosmological solutions of the condered models describing the accelerated and decelerated periods of the universe are found.
Revisiting Noether Symmetry of Palatini $F(R)$ gravity
Sk, Nayem
2016-01-01
Recently, Roshan et.al. has claimed in $\\mathrm{Phys. Lett. \\textbf{B668}, 238 (2008)}$ that Noether symmetry in the context of Palatini $F(R)$ theory of gravity admit $F(R)\\propto R^{s}$, (where $s$ is arbitrary) in matter domain era in Friedmann- Robertson-Walker (FRW) universe. But, it has been shown that the conserved current obtained under the process does not satisfy the field equations in general, except $s=\\frac{3}{2}$. Therefore, their claim is wrong.
Noether and Lie symmetries for charged perfect fluids
Kweyama, M C; Maharaj, S D
2013-01-01
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.
A late time accelerated FRW model with scalar and vector fields via Noether symmetry
Energy Technology Data Exchange (ETDEWEB)
Vakili, Babak, E-mail: b-vakili@iauc.ac.ir
2014-11-10
We study the evolution of a three-dimensional minisuperspace cosmological model by the Noether symmetry approach. The phase space variables turn out to correspond to the scale factor of a flat Friedmann–Robertson–Walker (FRW) model, a scalar field with potential function V(ϕ) with which the gravity part of the action is minimally coupled and a vector field of its kinetic energy is coupled with the scalar field by a coupling function f(ϕ). Then, the Noether symmetry of such a cosmological model is investigated by utilizing the behavior of the corresponding Lagrangian under the infinitesimal generator of the desired symmetry. We explicitly calculate the form of the coupling function between the scalar and the vector fields and also the scalar field potential function for which such symmetry exists. Finally, by means of the corresponding Noether current, we integrate the equations of motion and obtain exact solutions for the scale factor, scalar and vector fields. It is shown that the resulting cosmology is an accelerated expansion universe for which its expansion is due to the presence of the vector field in the early times, while the scalar field is responsible of its late time expansion.
A late time accelerated FRW model with scalar and vector fields via Noether symmetry
Directory of Open Access Journals (Sweden)
Babak Vakili
2014-11-01
Full Text Available We study the evolution of a three-dimensional minisuperspace cosmological model by the Noether symmetry approach. The phase space variables turn out to correspond to the scale factor of a flat Friedmann–Robertson–Walker (FRW model, a scalar field with potential function V(ϕ with which the gravity part of the action is minimally coupled and a vector field of its kinetic energy is coupled with the scalar field by a coupling function f(ϕ. Then, the Noether symmetry of such a cosmological model is investigated by utilizing the behavior of the corresponding Lagrangian under the infinitesimal generator of the desired symmetry. We explicitly calculate the form of the coupling function between the scalar and the vector fields and also the scalar field potential function for which such symmetry exists. Finally, by means of the corresponding Noether current, we integrate the equations of motion and obtain exact solutions for the scale factor, scalar and vector fields. It is shown that the resulting cosmology is an accelerated expansion universe for which its expansion is due to the presence of the vector field in the early times, while the scalar field is responsible of its late time expansion.
A late time accelerated FRW model with scalar and vector fields via Noether symmetry
Vakili, Babak
2014-01-01
We study the evolution of a three-dimensional minisuperspace cosmological model by the Noether symmetry approach. The phase space variables turn out to correspond to the scale factor of a flat Friedmann-Robertson-Walker (FRW) model, a scalar field with potential function $V(\\phi)$ with which the gravity part of the action is minimally coupled and a vector field its kinetic energy is coupled with the scalar field by a coupling function $f(\\phi)$. Then, the Noether symmetry of such a cosmological model is investigated by utilizing the behavior of the corresponding Lagrangian under the infinitesimal generator of the desired symmetry. We explicitly calculate the form of the coupling function between the scalar and the vector fields and also the scalar field potential function for which such symmetry exists. Finally, by means of the corresponding Noether current we integrate the equations of motion and obtain exact solutions for the scale factor, scalar and vector fields. It is shown that the resulting cosmology i...
A late time accelerated FRW model with scalar and vector fields via Noether symmetry
Vakili, Babak
2014-11-01
We study the evolution of a three-dimensional minisuperspace cosmological model by the Noether symmetry approach. The phase space variables turn out to correspond to the scale factor of a flat Friedmann-Robertson-Walker (FRW) model, a scalar field with potential function V (ϕ) with which the gravity part of the action is minimally coupled and a vector field of its kinetic energy is coupled with the scalar field by a coupling function f (ϕ). Then, the Noether symmetry of such a cosmological model is investigated by utilizing the behavior of the corresponding Lagrangian under the infinitesimal generator of the desired symmetry. We explicitly calculate the form of the coupling function between the scalar and the vector fields and also the scalar field potential function for which such symmetry exists. Finally, by means of the corresponding Noether current, we integrate the equations of motion and obtain exact solutions for the scale factor, scalar and vector fields. It is shown that the resulting cosmology is an accelerated expansion universe for which its expansion is due to the presence of the vector field in the early times, while the scalar field is responsible of its late time expansion.
Noether Gauge Symmetry of Dirac Field in (2 + 1-Dimensional Gravity
Directory of Open Access Journals (Sweden)
Ganim Gecim
2015-01-01
Full Text Available We consider a gravitational theory including a Dirac field that is nonminimally coupled to gravity in 2 + 1 dimensions. Noether gauge symmetry approach can be used to fix the form of coupling function F(Ψ and the potential V(Ψ of the Dirac field and to obtain a constant of motion for the dynamical equations. In the context of (2 + 1-dimensional gravity, we investigate cosmological solutions of the field equations using these forms obtained by the existence of Noether gauge symmetry. In this picture, it is shown that, for the nonminimal coupling case, the cosmological solutions indicate both an early-time inflation and late-time acceleration for the universe.
Noether symmetries of vacuum classes of pp-waves and the wave equation
Jamal, Sameerah; Shabbir, Ghulam
2016-06-01
The Noether symmetry algebras admitted by wave equations on plane-fronted gravitational waves with parallel rays are determined. We apply the classification of different metric functions to determine generators for the wave equation, and also adopt Noether's theorem to derive conserved forms. For the possible cases considered, there exist symmetry groups with dimensions two, three, five, six and eight. These symmetry groups contain the homothetic symmetries of the spacetime.
Noether-Mei symmetry of a discrete mechanico-electrical system
Institute of Scientific and Technical Information of China (English)
Zhang Wei-Wei; Fang Jian-Hui
2012-01-01
Noether-Mei symmetry of a discrete mechanico-electrical system on a regular lattice is investigated.Firstly,the Noether symmetry of a discrete mechanico-electrical system is reviewed,and the motion equations and energy equations are derived.Secondly,the definition of Noether Mei symmetry for the system is presented,and the criterion is derived.Thirdly,conserved quantities induced by Noethe-Mei symmetry with their existence conditions are obtained.Finally,an example is discussed to illustrate the results.
Noether Symmetry Analysis of the Dynamic Euler-Bernoulli Beam Equation
Johnpillai, A. G.; Mahomed, K. S.; Harley, C.; Mahomed, F. M.
2016-05-01
We study the fourth-order dynamic Euler-Bernoulli beam equation from the Noether symmetry viewpoint. This was earlier considered for the Lie symmetry classification. We obtain the Noether symmetry classification of the equation with respect to the applied load, which is a function of the dependent variable of the underlying equation. We find that the principal Noether symmetry algebra is two-dimensional when the load function is arbitrary and extends for linear and power law cases. For all cases, for each of the Noether symmetries associated with the usual Lagrangian, we construct conservation laws for the equation via the Noether theorem. We also provide a basis of conservation laws by using the adjoint algebra. The Noether symmetries pick out the special value of the power law, which is -7. We consider the Noether symmetry reduction for this special case, which gives rise to a first integral that is used for our numerical code. For this, we then find numerical solutions using an in-built function in MATLAB called bvp4c, which is a boundary value solver for differential equations that are depicted in five figures. The physical solutions obtained are for the deflection of the beam with an increase in displacement. These are given in four figures and discussed.
Noether symmetries and exact solutions of an Euler-Bernoulli beam model
Fatima, Aeeman; Mahomed, Fazal M.; Khalique, Chaudry Masood
2016-07-01
In this paper, a Noether symmetry analysis is carried out for an Euler-Bernoulli beam equation via the standard Lagrangian of its reduced scalar second-order equation which arises from the standard Lagrangian of the fourth-order beam equation via its Noether integrals. The Noether symmetries corresponding to the reduced equation is shown to be the inherited Noether symmetries of the standard Lagrangian of the beam equation. The corresponding Noether integrals of the reduced Euler-Lagrange equations are deduced which remarkably allows for three families of new exact solutions of the static beam equation. These are shown to contain all the previous solutions obtained from the standard Lie analysis and more.
Noether symmetries and conserved quantities for fractional Birkhoffian systems with time delay
Zhai, Xiang-Hua; Zhang, Yi
2016-07-01
The Noether symmetries and the conserved quantities for fractional Birkhoffian systems with time delay in terms of Riemann-Liouville fractional derivatives are proposed and studied. First, the fractional Pfaff-Birkhoff principle with time delay is proposed, and the fractional Birkhoff's equations with time delay are obtained. Second, based on the invariance of the fractional Pfaff action with time delay under a group of infinitesimal transformations, the Noether symmetric transformations and the Noether quasi-symmetric transformations of the system are defined, and the criteria of the Noether symmetries are established. Finally, the relationship between the symmetries and the conserved quantities are studied, and the Noether theorems for fractional Birkhoffian systems with time delay are established. Some examples are given to illustrate the application of the results.
Noether's Symmetry Theorem for Variational and Optimal Control Problems with Time Delay
Frederico, G. S. F.; Torres, D. F. M.
2012-01-01
We extend the DuBois-Reymond necessary optimality condition and Noether's symmetry theorem to the time delay variational setting. Both Lagrangian and Hamiltonian versions of Noether's theorem are proved, covering problems of the calculus of variations and optimal control with delays.
Lie Symmetry and Non-Noether Conserved Quantity for Hamiltonian Systems
Institute of Scientific and Technical Information of China (English)
吴惠彬
2004-01-01
A non-Noether conserved quantity for the Hamiltonian system is studied. A particular infinitesimal transformation is given and the determining equations of Lie symmetry are established. An existence theorem of the non-Noether conserved quantity is obtained. An example is given to illustrate the application of the result.
Constraining non-minimally coupled tachyon fields by Noether symmetry
de Souza, Rudinei C
2008-01-01
A model for a spatially flat homogeneous and isotropic Universe whose gravitational sources are a pressureless matter field and a tachyon field non-minimally coupled to the gravitational field is analyzed. Noether symmetry is used to find the expressions for the potential density and for the coupling function, and it is shown that both must be exponential functions of the tachyon field. Two cosmological solutions are investigated: (i) for the early Universe whose only source of the gravitational field is a non-minimally coupled tachyon field which behaves as an inflaton and leads to an exponential accelerated expansion and (ii) for the late Universe whose gravitational sources are a pressureless matter field and a non-minimally coupled tachyon field which plays the role of dark energy and is the responsible of the decelerated-accelerated transition period.
Exact Scalar-Tensor Cosmological Solutions via Noether Symmetry
Belinchón, J A; Mak, M K
2016-01-01
In this paper, we investigate the Noether symmetries of a generalized scalar-tensor, Brans-Dicke type cosmological model, in which we consider explicit scalar field dependent couplings to the Ricci scalar, and to the scalar field kinetic energy, respectively. We also include the scalar field self-interaction potential into the gravitational action. From the condition of the vanishing of the Lie derivative of the gravitational cosmological Lagrangian with respect to a given vector field we obtain three cosmological solutions describing the time evolution of a spatially flat Friedman-Robertson-Walker Universe filled with a scalar field. The cosmological properties of the solutions are investigated in detail, and it is shown that they can describe a large variety of cosmological evolutions, including models that experience a smooth transition from a decelerating to an accelerating phase.
Noether-Lie Symmetry of Lagrange Mechanical System%Lagrange系统的Noether-Lie对称性
Institute of Scientific and Technical Information of China (English)
顾书龙; 何龙庆
2007-01-01
研究了Lagrange力学系统的一种新对称性:Noether-Lie对称性及其守恒量.给出了Lagrange系统的Noether-Lie对称性的定义和判据,提出Lagrange系统的Noether-Lie对称性导致的Noether守恒量和Hojman守恒量.最后给出一个例子说明结果的应用.
Teleparallel dark energy model with a fermionic field via Noether symmetry
Energy Technology Data Exchange (ETDEWEB)
Kucukakca, Yusuf [Akdeniz University, Department of Physics, Faculty of Science, Antalya (Turkey)
2014-10-15
In the present work, we consider a model with a fermionic field that is non-minimally coupled to gravity in the framework of teleparallel gravity. In order to determine the forms of the coupling and potential function of fermionic field for the considered model, we use the Noether symmetry approach. By applying this approach, for the Friedman-Robertson-Walker metric, we obtain the respective potential and coupling functions as a linear and power-law form of the bilinear Ψ. Furthermore, we search for the exact cosmological solution of the model. It is shown that the fermionic field plays the role of dark energy. (orig.)
Noether-Lie Symmetry of Lagrange System%Lagrange系统的Noether-Lie对称性
Institute of Scientific and Technical Information of China (English)
梅凤翔
2005-01-01
研究Lagrange系统的对称性与守恒量.给出Lagrange系统Noether-Lie对称性的定义、判据,以及由Noether-Lie对称性导致的Noether守恒量和Hojman守恒量,举例说明结果的应用.
New conserved quantities of Noether-Mei symmetry of mechanical system in phase space
Institute of Scientific and Technical Information of China (English)
Fang Jian-Hui; Liu Yang-Kui; Zhang Xiao-Ni
2008-01-01
This paper studies two new types of conserved quantities deduced by Noether-Mei symmetry of mechanical system in phase space. The definition and criterion of Noether-Mei symmetry for the system are given. A coordination function is introduced, and the conditions under which the Noether-Mei symmetry leads to the two types of conserved quantities and the forms of the two types of conserved quantities are obtained. An illustrative example is given. The coordination function can be selected according to the demand for finding the gauge function, and the choice of the coordination function has multiformity, so more conserved quantities deduced from Noether-Mei symmetry of mechanical system can be obtained.
Lie symmetries and non-Noether conserved quantities for Hamiltonian canonical equations
Institute of Scientific and Technical Information of China (English)
Fu Jing-Li; Chen Li-Qun; Xie Feng-Ping
2004-01-01
This paper focuses on studying Lie symmetries and non-Noether conserved quantities of Hamiltonian dynamical systems in phase space. Based on the infinitesimal transformations with respect to the generalized coordinates and generalized momenta, we obtain the determining equations and structure equation of the Lie symmetry for Hamiltonian dynamical systems. This work extends the research of non-Noether conserved quantity for Hamilton canonical equations,and leads directly to a new type of non-Noether conserved quantities of the systems. Finally, an example is given to illustrate these results.
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
The symmetries and non-Noether conservation laws of Birkhoffian system with unilateral constraints are studied. The differential equations of motion of the system are established, and the criterions of Noether symmetry,Lie symmetry and Mei symmetry of the system are given. Two types of new conservation laws, called the Hojman conservation law and the Mei conservation law respectively, are obtained, and the intrinsic relations among the symmetries and the new conservation laws are researched. At the end of the paper, an example is given to illustrate the application of the results.
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.
Non-Noether symmetries of Hamiltonian systems with conformable fractional derivatives
Lin-Li, Wang; Jing-Li, Fu
2016-01-01
In this paper, we present the fractional Hamilton’s canonical equations and the fractional non-Noether symmetry of Hamilton systems by the conformable fractional derivative. Firstly, the exchanging relationship between isochronous variation and fractional derivatives, and the fractional Hamilton principle of the system under this fractional derivative are proposed. Secondly, the fractional Hamilton’s canonical equations of Hamilton systems based on the Hamilton principle are established. Thirdly, the fractional non-Noether symmetries, non-Noether theorem and non-Noether conserved quantities for the Hamilton systems with the conformable fractional derivatives are obtained. Finally, an example is given to illustrate the results. Project supported by the National Natural Science Foundation of China (Grant Nos. 11272287 and 11472247), the Program for Changjiang Scholars and Innovative Research Team in University, China (Grant No. IRT13097), and the Key Science and Technology Innovation Team Project of Zhejiang Province, China (Grant No. 2013TD18).
Classification of static plane symmetric spacetime via Noether gauge symmetries
Jhangeer, Adil; Iftikhar, Nazish; Naz, Tayyaba
2016-07-01
In this paper, general static plane symmetric spacetime is classified with respect to Noether operators. For this purpose, Noether theorem is used which yields a set of linear partial differential equations (PDEs) with unknown radial functions A(r), B(r) and F(r). Further, these PDEs are solved by taking different possibilities of radial functions. In the first case, all radial functions are considered same, while two functions are taken proportional to each other in second case, which further discussed by taking four different relationships between A(r), B(r) and F(r). For all cases, different forms of unknown functions of radial factor r are reported for nontrivial Noether operators with non-zero gauge term. At the end, a list of conserved quantities for each Noether operator Tables 1-4 is presented.
Schaft, Arjan van der
1981-01-01
The definitions of symmetries and conservation laws for autonomous (i.e. without external forces) Hamiltonian systems are generalized to Hamiltonian systems with inputs and outputs. It is shown that a symmetry implies the existence of a conservation law and vice versa; thereby generalizing Noether's
Cosmological viable Mimetic $f(R)$ and $f(R,T)$ theories via Noether symmetry
Momeni, D; Güdekli, E
2015-01-01
Extended $f(R)$ theories of gravity have been investigated from the symmetry point of view. We briefly has been investigated Noether symmetry of two types of extended $f(R)$ theories: $f(R,T)$ theory, in which curvature is coupled non minimally to the trace of energy momentum tensor $T_{\\mu\
Institute of Scientific and Technical Information of China (English)
顾书龙
2011-01-01
The research on the Noether symmetry and its conserved quantity for dynamics system is a relatively new direction of development in modern mathematical physics, and can be applied to quantum mechanics, mechanics of space flight and some fields in modern engineering science. In this paper, the Noether symmetry and the Noether conserved quantities of the H6non-Heiles system were studied. The determining equations of Noether symmetry for the system had been got. The Noether symmetry definition and criterion of Henon-Heiles system were given. A theorem asserting that the Noether symmetry for the system leads to the several conserved quantity was presented.%动力学系统的Noether对称性与守恒量研究一直是近代数学物理的一个重要的新发展方向,多应用于量子力学、空间飞行力学及现代工程力学领域.研究Hénon-Heiles系统动力学方程在群无限小变换下的Noether对称性,得到其确定方程,给出其Norther对称性的定义与判据,并由其Noether对称性直接导出几个Noether守恒量.
Institute of Scientific and Technical Information of China (English)
Fu Jing-Li; Chen Li-Qun; Chen Xian-Wei
2006-01-01
This paper investigates the momentum-dependent symmetries for nonholonomic nonconservative Hamilton canonical systems. The definition and determining equations of the momentum-dependent symmetries are presented, based on the invariance of differential equations under infinitesimal transformations with respect to the generalized coordinates and generalized momentums. The structure equation and the non-Noether conserved quantities of the systems are obtained. The inverse issues associated with the momentum-dependent symmetries are discussed. Finally, an example is discussed to further illustrate the applications.
Systematic Derivation of Noether Point Symmetries in Special Relativistic Field Theories
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.
A short review on Noether's theorems, gauge symmetries and boundary terms, for students
Bañados, Máximo
2016-01-01
This review is dedicated to some modern applications of the remarkable paper written in 1918 by E. Noether. On a single paper, Noether discovered the crucial relation between symmetries and conserved charges as well as the impact of gauge symmetries on the equations of motion. Almost a century has gone since the publication of this work and its applications have permeated modern physics. Our focus will be on some examples that have appeared recently in the literature. This review is aim at students, not researchers. The main three topics discussed are (i) global symmetries and conserved charges (ii) local symmetries and gauge structure of a theory (iii) boundary conditions and algebra of asymptotic symmetries. All three topics are discussed through examples.
Quintom cosmological model and some possible solutions using Lie and Noether symmetries
Dutta, Sourav; Chakraborty, Subenoy
2016-01-01
The present work deals with a quintom model of dark energy in the framework of a spatially flat isotropic and homogeneous Friedmann-Lemaitre-Robertson-Walker (FLRW) universe. At first, Lie point symmetry is imposed to the system and the unknown coupled potential of the model is determined. Then Noether symmetry, which is also a point like symmetry of the Lagrangian, is imposed on the physical system and the potential takes a general form. It is shown that the Lie algebra of Noether symmetry is a sub-algebra of the corresponding Lie algebra of the Lie symmetry. Finally, a point transformation in the three dimensional augmented space is performed suitably so that one of the variables become cyclic and as a result there is considerable simplification to the physical system. Hence conserved quantities (i.e, constants of motion) are expressed in a compact form and cosmological solutions are evaluated and analyzed in the present context.
Chaplygin gas of Tachyon Nature Imposed by Noether Symmetry and constrained via H(z) data
Gardai Collodel, Lucas; Medeiros Kremer, Gilberto
2016-04-01
An action of general form is proposed for a Universe containing matter, radiation and dark energy. The latter is interpreted as a tachyon field non-minimally coupled to the scalar curvature. The Palatini approach is used when varying the action so the connection is given by a more generic form. Both the self-interaction potential and the non-minimally coupling function are obtained by constraining the system to present invariability under global point transformation of the fields (Noether Symmetry). The only possible solution is shown to be that of minimal coupling and constant potential (Chaplygin gas). The behavior of the dynamical properties of the system is compared to recent observational data, which infers that the tachyon field must indeed be dynamical.
Bluhm, Robert
2016-01-01
Gravitational effective field theories with nondynamical backgrounds explicitly break diffeomorphism and local Lorentz invariance. At the same time, to maintain observer independence the action describing these theories is required to be mathematically invariant under general coordinate transformations and changes of local Lorentz bases. These opposing effects of having broken spacetime symmetries but invariance under mathematical observer transformations can result in theoretical inconsistency unless certain conditions hold. The consistency constraints that must hold originate from Noether identities associated with the mathematical observer invariances in the action. These identities are examined in detail and are used to investigate gravity theories with nondynamical backgrounds, including when a St\\"uckelberg approach is used. Specific examples include gravity theories with fixed scalar or tensor backgrounds, Einstein-Maxwell theory with a fixed external current, and massive gravity.
Bluhm, Robert; Šehić, Amar
2016-11-01
Gravitational effective field theories with nondynamical backgrounds explicitly break diffeomorphism and local Lorentz invariance. At the same time, to maintain observer independence the action describing these theories is required to be mathematically invariant under general coordinate transformations and changes of local Lorentz bases. These opposing effects of having broken spacetime symmetries but invariance under mathematical observer transformations can result in theoretical inconsistency unless certain conditions hold. The consistency constraints that must hold originate from Noether identities associated with the mathematical observer invariances in the action. These identities are examined in detail and are used to investigate gravity theories with nondynamical backgrounds, including when a Stückelberg approach is used. Specific examples include gravity theories with fixed scalar or tensor backgrounds, Einstein-Maxwell theory with a fixed external current, and massive gravity.
Noether-Type Symmetries and Associated Conservation Laws of Some Systems of Nonlinear PDEs
Institute of Scientific and Technical Information of China (English)
MEI Jian-Qin
2009-01-01
The algorithm for constructing conservation laws of Etder-Lagrange--type equations via Noether-type symmetry operators associated with partial Lagrangian has been presented. As applications, many new conservation laws of some important systems of nonlinear partial differential equations have been obtained.
Noether symmetries and anisotropic universe models in f(R, T) gravity
Sharif, M.; Nawazish, Iqra
2017-08-01
This paper investigates the existence of Noether symmetries of some anisotropic homogeneous universe models in non-minimally coupled f(R, T) gravity (R and T represent Ricci scalar and trace of the energy-momentum tensor). We evaluate symmetry generators and the corresponding conserved quantities for two models of this theory admitting direct and indirect non-minimal curvature-matter coupling. We also discuss exact solutions for dust as well as non-dust matter distribution and study the physical behavior of some cosmological parameters through these solutions. For dust distribution, the exact solution corresponds to power-law expansion and Einstein universe while exponential expansion appears for non-dust matter. The graphical analysis of these solutions and cosmological parameters provide consistent results with recent observations about accelerated cosmic expansion. We conclude that Noether symmetry generators and conserved quantities exist for both models.
Self-acceleration and matter content in bicosmology from Noether Symmetries
Bouhmadi-López, Mariam; Martín-Moruno, Prado
2016-01-01
We consider the existence of Noether symmetries in bigravity cosmologies in order to constrain the material content minimally coupled to the gravitational sector that we are not inhabiting. Interestingly, a Noether symmetry not only constrain the matter content of the universe we do not inhabit but also comes as a sort of bonus on the form of a very interesting dynamics of the universe we live in. In fact, by assuming that our universe is filled with standard matter and radiation, we show that the existence of a Noether symmetry implies the existence of a vacuum energy in our universe that can explain, in a natural way, the current acceleration of the universe. This vacuum energy is intrinsic to the model and can be realized either for a theory that is not properly a bigravity model or for a genuinely bimetric scenario. In fact, it would correspond to a "mono"-universe with a $\\Lambda$CDM matter symmetry or to a bimetric world where our universe would have once again a $\\Lambda$CDM matter symmetry while the n...
Paliathanasis, A.; Krishnakumar, K.; Leach, P. G. L.
2016-04-01
We discuss the relationship between the Noether point symmetries of the geodesic Lagrangian, in a (pseudo)Riemannian manifold, with the elements of the Homothetic algebra of the space. We observe that the classification problem of the Noether symmetries for the geodesic Lagrangian is equivalent with the classification of the Homothetic algebra of the space, which in the case of a Friedmann-Lemaître-Robertson-Walker spacetime is a well-known result in the literature.
Structure properties and Noether symmetries for super-long elastic slender rod
Institute of Scientific and Technical Information of China (English)
Fu Jing-Li; Zhao Wei-Jia; Weng Yu-Quan
2008-01-01
DNA is a nucleic acid molecule with double-helical structures that are special symmetrical structures attracting great attention of numerous researchers. The super-long elastic slender rod, an important structural model of DNA and other long-train molecules, is a useful tool in analysing the symmetrical properties and the stabilities of DNA. This paper studies the structural properties of a super-long elastic slender rod as a structural model of DNA by using Kirchhoff's analogue technique and presents the Noether symmetries of the model by using the method of infinitesimal transformation. Based on Kirchhoff's analogue it analyses the generalized Hamilton canonical equations. The infinitesimal transformations with respect to the radial coordinate, the generalized coordinates, and the quasi-momenta of the model are introduced. The Noether symmetries and conserved quantities of the model are obtained.
Kantowski-Sachs cosmological solutions in the generalized teleparallel gravity via Noether symmetry
Motavalli, H.; Akbarieh, A. Rezaei; Nasiry, M.
2016-04-01
We study the f(T) theory as an extension of teleparallel gravity and consider the Noether symmetry of Kantowski-Sachs (KS) anisotropic model for this theory. We specify the explicit teleparallel form of f(T) and find the corresponding exact cosmological solutions under the assumption that the Lagrangian admits the Noether symmetry. It is found that the universe experiences a power law expansion for the scale factors in the context of f(T) theory. By deriving equation of state (EOS) parameter, we show that the universe passes through the phantom and ΛCDM theoretical scenarios. In this way, we estimate a lower limit age for the universe in excellent agreement with the value reported from recent observations. When KS model reduces to the flat Friedmann-Robertson-Walker (FRW) metric, our results are properly transformed into the corresponding values.
Some exact solutions in f(𝒢,T) gravity via Noether symmetries
Shamir, M. Farasat; Ahmad, Mushtaq
2017-05-01
This paper is devoted to investigate the recently proposed modified Gauss-Bonnet f(𝒢,T) gravity, with 𝒢, the Gauss-Bonnet term, coupled with T, the trace of energy-momentum tensor. We have used the Noether symmetry methodology to discuss some cosmologically important f(𝒢,T) gravity models with anisotropic background. In particular, the Noether symmetry equations for modified f(𝒢,T) gravity are reported for locally rotationally symmetric Bianchi type I universe. Explicitly, two models have been proposed to explore the exact solutions and the conserved quantities. It is concluded that the specific models of modified Gauss-Bonnet gravity may be used to reconstruct ΛCDM cosmology without involving any cosmological constant.
A study of phantom scalar field cosmology using Lie and Noether symmetries
Dutta, Sourav
2016-01-01
The paper deals with phantom scalar field cosmology in Einstein gravity. At first using Lie symmetry, the coupling function to the kinetic term and the potential function of the scalar field and the equation of state parameter of the matter field are determined and a simple solution is obtained. Subsequently, Noether symmetry is imposed on the Lagrangian of the system. The symmetry vector is obtained and the potential takes a very general form from which potential using Lie Symmetry can be obtained as a particular case. Then we choose a point transformation $(a,\\phi)\\rightarrow(u,v)$ such that one of the transformed variables (say u) is a cyclic for the Lagrangian. Using conserved charge (corresponding to the cyclic coordinate) and the constant of motion, solutions are obtained.
A study of positive energy condition in Bianchi V spacetimes via Noether symmetries
Ali, Sajid
2015-01-01
In this paper we use Noether symmetries of the geodesic Lagrangian in Bianchi V spacetimes to study various cosmological solutions of Einstein's field equations. Our first result is the identification of the subalgebras of Noether symmetries of the equations of motions in such spacetimes with dimension 4, 5, 6, 7, 9 or 10 of the maximal algebra of Lie point symmetries of dimension 13. Secondly we give physical interpretation of new cosmological solutions which satisfy positive energy condition and yield critical bounds on the expansion coefficient $\\alpha$, in which the underlying non-flat spacetimes carry interesting physical properties. Specifically the energy density behaves in one of the following ways. (i) It is positive and constant for all time. (ii) It varies with time and attains a global maximum after some time and then asymptotically converges to zero. (iii) It increases for all time and attains a maximum value at the asymptotic limit $t\\rightarrow \\infty$. In particular a non-flat spacetime is obt...
A study of positive energy condition in Bianchi V spacetimes via Noether symmetries
Energy Technology Data Exchange (ETDEWEB)
Ali, Sajid; Hussain, Ibrar [National University of Sciences and Technology, Department of Basic Sciences, School of Electrical Engineering and Computer Science, Islamabad (Pakistan)
2016-02-15
In this paper we use Noether symmetries of the geodesic Lagrangian in Bianchi V spacetimes to study various cosmological solutions of Einstein's field equations. Our first result is the identification of the subalgebras of Noether symmetries of the equations of motion in such spacetimes with dimension 4, 5, 6, 7, 9 or 10 of the maximal algebra of Lie point symmetries of dimension 13. Second, we give a physical interpretation of new cosmological solutions which satisfy the positive energy condition and yield critical bounds on the expansion coefficient α, in which the underlying nonflat spacetimes have interesting physical properties. Specifically the energy density behaves in one of the following ways. (i) It is positive and constant for all time. (ii) It varies with time and attains a global maximum after some time and then asymptotically converges to zero. (iii) It increases for all time and attains a maximum value at the asymptotic limit t → ∞ In particular a non-flat spacetime is obtained that mimics the expansion in a flat FRW universe dominated by vacuum energy such that the expansion factor has the same form in both. However, the energy density is dynamical in the former. (orig.)
Directory of Open Access Journals (Sweden)
Adil Jhangeer
2016-01-01
Full Text Available Petrov Type D-Levi-Civita (DLC space-time is considered in two different coordinates, that is, spherical and cylindrical. Noether gauge symmetries and their corresponding conserved quantities for respective metric with the restricted range of parameters and coordinates are discussed.
Revisiting conserved currents in F(R) theory of gravity via Noether symmetry
Sk., Nayem; 10.1088/0256-307X/30/2/020401
2013-01-01
Noether symmetry of F(R) theory of gravity in vacuum and in the presence of pressureless dust yields F(R) \\propto R^{3/2} along with the conserved current \\frac{d}{dt}(a\\sqrt R) in Robertson-Walker metric and nothing else. Still some authors recently claimed to have obtained four conserved currents setting F(R) \\propto R^{3/2} a-priori, taking time translation along with a gauge term. We show that the first one of these does not satisfy the field equations and the second one is the Hamiltonian which is constrained to vanish in gravity and thus a part and parcel of the field equations. We also show that the other two conserved currents, which do not contain time translation are the same in disguise and identical to the one mentioned above. Thus the claim is wrong.
The Mathematics of Truth and Beauty: Emmy Noether, Symmetry and the Seduction of a Science Writer
Cole, K. C.
1998-05-01
The universe is a complicated place, and journalists, astronomers, philosophers and poets are all preoccupied with trying to make sense of it. Curiously, many people outside the sciences do not make use of one of the most powerful tools available: the language of mathematics. Mathematics brings surprising clarity to an astonishing range of issues, from cosmic questions (the fate of the universe), to social controversy (race and IQ scores) to matters of public policy (voting and fairness). These tools are easily accessible to lay people--including even reporters, and females, despite persistent assumptions to the contrary. This writer, in particular became entranced by the connection between fundamental laws of nature and symmetry established by the mathematician Emmy Noether--and its implications "outside the walls" of science.
Seidl, Gerhart
2014-01-01
We present a simple generalization of Noether's theorem for discrete symmetries in relativistic continuum field theories. We calculate explicitly the conserved current for several discrete spacetime and internal symmetries. In addition, we formulate an analogue of the Ward-Takahashi identity for the Noether current associated with a discrete symmetry.
Noether Symmetries and Covariant Conservation Laws in Classical, Relativistic and Quantum Physics
Directory of Open Access Journals (Sweden)
Lorenzo Fatibene
2010-04-01
Full Text Available We review the Lagrangian formulation of (generalised Noether symmetries in the framework of Calculus of Variations in Jet Bundles, with a special attention to so-called “Natural Theories” and “Gauge-Natural Theories” that include all relevant Field Theories and physical applications (from Mechanics to General Relativity, to Gauge Theories, Supersymmetric Theories, Spinors, etc.. It is discussed how the use of Poincar´e–Cartan forms and decompositions of natural (or gauge-natural variational operators give rise to notions such as “generators of Noether symmetries”, energy and reduced energy flow, Bianchi identities, weak and strong conservation laws, covariant conservation laws, Hamiltonian-like conservation laws (such as, e.g., so-calledADMlaws in General Relativity with emphasis on the physical interpretation of the quantities calculated in specific cases (energy, angular momentum, entropy, etc.. A few substantially new and very recent applications/examples are presented to better show the power of the methods introduced: one in Classical Mechanics (definition of strong conservation laws in a frame-independent setting and a discussion on the way in which conserved quantities depend on the choice of an observer; one in Classical Field Theories (energy and entropy in General Relativity, in its standard formulation, in its spin-frame formulation, in its first order formulation “à la Palatini” and in its extensions to Non-Linear Gravity Theories; one in Quantum Field Theories (applications to conservation laws in Loop Quantum Gravity via spin connections and Barbero–Immirzi connections.
Paliathanasis, Andronikos; Tsamparlis, Michael
2016-09-01
We study the Lie and Noether point symmetries of a class of systems of second-order differential equations with n independent and m dependent variables (n × m systems). We solve the symmetry conditions in a geometric way and determine the general form of the symmetry vector and of the Noetherian conservation laws. We prove that the point symmetries are generated by the collineations of two (pseudo)metrics, which are defined in the spaces of independent and dependent variables. We demonstrate the general results in two special cases (a) a system of m coupled Laplace equations and (b) the Klein-Gordon equation of a particle in the context of Generalized Uncertainty Principle. In the second case we determine the complete invariant group of point transformations, and we apply the Lie invariants in order to find invariant solutions of the wave function for a spin-0 particle in the two dimensional hyperbolic space.
Paliathanasis, Andronikos
2016-01-01
We study the Lie and Noether point symmetries of a class of systems of second-order differential equations with $n$ independent and $m$ dependent variables ($n\\times m$ systems). We solve the symmetry conditions in a geometric way and determine the general form of the symmetry vector and of the Noetherian conservation laws. We prove that the point symmetries are generated by the collineations of two (pseudo)metrics, which are defined in the spaces of independent and dependent variables. We demonstrate the general results in two special cases (a) a system of $m$ coupled Laplace equations and (b) the Klein-Gordon equation of a particle in the context of Generalized Uncertainty Principle. In the second case we determine the complete invariant group of point transformations, and we apply the Lie invariants in order to find invariant solutions of the wave function for a spin-$0$ particle in the two dimensional hyperbolic space.
Institute of Scientific and Technical Information of China (English)
张毅; 丁金凤
2014-01-01
为了进一步揭示力学系统的对称性与守恒量之间的内在关系，基于 El-Nabulsi 分数阶模型提出并研究了广义 Birkhoff 系统的 Noether 定理。首先，提出分数阶广义 El-Nabulsi-Pfaff-Birkhoff 原理，建立广义 El-Nabulsi-Birkhoff 方程。其次，基于 El-Nabulsi-Pfaff 作用量在无限小变换下的不变性，给出广义 Birkhoff 系统 Noether 对称性的定义和判据。最后，提出广义 Birkhoff系统的 Noether 定理。该文研究结果可进一步应用于完整和非完整约束系统。%To further reveal the inner relationships between the symmetries and conserved quantities of mechanical systems,a Noether's theorem of generalized Birkhoff systems is proposed and studied based on El-Nabulsi fractional model. Firstly,a generalized El-Nabulsi-Pfaff-Birkhoff fractional principle is presented, and generalized El-Nabulsi-Birkhoff equations are established; secondly, based on the invariance of the El-Nabulsi-Pfaff action under the infinitesimal transformation,the definitions and criteria of the Noether symmetries of generalized Birkhoff fractional systems are given; finally, a Noether's theorem for generalized Birkhoff fractional systems is proposed. The research results may be applied to systems with holonomic or non-holonomic constraints.
Hamilton formalism and Noether symmetry for mechanico-electrical systems with fractional derivatives
Institute of Scientific and Technical Information of China (English)
Zhang Shi-Hua; Chen Ben-Yong; Fu Jing-Li
2012-01-01
This paper presents extensions to the traditional calculus of variations for mechanico-electrical systems containing fractional derivatives.The Euler-Lagrange equations and the Hamilton formalism of the mechanico-electrical systems with fractional derivatives are established.The definition and the criteria for the fractional generalized Noether quasisymmetry are presented. Furthermore,the fractional Noether theorem and conseved quantities of the systems are obtained by virtue of the invariance of the Hamiltonian action under the infinitesimal transformations.An example is presented to illustrate the application of the results.
Institute of Scientific and Technical Information of China (English)
张毅
2013-01-01
The Noether symmetry and the conserved quantity for a fractional action-like variational problem in phase space are studied based on the method of fractional dynamics modeling presented by ElNabulsi,namely fractional action-like variational approach.First,the fractional action-like variational problem in phase space is established,and the fractional action-like Hamilton canonical equations are obtained.Secondly,the definitions and criteria of the fractional action-like Noether (quasi-) symmetrical transformations are presented in terms of the invariance of the fractional action-like integral of Hamilton under the infinitesimal transformation of group.Finally,the Noether theorems for the fractional actionlike Hamiltonian system are given,the relationship between the Noether symmetry and the conserved quantity of the system is established.An example is given to illustrate the application of the results.%基于El-Nabulsi提出的分数阶动力学建模方法,即类分数阶变分方法,研究相空间中类分数阶变分问题与Noether对称性和守恒量.建立了相空间中类分数阶变分问题,得到了类分数阶Hamilton正则方程；基于类分数阶Hamilton作用量在无限小群变换下的不变性,提出了相空间中类分数阶Noether(准)对称变换的定义和判据；给出了类分数阶Hamilton系统的Noether定理,建立了类分数阶Noether对称性与守恒量之间的内在关系,并举例说明结果的应用.
Noether-Lie symmetry of non-holonomic mechanical system%非完整力学系统的Noether-Lie对称性
Institute of Scientific and Technical Information of China (English)
方建会; 丁宁; 王鹏
2006-01-01
研究了非完整力学系统的一种新对称性--Noether-Lie 对称性及其守恒量. 给出了非完整力学系统Noether -Lie对称性的定义和判据,提出系统的Noether-Lie对称性导致Noether守恒量和广义Hojman守恒量的定理. 举例说明了结果的应用. Hojman守恒量是所给出的广义Hojman守恒量的特例.
Applications of Noether conservation theorem to Hamiltonian systems
Mouchet, Amaury
2016-09-01
The Noether theorem connecting symmetries and conservation laws can be applied directly in a Hamiltonian framework without using any intermediate Lagrangian formulation. This requires a careful discussion about the invariance of the boundary conditions under a canonical transformation and this paper proposes to address this issue. Then, the unified treatment of Hamiltonian systems offered by Noether's approach is illustrated on several examples, including classical field theory and quantum dynamics.
Applications of Noether conservation theorem to Hamiltonian systems
Mouchet, Amaury
2016-01-01
The Noether theorem connecting symmetries and conservation laws can be applied directly in a Hamiltonian framework without using any intermediate Lagrangian formulation. This requires a careful discussion about the invariance of the boundary conditions under a canonical transformation and this paper proposes to address this issue. Then, the unified treatment of Hamiltonian systems offered by Noether's approach is illustrated on several examples, including classical field theory and quantum dynamics.
Institute of Scientific and Technical Information of China (English)
张毅; 陈甦
2005-01-01
The effects of non-conservative forces and nonholonomic constraints on Noether symmetries and conserved quantities of a Hamilton system are studied. When non-conservative forces or nonholonomic constraints are exerted on a Hamilton system,the Noether symmetries and the conserved quantities of the system may vary. It can be seen that some Noether symmetries disappear, some new Noether symmetries emerge, and under certain conditions some Noether symmetries will still remain. In this paper, the conditions under which the Noether symmetries and the conserved quantities of the system will remain are respectively obtained, and two examples are given to illustrate the application of the results.%研究非保守力和非完整约束对Hamilton系统的Noether对称性的影响.Hamilton系统受到非保守力或非完整约束作用时,系统的Noether对称性和守恒量都会发生变化.原有的一些Noether对称性消失了,一些新的Noether对称性产生了,在一定条件下,一些Noether对称性仍保持不变.文中分别给出了系统的Noether对称性以及守恒量保持不变的条件,并举例说明结果的应用.
Institute of Scientific and Technical Information of China (English)
吴润衡; 邹杰涛
2001-01-01
Consider Lie symmetries and Noether symmetries of nonholonomic systems of non-Chetaev's type. Here nonholonomic mechanical systems with constant or variablemass with Chetaev's type or non-Chetaev's type constraints are studied, and the criteria to show the relations between Lie symmetries and Noether symmetries of nonholonomic systems of non-Chetaev's type is given.%研究非Chetaev型非完整系统的Lie对称性与Noether对称性，具体研究了非Chetaev型常质量非完整系统和非Chetaev型变质量非完整系铳的Lie对称性与Noether对称性.给出Lie对称性导致Noether对称性以及Noether对称性导致Lie对称性的条件.
Paliathanasis, Andronikos; Tsamparlis, Michael
2016-01-01
We show that the recent results of \\ [Int. J. Mod. Phys. D 25 (2016) 1650051] on the application of Lie/Noether symmetries in scalar field cosmology are well-known in the literature while the problem could have been solved easily under a coordinate transformation. That follows from the property, that the admitted group of invariant transformations of dynamical system is independent on the coordinate system.
Dutta, Sourav; Panja, Madan Mohan; Chakraborty, Subenoy
2016-06-01
Non-minimally coupled scalar field cosmology has been studied in this work within the framework of Einstein gravity. In the background of homogeneous and isotropic Friedmann-Lemaitre-Robertson-Walker (FLRW) spacetime non-minimally coupled scalar field having self-interacting potential is taken as the source of the matter content. The constraint of imposing Noether symmetry on the Lagrangian of the system not only determines the infinitesimal generator (the symmetry vector) but also the coupling function and the self-interacting potential for the scalar field. By choosing appropriately a point transformation in the augmented space, one of the transformed variables is cyclic for the Lagrangian. Finally, using constants of motion, the solutions are analyzed.
A Time scales Noether's theorem
Anerot, Baptiste; Cresson, Jacky; Pierret, Frédéric
2016-01-01
We prove a time scales version of the Noether's theorem relating group of symmetries and conservation laws. Our result extends the continuous version of the Noether's theorem as well as the discrete one and corrects a previous statement of Bartosiewicz and Torres in \\cite{BT}.
Institute of Scientific and Technical Information of China (English)
金世欣; 张毅
2015-01-01
The Noether symmetries and the conserved quantities of a mechanical system with time delay based on Caputo fractional derivatives are proposed and studied.Firstly,the fractional Lagrange equa-tions with time delay are established.Secondly,based upon the invariance of the fractional Hamilton ac-tion with time delay under the group of infinitesimal transformations,the fractional Noether symmetric transformations,the definitions and criteria of the Noether quasi-symmetric transformations and general-ized Noether quasi-symmetric transformations with time delay are given.Finally,the relationship between the fractional symmetries and the fractional conserved quantities with time delay are studied.At the end, an example is given to illustrate the application of the results.%提出并研究基于 Caputo 分数阶导数的含时滞的力学系统的 Noether 对称性与守恒量。建立了含时滞的非保守系统的分数阶运动微分方程；根据系统的含时滞的分数阶 Hamilton 作用量在无限小群变换下的泛函不变性，给出了含时滞的分数阶 Noether 对称变换，Noether 准对称变换以及 Noether 广义准对称变换的定义判据；研究了含时滞的分数阶 Noether 对称性与守恒量之间的联系，并举例说明结果的应用。
Webb, G M; McKenzie, J F; Hu, Q; Zank, G P
2013-01-01
Conservation laws in ideal gas dynamics and magnetohydrodynamics (MHD) associated with fluid relabelling symmetries are derived using Noether's first and second theorems. Lie dragged invariants are discussed in terms of the MHD Casimirs. A nonlocal conservation law for fluid helicity applicable for a non-barotropic fluid involving Clebsch variables is derived using Noether's theorem, in conjunction with a fluid relabelling symmetry and a gauge transformation. A nonlocal cross helicity conservation law involving Clebsch potentials, and the MHD energy conservation law are derived by the same method. An Euler Poincar\\'e variational approach is also used to derive conservation laws associated with fluid relabelling symmetries using Noether's second theorem.
Institute of Scientific and Technical Information of China (English)
王肖肖; 孙现亭; 张美玲; 解银丽; 贾利群
2012-01-01
Noether symmetry and Noether conserved quantity of Nielsen equation in a dynamical system of the relative motion with nonholonomic constraint of Chetaev＇s type are studied.The differential equation of motion of Nielsen equation for the system,the definition and the criterion of Noether symmetry,and the expression of Noether conserved quantity deduced directly from Noether symmetry for the system are obtained.An example is given to illustrate the application of the results.%研究Chetaev型约束的相对运动动力学系统Nielsen方程的Noether对称性与Noether守恒量.对Chetaev型约束的相对运动力学系统Nielsen方程的运动微分方程、Noether对称性定义和判据进行具体的研究,得到了Noether对称性直接导致的Noether守恒量的表达式.最后举例说明结果的应用.
Modified Noether theorem and arrow of time in quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Asadov, V V; Kechkin, O V, E-mail: asadov@neurok.co, E-mail: kechkin@gmail.co [Neur OK-III, Lomonosov Moscow State University, Vorob' jovy Gory, 119899 Moscow (Russian Federation)
2010-06-01
Relativistic quantum mechanics is presented with modified Noether theorem. It was shown that Noether charges are related with thermodynamic potentials in such scheme. Broken symmetries generated by thermodynamic mode lead to gravity appearance as effective quantum field.
Noether theorems and higher derivatives
Townsend, Paul K
2016-01-01
A simple proof of Noether's first theorem involves the promotion of a constant symmetry parameter $\\epsilon$ to an arbitrary function of time; the Noether charge $Q$ is then the coefficient of $\\dot\\epsilon$ in the variation of the action. Here we examine the validity of this proof for Lagrangian mechanics with arbitrarily-high time derivatives, in which context "higher-level" analogs of Noether's theorem can be similarly proved, and "Noetherian charges" read off from, e.g. the coefficient of $\\ddot \\epsilon$ in the variation of the action. While $Q=0$ implies a restricted gauge invariance, an unrestricted gauge invariance requires zero Noetherian charges too. Some illustrative examples are considered.
Invariance of the Noether charge
Silagadze, Z K
2016-01-01
Surprisingly, an interesting property of the Noether charge that it is by itself invariant under the corresponding symmetry transformation is never discussed in quantum field theory or classical mechanics textbooks we have checked. This property is also almost never mentioned in articles devoted to Noether's theorem. Nevertheless, to prove this property in the context of Lagrangian formalism is not quite trivial and the proof, outlined in this article, can constitute an useful and interesting exercise for students.
Institute of Scientific and Technical Information of China (English)
王廷志; 孙现亭; 贾利群
2014-01-01
在分析非完整力学系统Hamilton方程的Noether-Mei对称性与守恒量的基础上,给出该系统Hamilton方程的Noether-Mei对称性定义和判据,得到非完整力学系统Hamilton方程的Noether-Mei对称性导致的Noether守恒量和Mei守恒量,并给出应用算例.
The coordinate-independent Noether approach to energy-momentum localization
Mitsou, Ermis
2013-01-01
We derive the Noether current associated to the symmetry of active diffeomorphisms, that is, the pushforwards along the integral lines of any vector field. Evaluating it on the vielbein vectors provides an energy-momentum tensor for generally covariant field theory. The matter-independent part then corresponds to the energy-momentum tensor of the gravitational field. It is traceless in four dimensions, quadratic in the first derivatives of the vielbein and gives the standard result when evaluated on linear gravitational waves. However, it is not covariant under local Lorentz transformations and we discuss the conceptual implications of this fact. Moreover, unlike its matter counterpart, it fails to provide a faithful measure of gravitational activity since it can be non-zero for trivial solutions and zero for non-trivial ones. We compute it, as well as the corresponding energy charge, on some standard space-time examples for some simple frames. Our study also contains interesting by-products. For instance, we...
Noether symmetric classical and quantum scalar field cosmology
Vakili, Babak
2011-01-01
We study the evolution of a two dimensional minisuperspace cosmological model in classical and quantum levels by the Noether symmetry approach. The phase space variables turn out to correspond to the scale factor of a Friedmann-Robertson-Walker (FRW) model and a scalar field with which the action of the model is augmented. It is shown that the minisuperspace of such a model is a two dimensional manifold with vanishing Ricci scalar. We present a coordinate transformation which cast the corresponding minisuper metric to a Minkowskian or Euclidean one according to the choices of an ordinary or phantom model for the scalar field. Then, the Noether symmetry of such a cosmological model is investigated by utilizing the behavior of the corresponding Lagrangian under the infinitesimal generators of the desired symmetry. We explicitly calculate the form of the scalar field potential functions for which such symmetries exist. For these potential functions, the exact classical and quantum solutions in the cases where th...
Second Noether theorem for quasi-Noether systems
Rosenhaus, V.; Shankar, R.
2016-04-01
Quasi-Noether differential systems are more general than variational systems and are quite common in mathematical physics. They include practically all differential systems of interest, at least those that have conservation laws. In this paper, we discuss quasi-Noether systems that possess infinite-dimensional (infinite) symmetries involving arbitrary functions of independent variables. For quasi-Noether systems admitting infinite symmetries with arbitrary functions of all independent variables, we state and prove an extension of the second Noether theorem. In addition, we prove that infinite sets of conservation laws involving arbitrary functions of all independent variables are trivial and that the associated differential system is under-determined. We discuss infinite symmetries and infinite conservation laws of two important examples of non-variational quasi-Noether systems: the incompressible Euler equations and the Navier-Stokes equations in vorticity formulation, and we show that the infinite sets of conservation laws involving arbitrary functions of all independent variables are trivial. We also analyze infinite symmetries involving arbitrary functions of not all independent variables, prove that the fluxes of conservation laws in these cases are total divergences on solutions, and demonstrate examples of this situation.
Lie Groupoids in Classical Field Theory I: Noether's Theorem
Costa, Bruno T; Pêgas, Luiz Henrique P
2015-01-01
In the two papers of this series, we initiate the development of a new approach to implementing the concept of symmetry in classical field theory, based on replacing Lie groups/algebras by Lie groupoids/algebroids, which are the appropriate mathematical tools to describe local symmetries when gauge transformations are combined with space-time transformations. Here, we outline the basis of the program and, as a first step, show how to (re)formulate Noether's theorem about the connection between symmetries and conservation laws in this approach.
Higher-Stage Noether Identities and Second Noether Theorems
Directory of Open Access Journals (Sweden)
G. Sardanashvily
2015-01-01
Noether theorems associate with the above-mentioned Koszul–Tate complex a certain cochain sequence whose ascent operator consists of the gauge and higher-order gauge symmetries of a Lagrangian system. If gauge symmetries are algebraically closed, this operator is extended to the nilpotent BRST operator which brings the above-mentioned cochain sequence into the BRST complex and provides a BRST extension of an original Lagrangian.
Axial Current and Noether Charge
Mahato, Prasanta
2012-01-01
A decade ago, a Lagrangian density has been proposed by the author where only the local symmetries of the Lorentz subgroup of (A)ds group is retained. This formalism has been found to produce some results encompassing that of standard Einstein-Hilbert formalism. In the present article, the conserved axial vector matter currents, constructed in some earlier paper, have been found to be a result of Noether's theorem. PACS: 04.20.Fy, 04.20.Cv, 11.40.-q Keywords: Torsion, Axial Current, Noether's Theorem
Faddeev-Jackiw approach to hidden symmetries
Wotzasek, C
1994-01-01
The study of hidden symmetries within Dirac's formalism does not possess a systematic procedure due to the lack of first-class constraints to act as symmetry generators. On the other hand, in the Faddeev-Jackiw approach, gauge and reparametrization symmetries are generated by the null eigenvectors of the sympletic matrix and not by constraints, suggesting the possibility of dealing systematically with hidden symmetries through this formalism. It is shown in this paper that indeed hidden symmetries of noninvariant or gauge fixed systems are equally well described by null eigenvectors of the sympletic matrix, just as the explicit invariances. The Faddeev-Jackiw approach therefore provide a systematic algorithm for treating all sorts of symmetries in an unified way. This technique is illustrated here by the SL(2,R) Kac-Moody current algebra of the 2-D induced gravity proposed by Polyakov, which is a hidden symmetry in the canonical approach of constrained systems via Dirac's method, after conformal and reparamet...
Institute of Scientific and Technical Information of China (English)
丁金凤; 张毅
2014-01-01
基于El-Nabulsi动力学模型，提出并研究了Birkhoff系统基于按指数律拓展的分数阶积分的变分问题的Noether对称性与守恒量。基于按指数律拓展的分数阶积分的El-Nabulsi-Pfaff-Birkhoff变分问题，建立起与之对应的El-Nabulsi-Birkhoff方程；基于El-Nabulsi-Pfaff作用量在无限小变换下的不变性，给出系统的Noether对称变换和Noether准对称变换的定义和判据。该研究建立Birkhoff系统基于按指数律拓展的分数阶积分的变分问题的Noether定理，揭示了该模型下系统的Noether对称性和守恒量之间的关系。文末举例说明结果的应用。%Based on El-Nabulsi dynamical model,the Noether symmetries and the conserved quantities for the variational problem of Birkhoffian system from extended exponentially fractional integral are pres-ented and studied.Firstly,the El-Nabulsi-Pfaff-Birkhoff variational problem from extended exponentially fractional integral is presented,then the corresponding El-Nabulsi-Birkhoff equations are derived.Sec-ondly,the definitions and the criteria of the Noether symmetric transformations and the Noether quasi-symmetric transformations of the system are given,which are based on the invariance of El-Nabulsi-Pfaff action under the infinitesimal transformations of group.Finally,the Noether theorem for the variational problem of Birkhoffian system from extended exponentially fractional integral is established,which reveals the inner relationship between a Noether symmetry and a conserved quantity.An example is given to il-lustrate the application of the results.
Noether's theory of generalized linear nonholonomic mechanical systems
Institute of Scientific and Technical Information of China (English)
Dong Wen-Shan; Huang Bao-Xin; Fang Jian-Hui
2011-01-01
By introducing the quasi-symmetry of the infinitesimal transformation of the transformation group Gr, the Noether's theorem and the Noether's inverse theorem for generalized linear nonholonomic mechanical systems are obtained in a generalized compound derivative space. An example is given to illustrate the application of the result.
Optical chirality in gyrotropic media: symmetry approach
Proskurin, Igor; Ovchinnikov, Alexander S.; Nosov, Pavel; Kishine, Jun-ichiro
2017-06-01
We discuss optical chirality in different types of gyrotropic media. Our analysis is based on the formalism of nongeometric symmetries of Maxwell’s equations in vacuum generalized to material media with given constituent relations. This approach enables us to directly derive conservation laws related to nongeometric symmetries. For isotropic chiral media, we demonstrate that like a free electromagnetic field, both duality and helicity generators belong to the basis set of nongeometric symmetries that guarantees the conservation of optical chirality. In gyrotropic crystals, which exhibit natural optical activity, the situation is quite different from the case of isotropic media. For light propagating along a certain crystallographic direction, there arises two distinct cases: (1) the duality is broken but the helicity is preserved, or (2) only the duality symmetry survives. We show that the existence of one of these symmetries (duality or helicity) is enough to define optical chirality. In addition, we present examples of low-symmetry media, where optical chirality cannot be defined.
A Noether Theorem for Markov Processes
Baez, John C
2012-01-01
Noether's theorem links the symmetries of a quantum system with its conserved quantities, and is a cornerstone of quantum mechanics. Here we prove a version of Noether's theorem for Markov processes. In quantum mechanics, an observable commutes with the Hamiltonian if and only if its expected value remains constant in time for every state. For Markov processes that no longer holds, but an observable commutes with the Hamiltonian if and only if both its expected value and standard deviation are constant in time for every state.
Noether's second theorem in a general setting: reducible gauge theories
Energy Technology Data Exchange (ETDEWEB)
Bashkirov, D [Department of Theoretical Physics, Moscow State University, 117234 Moscow (Russian Federation); Giachetta, G [Department of Mathematics and Informatics, University of Camerino, 62032 Camerino, MC (Italy); Mangiarotti, L [Department of Mathematics and Informatics, University of Camerino, 62032 Camerino, MC (Italy); Sardanashvily, G [Department of Theoretical Physics, Moscow State University, 117234 Moscow (Russian Federation)
2005-06-10
We prove Noether's direct and inverse second theorems for Lagrangian systems on fibre bundles in the case of gauge symmetries depending on derivatives of dynamic variables and parameters of an arbitrary order. The appropriate notions of a reducible gauge symmetry and Noether identity are formulated, and their equivalence by means of a certain intertwining operator is proved.
A Heavy Quark Symmetry Approach to Baryons
Energy Technology Data Exchange (ETDEWEB)
Albertus, C. [Departamento de Fisica Moderna. Facultad de Ciencias, Universidad de Granada, E-18071 Granada (Spain); Amaro, J.E. [Departamento de Fisica Moderna. Facultad de Ciencias, Universidad de Granada, E-18071 Granada (Spain); Hernandez, E. [Grupo de Fisica Nuclear. Facultad de Ciencias, Universidad de Salamanca, E-37008 Salamanca (Spain); Nieves, J. [Departamento de Fisica Moderna. Facultad de Ciencias, Universidad de Granada, E-18071 Granada (Spain)
2005-06-13
We evaluate different properties of baryons with a heavy c or b quark. The use of Heavy Quark Symmetry (HQS) provides with an important simplification of the non relativistic three body problem which can be solved by means of a simple variational approach. This scheme is able to reproduce previous results obtained with more involved Faddeev calculations. The resulting wave functions are parametrized in a simple manner, and can be used to calculate further observables.
Araki, Keisuke
2015-01-01
The dynamics of an incompressible, dissipationless Hall magnetohydrodynamic medium are formulated as a Lagrangian dynamical system on a direct product of two volume-preserving diffeomorphism groups. The hybrid and magnetic helicities are shown to emerge, respectively, from the application of the particle relabeling symmetry for ion and electron flows to Noether's first theorem, while the constant of motion associated with the theorem is generally given by their arbitrary linear combination. Double Beltrami flows, which are obtained here as eigenfunctions of the linear operator that generates the action-preserving perturbation from the generalized velocity, are found to provide a family of orthogonal function bases that yields the spectral representation of the equation of motion with a remarkably simple form. Considering the influence of a uniform background magnetic field and the Hall term effect vanishing limit, the generalized Els\\"asser variables are found to be the most suitable for avoiding problems wit...
Black hole entropy and Lorentz-diffeomorphism Noether charge
Jacobson, Ted; Mohd, Arif
2015-01-01
We show that, in the first or second order orthonormal frame formalism, black hole entropy is the horizon Noether charge for a combination of diffeomorphism and local Lorentz symmetry involving the Lie derivative of the frame. The Noether charge for diffeomorphisms alone is unsuitable, since a regular frame cannot be invariant under the flow of the Killing field at the bifurcation surface. We apply this formalism to Lagrangians polynomial in wedge products of the frame field 1-form and curvat...
The Second Noether Theorem on Time Scales
Malinowska, Agnieszka B.; Natália Martins
2013-01-01
We extend the second Noether theorem to variational problems on time scales. As corollaries we obtain the classical second Noether theorem, the second Noether theorem for the $h$ -calculus and the second Noether theorem for the $q$ -calculus.
Noether-Like Theorems for Causal Variational Principles
Finster, Felix
2015-01-01
The connection between symmetries and conservation laws as made by Noether's theorem is extended to the context of causal variational principles and causal fermion systems. Different notions of continuous symmetries are introduced. It is proven that these symmetries give rise to corresponding conserved quantities, expressed in terms of so-called surface layer integrals. In a suitable limiting case, the Noether-like theorems for causal fermion systems reproduce charge conservation and the conservation of energy and momentum in Minkowski space. Thus the conservation of charge and energy-momentum are found to be special cases of general conservation laws which are intrinsic to causal fermion systems.
Symmetries of Differential equations and Applications in Relativistic Physics
Paliathanasis, Andronikos
2015-01-01
In this thesis, we study the one parameter point transformations which leave invariant the differential equations. In particular we study the Lie and the Noether point symmetries of second order differential equations. We establish a new geometric method which relates the point symmetries of the differential equations with the collineations of the underlying manifold where the motion occurs. This geometric method is applied in order the two and three dimensional Newtonian dynamical systems to be classified in relation to the point symmetries; to generalize the Newtonian Kepler-Ermakov system in Riemannian spaces; to study the symmetries between classical and quantum systems and to investigate the geometric origin of the Type II hidden symmetries for the homogeneous heat equation and for the Laplace equation in Riemannian spaces. At last but not least, we apply this geometric approach in order to determine the dark energy models by use the Noether symmetries as a geometric criterion in modified theories of gra...
Geometric Approach to Lie Symmetry of Discrete Time Toda Equation
Institute of Scientific and Technical Information of China (English)
JIA Xiao-Yu; WANG Na
2009-01-01
By using the extended Harrison and Estabrook geometric approach,we investigate the Lie symmetry of discrete time Toda equation from the geometric point of view.Its one-dimensional continuous symmetry group is presented.
Torsional Newton-Cartan Geometry from the Noether Procedure
Festuccia, Guido; Hartong, Jelle; Obers, Niels A
2016-01-01
We apply the Noether procedure for gauging space-time symmetries to theories with Galilean symmetries, analyzing both massless and massive (Bargmann) realizations. It is shown that at the linearized level the Noether procedure gives rise to (linearized) torsional Newton-Cartan geometry. In the case of Bargmann theories the Newton-Cartan form $M_\\mu$ couples to the conserved mass current. We show that even in the case of theories with massless Galilean symmetries it is necessary to introduce the form $M_\\mu$ and that it couples to a topological current. Further, we show that the Noether procedure naturally gives rise to a distinguished affine (Christoffel type) connection that is linear in $M_\\mu$ and torsionful. As an application of these techniques we study the coupling of Galilean electrodynamics to TNC geometry at the linearized level.
Torsional Newton-Cartan geometry from the Noether procedure
Festuccia, Guido; Hansen, Dennis; Hartong, Jelle; Obers, Niels A.
2016-11-01
We apply the Noether procedure for gauging space-time symmetries to theories with Galilean symmetries, analyzing both massless and massive (Bargmann) realizations. It is shown that at the linearized level the Noether procedure gives rise to (linearized) torsional Newton-Cartan geometry. In the case of Bargmann theories the Newton-Cartan form Mμ couples to the conserved mass current. We show that even in the case of theories with massless Galilean symmetries it is necessary to introduce the form Mμ and that it couples to a topological current. Further, we show that the Noether procedure naturally gives rise to a distinguished affine (Christoffel type) connection that is linear in Mμ and torsionful. As an application of these techniques we study the coupling of Galilean electrodynamics to TNC geometry at the linearized level.
Lie Symmetrical Non-Noether Conserved Quantities of Poincaré-Chetaev Equations
Institute of Scientific and Technical Information of China (English)
ZHANG Peng-Yu; FANG Jian-Hui
2005-01-01
In the present paper the Lie symmetrical non-Noether conserved quantity of the Poincaré-Chetaev equations under the general infinitesimal transformations of Lie groups is discussed. First, we establish the determining equations of Lie symmetry of the equations. Second, the Lie symmetrical non-Noether conserved quantity of the equations is deduced.
The Lie symmetrical non-Noether conserved quantity of holonomic Hamiltonian system
Institute of Scientific and Technical Information of China (English)
Fang Jian-Hui; Liao Yong-Pan; Peng Yong
2004-01-01
In this paper, we study the Lie symmetrical non-Noether conserved quantity of a holonomic Hamiltonian system under the general infinitesimal transformations of groups. Firstly, we establish the determining equations of Lie symmetry of the system. Secondly, the Lie symmetrical non-Noether conserved quantity of the system is deduced. Finally,an example is given to illustrate the application of the result.
Non-Noether conserved quantity for differential equations of motion in the phase space
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
A non-Noether conserved quantity for the differential equations of motion of mechanical systems in the phase space is studied. The differential equations of motion of the systems are established and the determining equations of Lie symmetry are given. An existence theorem of non-Noether conserved quantity is obtained. An example is given to illustrate the application of the result.
New non-Noether conserved quantities of mechanical system in phase space
Institute of Scientific and Technical Information of China (English)
Yan Xiang-Hong; Fang Jian-Hui
2006-01-01
This paper focuses on studying non-Noether conserved quantities of Lie symmetry and of form invariance for a mechanical system in phase space under the general infinitesimal transformation of groups. We obtain a new non-Noether conserved quantity of Lie symmetry of the system, and Hojman and Mei's results are of special cases of our conclusion. We find a condition under which the form invariance of the system will lead to a Lie symmetry, and, further,obtain a new non-Noether conserved quantity of form invariance of the system. An example is given finally to illustrate these results.
Dynamics symmetries of Hamiltonian system on time scales
Energy Technology Data Exchange (ETDEWEB)
Peng, Keke, E-mail: pengkeke88@126.com; Luo, Yiping, E-mail: zjstulyp@126.com [Department of Physics, Zhejiang Sci-Tech University, Hangzhou 310018 (China)
2014-04-15
In this paper, the dynamics symmetries of Hamiltonian system on time scales are studied. We study the symmetries and quantities based on the calculation of variation and Lie transformation group. Particular focus lies in: the Noether symmetry leads to the Noether conserved quantity and the Lie symmetry leads to the Noether conserved quantity if the infinitesimal transformations satisfy the structure equation. As the new application of result, at end of the article, we give a simple example of Noether symmetry and Lie symmetry on time scales.
Dynamics symmetries of Hamiltonian system on time scales
Peng, Keke; Luo, Yiping
2014-04-01
In this paper, the dynamics symmetries of Hamiltonian system on time scales are studied. We study the symmetries and quantities based on the calculation of variation and Lie transformation group. Particular focus lies in: the Noether symmetry leads to the Noether conserved quantity and the Lie symmetry leads to the Noether conserved quantity if the infinitesimal transformations satisfy the structure equation. As the new application of result, at end of the article, we give a simple example of Noether symmetry and Lie symmetry on time scales.
Campoamor-Stursberg, R.
2016-08-01
Using the general solution of the differential equation x¨(t) +g1(t) x˙ +g2(t) x = 0 , a generic basis of the point-symmetry algebra sl(3 , R) is constructed. Deriving the equation from a time-dependent Lagrangian, the basis elements corresponding to Noether symmetries are deduced. The generalized Lewis invariant is constructed explicitly using a linear combination of Noether symmetries. The procedure is generalized to the case of systems of second-order ordinary differential equations with maximal sl(n + 2 , R) -symmetry, and its possible adaptation to the inhomogeneous non-linear case illustrated by an example.
Nucci, M. C.
2016-09-01
We review some of our recent work devoted to the problem of quantization with preservation of Noether symmetries, finding hidden linearity in superintegrable systems, and showing that nonlocal symmetries are in fact local. In particular, we derive the Schrödinger equation for the isochronous Calogero goldfish model using its relation to Darwin equation. We prove the linearity of a classical superintegrable system on a plane of nonconstant curvature. We find the Lie point symmetries that correspond to the nonlocal symmetries (also reinterpreted as λ-symmetries) of the Riccati chain.
Gilmore-Perelomov symmetry based approach to photonic lattices
Vergara, Liliana Villanueva
2015-01-01
We revisit electromagnetic field propagation through tight-binding arrays of coupled photonic waveguides, with properties independent of the propagation distance, and recast it as a symmetry problem. We focus our analysis on photonic lattices with underlying symmetries given by three well-known groups, $SU(2)$, $SU(1,1)$ and Heisenberg-Weyl, to show that disperssion relations, normal states and impulse functions can be constructed following a Gilmore-Perelomov coherent state approach. Furthermore, this symmetry based approach can be followed for each an every lattice with an underlying symmetry given by a dynamical group.
Lie Symmetrical Non-Noether Conserved Quantity of Mechanical System in Phase Space
Institute of Scientific and Technical Information of China (English)
FANGJian-Hui; PENGYong; LIAOYong-Pan; LIHong
2004-01-01
In this paper, we study the Lie symmetrical non-Noether conserved quantity of the differential equations of motion of mechanical system in phase space under the general infinitesimal transformations of groups. Firstly. we give the determining equations of the Lie symmetry of the system. Secondly, the non-Noether conserved quantity of the Lie symmetry is derived. Finally, an example is given to illustrate the application of the result.
FORM INVARIANCE AND NOETHER SYMMETRICAL CONSERVED QUANTITY OF RELATIVISTIC BIRKHOFFIAN SYSTEMS
Institute of Scientific and Technical Information of China (English)
罗绍凯
2003-01-01
A form invariance of the relativistic Birkhoffian system is studied, and the conserved quantities of the system are obtained. Under the infinitesimal transformation of groups, the definition and criteria of the form invariance of the system were given. In view of the invariance of relativistic Pfaff-Birkhoff-D'Alembert principle under the infinitesimal transformation of groups, the theory of Noether symmetries of the relativistic Birkhoffian system were constructed. The relation between the form invariance and the Noether symmetry is studied, and the results show that the form invariance can also lead to the Noether symmetrical conserved quantity of the relativistic Birkhoffian system under certain conditions.
Symmetries of stochastic differential equations: A geometric approach
Energy Technology Data Exchange (ETDEWEB)
De Vecchi, Francesco C., E-mail: francesco.devecchi@unimi.it; Ugolini, Stefania, E-mail: stefania.ugolini@unimi.it [Dipartimento di Matematica, Università degli Studi di Milano, via Saldini 50, Milano (Italy); Morando, Paola, E-mail: paola.morando@unimi.it [DISAA, Università degli Studi di Milano, via Celoria 2, Milano (Italy)
2016-06-15
A new notion of stochastic transformation is proposed and applied to the study of both weak and strong symmetries of stochastic differential equations (SDEs). The correspondence between an algebra of weak symmetries for a given SDE and an algebra of strong symmetries for a modified SDE is proved under suitable regularity assumptions. This general approach is applied to a stochastic version of a two dimensional symmetric ordinary differential equation and to the case of two dimensional Brownian motion.
Symmetries in proteins: A knot theory approach
Chen, Shi-Jie; Dill, Ken A.
1996-04-01
Whereas the symmetries of small molecules are described by the methods of group theory, there is no corresponding way to describe the complex symmetries in proteins. We develop a quantitative method to define and classify symmetries in compact polymers, based on the mathematical theory of graphs and knots. We represent different chain folds by their ``polymer graphs,'' equivalent to contact maps. We transform those graphs into mathematical knots to give a parsing of different possible chain folds into conformational taxonomies. We use Alexander-Conway knot polynomials to characterize the knots. We find that different protein structures with the same tertiary fold, e.g., a βαβ motif with different lengths of α helix and β sheet, can be described in terms of the different powers of the propagation matrices of the knot polynomial. This identifies a fundamental type of topological length invariance in proteins, ``elongatable'' symmetries. For example, ``helix,'' ``sheet,'' ``helix-turn-helix,'' and other secondary, supersecondary, and tertiary structures define structures of any chain length. Possibly the nine superfolds identified by Thornton et al. have elongatable symmetries.
Higgsless approach to electroweak symmetry breaking
Grojean, Christophe
2007-01-01
Higgsless models are an attempt to achieve a breaking of the electroweak symmetry via boundary conditions at the end-points of a fifth dimension compactified on an interval, as an alternative to the usual Higgs mechanism. There is no physical Higgs scalar in the spectrum and the perturbative unitarity violation scale is delayed via the exchange of massive spin-1 KK resonances. The correct mass spectrum is reproduced in a model in warped space, which inherits a custodial symmetry from a left–right gauge symmetry in the bulk. Phenomenological challenges as well as collider signatures are presented. From the AdS/CFT perspective, this model appears as a weakly coupled dual to walking technicolour models.
Black hole entropy and Lorentz-diffeomorphism Noether charge
Jacobson, Ted
2015-01-01
We show that, in the first or second order orthonormal frame formalism, black hole entropy is the horizon Noether charge for a combination of diffeomorphism and local Lorentz symmetry involving the Lie derivative of the frame. The Noether charge for diffeomorphisms alone is unsuitable, since a regular frame cannot be invariant under the flow of the Killing field at the bifurcation surface. We apply this formalism to Lagrangians polynomial in wedge products of the frame field 1-form and curvature 2-form, including general relativity, Lovelock gravity, and "topological" terms in four dimensions.
Thermodynamic Entropy as a Noether Invariant
Sasa, Shin-ichi; Yokokura, Yuki
2016-04-01
We study a classical many-particle system with an external control represented by a time-dependent extensive parameter in a Lagrangian. We show that thermodynamic entropy of the system is uniquely characterized as the Noether invariant associated with a symmetry for an infinitesimal nonuniform time translation t →t +η ℏβ , where η is a small parameter, ℏ is the Planck constant, β is the inverse temperature that depends on the energy and control parameter, and trajectories in the phase space are restricted to those consistent with quasistatic processes in thermodynamics.
Symmetry analysis and conservation laws of the Drinfeld-Sokolov-Wilson system
Zhao, Zhonglong; Zhang, Yufeng; Han, Zhong
2014-07-01
In this paper, Lie symmetry analysis is performed on the Drinfeld-Sokolov-Wilson system. We get the corresponding Lie algebra and similarity reductions of the system. In addition, we utilize Noether's approach and the new conservation theorem deriving the conservation laws of this system.
Random matrix model approach to chiral symmetry
Verbaarschot, J J M
1996-01-01
We review the application of random matrix theory (RMT) to chiral symmetry in QCD. Starting from the general philosophy of RMT we introduce a chiral random matrix model with the global symmetries of QCD. Exact results are obtained for universal properties of the Dirac spectrum: i) finite volume corrections to valence quark mass dependence of the chiral condensate, and ii) microscopic fluctuations of Dirac spectra. Comparisons with lattice QCD simulations are made. Most notably, the variance of the number of levels in an interval containing $n$ levels on average is suppressed by a factor $(\\log n)/\\pi^2 n$. An extension of the random matrix model model to nonzero temperatures and chemical potential provides us with a schematic model of the chiral phase transition. In particular, this elucidates the nature of the quenched approximation at nonzero chemical potential.
Emmy Noether, Greatest Woman Mathematician.
Kimberling, Clark
1982-01-01
A brief history of Amalie Emmy Noether is presented, citing many of her contributions to mathematics and physics. Major credit for the development of modern algebra should probably be given to her. Reference is made to Noether's theorem and Noetherian Rings. (MP)
The Second Noether Theorem on Time Scales
Directory of Open Access Journals (Sweden)
Agnieszka B. Malinowska
2013-01-01
Full Text Available We extend the second Noether theorem to variational problems on time scales. As corollaries we obtain the classical second Noether theorem, the second Noether theorem for the h-calculus and the second Noether theorem for the q-calculus.
The second Noether theorem on time scale
Malinowska, Agnieszka B.; Martins, Natália
2014-01-01
We extend the second Noether theorem to variational problems on time scales. Our result provides as corollaries the classical second Noether theorem, the second Noether theorem for the $h$-calculus and the second Noether theorem for the $q$-calculus.
Extending Noether's theorem by quantifying the asymmetry of quantum states.
Marvian, Iman; Spekkens, Robert W
2014-05-13
Noether's theorem is a fundamental result in physics stating that every symmetry of the dynamics implies a conservation law. It is, however, deficient in several respects: for one, it is not applicable to dynamics wherein the system interacts with an environment; furthermore, even in the case where the system is isolated, if the quantum state is mixed then the Noether conservation laws do not capture all of the consequences of the symmetries. Here we address these deficiencies by introducing measures of the extent to which a quantum state breaks a symmetry. Such measures yield novel constraints on state transitions: for nonisolated systems they cannot increase, whereas for isolated systems they are conserved. We demonstrate that the problem of finding non-trivial asymmetry measures can be solved using the tools of quantum information theory. Applications include deriving model-independent bounds on the quantum noise in amplifiers and assessing quantum schemes for achieving high-precision metrology.
Extending Noether's theorem by quantifying the asymmetry of quantum states
Marvian, Iman
2014-01-01
Noether's theorem is a fundamental result in physics stating that every symmetry of the dynamics implies a conservation law. It is, however, deficient in several respects: (i) it is not applicable to dynamics wherein the system interacts with an environment, and (ii) even in the case where the system is isolated, if the quantum state is mixed then the Noether conservation laws do not capture all of the consequences of the symmetries. To address these deficiencies, we introduce measures of the extent to which a quantum state breaks a symmetry. Such measures yield novel constraints on state transitions: for nonisolated systems, they cannot increase, while for isolated systems they are conserved. We demonstrate that the problem of finding nontrivial asymmetry measures can be solved using the tools of quantum information theory. Applications include deriving model-independent bounds on the quantum noise in amplifiers and assessing quantum schemes for achieving high-precision metrology.
Understanding topological symmetry: a heuristic approach to its determination.
Contreras, M L; Alvarez, J; Guajardo, D; Rozas, R
2008-03-01
An algorithm based on heuristic rules for topological symmetry perception of organic structures having heteroatoms, multiple bonds, and any kind of cycle, and configuration, is presented. This algorithm identifies topological symmetry planes and sets of equivalent atoms in the structure, named symmetry atom groups (SAGs). This approach avoids both the need to explore the entire graph automorphism groups, and to encompass cycle determination, resulting in a very effective computer processing. Applications to several structures, some of them highly symmetrical such as dendrimers, are presented.
Momeni, Davood
2014-01-01
The symmetry issue for Galileons has been studied. In particular we address scaling (conformal) and Noether symmetrized Galileons. We have been proven a series of theorems about the form of Noether conserved charge (current) for irregular (not quadratic) dynamical systems. Special attentions have been made on Galileons. We have been proven that for Galileons always is possible to find a way to "symmetrized" Galileo's field .
Struckmeier, Jürgen; Vasak, David
2016-01-01
We present the derivation of the Yang-Mills gauge theory based on the covariant Hamiltonian representation of Noether's theorem. As the starting point, we re-formulate our previous presentation of the canonical Hamiltonian derivation of Noether's theorem. The formalism is then applied to derive the Yang-Mills gauge theory. The Noether currents of U(1) and SU(N) gauge theories are derived from the respective infinitesimal generating functions of the pertinent symmetry transformations which maintain the form of the Hamiltonian.
Lie Symmetrical Non-Noether Conserved Quantity of Mechanical System in Phase Space
Institute of Scientific and Technical Information of China (English)
FANG Jian-Hui; PENG Yong; LIAO Yong-Pan; LI Hong
2004-01-01
In this paper, we study the Lie symmetrical non-Noether conserved quantity of the differential equations ofmotion of mechanical system in phase space under the general infinitesimal transformations of groups. Firstly, we givethe determining equations of the Lie symmetry of the system. Secondly, the non-Noether conserved quantity of the Liesymmetry is derived. Finally, an example is given to illustrate the application of the result.
Non-Noether Conserved Quantity of Poincaré-Chetaev Equations of a Generalized Classical Mechanics
Institute of Scientific and Technical Information of China (English)
ZHANG Peng-Yu; FANG Jian-Hui; WANG Peng; DING Ning
2006-01-01
In the present paper the Lie symmetrical non-Noether conserved quantity of the Poincaré-Chetaev equations of a generalized classical mechanics under the general infinitesimal transformations of Lie groups is discussed. First, we establish the determining equations of Lie symmetry of the equations. Second, the Lie symmetrical non-Noether conserved quantity of the equations is deduced. Finally, an example is given to illustrate the application of the results.
A rate distortion approach to protein symmetry.
Wallace, Rodrick
2010-08-01
A spontaneous symmetry breaking argument is applied to the problem of protein folding, via a rate distortion analysis of the relation between genome coding and the final condensation of the protein molten globule that is, in spirit, analogous to Tlusty's (2007) exploration of the evolution of the genetic code. In the 'energy' picture, the average distortion between codon message and final protein structure, under constraints driven by evolutionary selection, serves as a temperature analog, so that low values limit the possible distribution of protein forms, producing the canonical folding funnel. A dual 'developmental' perspective sees the rate distortion function itself as the temperature analog, and permits incorporation of chaperons or toxic exposures as catalysts, driving the system to different possible outcomes or affecting the rate of convergence. The rate distortion function appears constrained by the availability of metabolic free energy, with implications for prebiotic evolution, and a nonequilibrium empirical Onsager treatment provides an adaptable statistical model that can be fitted to data, in the same manner as a regression equation. In sum, mechanistic models of protein folding fail to account for the observed spectrum of protein folding and aggregation disorders, suggesting that a biologically based cognitive paradigm describing folding will be needed for understanding the etiology, prevention, and treatment of these diseases. The developmental formalism introduced here may contribute substantially to such a paradigm.
N= 4 Supersymmetric Quantum Mechanical Model: Novel Symmetries
Krishna, S
2016-01-01
We discuss a set of novel discrete symmetry transformations of the N = 4 supersymmetric quantum mechanical model of a charged particle moving on a sphere in the background of Dirac magnetic monopole. The usual five continuous symmetries (and their conserved Noether charges) and two discrete symmetries together provide the physical realizations of the de Rham cohomological operators of differential geometry. We have also exploited the supervariable approach to derive the nilpotent N = 4 SUSY transformations and provided the geometrical interpretation in the language of translational generators along the Grassmannian directions onto (1, 4)-dimensional supermanifold.
𝒩 = 4 supersymmetric quantum mechanical model: Novel symmetries
Krishna, S.
2017-04-01
We discuss a set of novel discrete symmetry transformations of the 𝒩 = 4 supersymmetric quantum mechanical model of a charged particle moving on a sphere in the background of Dirac magnetic monopole. The usual five continuous symmetries (and their conserved Noether charges) and two discrete symmetries together provide the physical realizations of the de Rham cohomological operators of differential geometry. We have also exploited the supervariable approach to derive the nilpotent 𝒩 = 4 SUSY transformations and provided the geometrical interpretation in the language of translational generators along the Grassmannian directions 𝜃α and 𝜃¯α onto (1, 4)-dimensional supermanifold.
Lie Symmetries and Criticality of Semilinear Differential Systems
Directory of Open Access Journals (Sweden)
Yuri Bozhkov
2007-03-01
Full Text Available We discuss the notion of criticality of semilinear differential equations and systems, its relations to scaling transformations and the Noether approach to Pokhozhaev's identities. For this purpose we propose a definition for criticality based on the S. Lie symmetry theory. We show that this definition is compatible with the well-known notion of critical exponent by considering various examples. We also review some related recent papers.
The symmetries and conservation laws of some Gordon-type equations in Milne space-time
Indian Academy of Sciences (India)
S Jamal; A H Kara; A H Bokhari; F D Zaman
2013-05-01
In this letter, the Lie point symmetries of a class of Gordon-type wave equations that arise in the Milne space-time are presented and analysed. Using the Lie point symmetries, it is showed how to reduce Gordon-type wave equations using the method of invariants, and to obtain exact solutions corresponding to some boundary values. The Noether point symmetries and conservation laws are obtained for the Klein–Gordon equation in one case. Finally, the existence of higher-order variational symmetries of a projection of the Klein–Gordon equation is investigated using the multiplier approach.
Nilpotent Symmetries of a Rigid Rotor: Supervariable Approach
Shukla, D; Malik, R P
2014-01-01
We exploit the standard techniques of the supervariable approach to derive the nilpotent Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry transformations for the toy model of a rigid rotor and provide the geometrical meaning and interpretation to them. Furthermore, we also derive the nilpotent (anti-)co-BRST symmetry transformations for this theory using the above supervariable technique. We capture the (anti-)BRST and (anti-)co-BRST invariance of the Lagrangian of our present theory within the ambit of augmented supervariable formalism. In addition, we express the (anti-)BRST and (anti-)co-BRST charges in terms of the supervariables (obtained after the application of the (dual-)horizontality conditions and (anti-)BRST and (anti-)co-BRST invariant restrictions) to provide the geometrical interpretation for their nilpotency and anticommutativity properties. The application of the dual-horizontality condition and ensuing (anti-)co-BRST symmetries are the novel features in our present investigation.
Ultimate generalization of Noether's theorem in the realm of Hamiltonian point dynamics
Struckmeier, Jürgen
2012-01-01
Noether's theorem in the realm of point dynamics establishes the correlation of a constant of motion of a Hamilton-Lagrange system with a particular symmetry transformation that preserves the form of the action functional. Although usually derived in the Lagrangian formalism, the natural context for deriving Noether's theorem for first-order Lagrangian systems is the Hamiltonian formalism. The reason is that the class of transformations that leave the action functional invariant coincides with the class of canonical transformations. As a result, any invariant of a Hamiltonian system can be correlated with a symmetry transformation simply by means of the canonical transformation rules. As this holds for any invariant, we thereby obtain the most general representation of Noether's theorem. In order to allow for symmetry mappings that include a transformation of time, we must refer to the extended Hamiltonian formalism. This formalism enables us to define generating functions of canonical transformations that al...
Noether-type theorem for discrete nonconservative dynamical systems with nonregular lattices
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
We investigate Noether symmetries and conservation laws of the discrete nonconserved systems with nonregular lattices. The operators of discrete transformation and discrete differentiation to the right and left are introduced for the systems. Based on the invariance of discrete Hamilton action on nonregular lattices of the systems with the nonconserved forces under the infinitesimal transformations with respect to the time and generalized coordinates, we give the discrete analog of generalized variational formula. From this formula we derive the discrete analog of generalized Noether-type identity, and then we present the generalized quasi-extremal equations and properties of these equations for the systems. We also obtain the discrete analog of Noether-type conserved laws and the discrete analog of generalized Noether theorems for the systems. We discuss an example to illustrate these results.
Noether-type theory for discrete mechanico-electrical dynamical systems with nonregular lattices
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
We investigate Noether symmetries and conservation laws of the discrete mechanico-electrical systems with nonregular lattices.The operators of discrete transformation and discrete differentiation to the right and left are introduced for the systems.Based on the invariance of discrete Hamilton action on nonregular lattices of the systems with the dissipation forces under the infinitesimal transformations with respect to the time,generalized coordinates and generalized charge quantities,we work out the discrete analog of the generalized variational formula.From this formula we derive the discrete analog of generalized Noether-type identity,and then we present the generalized quasi-extremal equations and properties of these equations for the systems.We also obtain the discrete analog of Noether-type conserved laws and the discrete analog of generalized Noether theorems for the systems.Finally we use an example to illustrate these results.
On PT Symmetry Systems: Invariance, Conservation Laws, and Reductions
Directory of Open Access Journals (Sweden)
P. Masemola
2014-01-01
results in a scalar cubic Schrödinger equation. We investigate the relationship between the conservation laws and Lie symmetries and investigate a Lagrangian, corresponding Noether symmetries, conserved vectors, and exact solutions via “double reductions.”
Algebraic and combinatorial Brill-Noether theory
Caporaso, Lucia
2011-01-01
The interplay between algebro-geometric and combinatorial Brill-Noether theory is studied. The Brill-Noether variety of a graph shown to be non-empty if the Brill-Noether number is non-negative, as a consequence of the analogous fact for smooth projective curves. Similarly, the existence of a graph for which the Brill-Noether variety is empty implies the emptiness of the corresponding Brill-Noether variety for a general curve. The main tool is a refinement of Baker's Specialization Lemma.
Cartan geometries and their symmetries a Lie algebroid approach
Crampin, Mike
2016-01-01
In this book we first review the ideas of Lie groupoid and Lie algebroid, and the associated concepts of connection. We next consider Lie groupoids of fibre morphisms of a fibre bundle, and the connections on such groupoids together with their symmetries. We also see how the infinitesimal approach, using Lie algebroids rather than Lie groupoids, and in particular using Lie algebroids of vector fields along the projection of the fibre bundle, may be of benefit. We then introduce Cartan geometries, together with a number of tools we shall use to study them. We take, as particular examples, the four classical types of geometry: affine, projective, Riemannian and conformal geometry. We also see how our approach can start to fit into a more general theory. Finally, we specialize to the geometries (affine and projective) associated with path spaces and geodesics, and consider their symmetries and other properties.
Application of Noether's theorem to extended particles
Energy Technology Data Exchange (ETDEWEB)
Smida, A; Hachemane, M; Hamici, A H [Faculte de Physique, USTHB B.P.32 El-Alia Bab-Ezzouar 16111 Alger (Algeria)], E-mail: hachemane@wissal.dz
2008-08-15
We consider an approach similar to field theory for the application of Noether theorem to extended paticles. We obtain Euler-Lagrange equations for the extended particles as well as an equation binding the internal and external currents. The concrete case of spin 1/2 is considered in detail.
Semiclassical approach to discrete symmetries in quantum chaos
Joyner, Chris; Sieber, Martin
2012-01-01
We use semiclassical methods to evaluate the spectral two-point correlation function of quantum chaotic systems with discrete geometrical symmetries. The energy spectra of these systems can be divided into subspectra that are associated to irreducible representations of the corresponding symmetry group. We show that for (spinless) time reversal invariant systems the statistics inside these subspectra depend on the type of irreducible representation. For real representations the spectral statistics agree with those of the Gaussian Orthogonal Ensemble (GOE) of Random Matrix Theory (RMT), whereas complex representations correspond to the Gaussian Unitary Ensemble (GUE). For systems without time reversal invariance all subspectra show GUE statistics. There are no correlations between non-degenerate subspectra. Our techniques generalize recent developments in the semiclassical approach to quantum chaos allowing one to obtain full agreement with the two-point correlation function predicted by RMT, including oscilla...
Superfield Approach To Exact And Unique Nilpotent Symmetries
Malik, R P
2005-01-01
In the framework of usual superfield approach, we derive the exact local, covariant, continuous and off-shell nilpotent Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry transformations for the U(1) gauge field ($A_\\mu$) and the (anti-)ghost fields ($(\\bar C)C$) of the Lagrangian density of a four ($3 + 1$)-dimensional QED by exploiting the horizontality condition defined on the six ($4 + 2)$-dimensional supermanifold. The long-standing problem of the exact derivation of the above nilpotent symmetry transformations for the matter (Dirac) fields ($\\bar \\psi, \\psi$), in the framework of superfield formulation, is resolved by a new restriction on the $(4 + 2)$-dimensional supermanifold. This new gauge invariant restriction on the supermanifold, due to the augmented superfield formalism, owes its origin to the (super) covariant derivatives. The geometrical interpretations for all the above off-shell nilpotent transformations are provided in the framework of augmented superfield formalism.
Symmetries and Mei Conserved Quantities of Nonholonomic Controllable Mechanical Systems
Institute of Scientific and Technical Information of China (English)
XIA Li-Li; LI Yuan-Cheng; WANG Jing; HOU Qi-Bao
2006-01-01
This paper concentrates on studying the symmetries and a new type of conserved quantities called Mei conserved quantity. The criterions of the Mei symmetry, the Noether symmetry and the Lie symmetry are given. The conditions and the forms of the Mei conserved quantities deduced from these three symmetries are obtained. An example is given to illustrate the application of the result.
Noether, Partial Noether Operators and First Integrals for the Coupled Lane-Emden System
Muatjetjeja, Ben; Khalique, Chaudry
2010-01-01
Systems of Lane-Emden equations arise in the modelling of several physical phenomena, such as pattern formation, population evolution and chemical reactions. In this paper we construct Noether and partial Noether operators corresponding to a Lagrangian and a partial Lagrangian for a coupled Lane-Emden system. Then the first integrals with respect to Noether and partial Noether operators are obtained for the Lane-Emden system under consideration. We show that the first integrals for both the N...
An extension of the Noether theorem: Accompanying equations possessing conservation laws
Dorodnitsyn, V. A.; Ibragimov, N. H.
2014-02-01
It is shown that the Noether theorem can be extended for some equations associated (accompanying) with Euler-Lagrange equation. Each symmetry of Lagrangian yields a class of accompanying equations possessing conservation law (first integral). The generalization is done for canonical Hamiltonian equations as well.
Poincaré symmetries and the Yang-Mills gradient flow
Patella, A; Rago, A
2014-01-01
The latest developments have shown how to use the gradient flow (or Wilson flow, on the lattice) for the exploration of symmetries, and the definition of the corresponding renormalized Noether currents. In particular infinitesimal translations can be introduced along the gradient flow for gauge theories, and the corresponding Ward identities can be derived. When applied to lattice gauge theories, this approach leads to a possible strategy to renormalize the energy-momentum tensor nonperturbatively, and to study dilatations and scale invariance.
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…
A unified theory for wall turbulence via a symmetry approach
She, Zhen-Su; Chen, Xi; Hussain, Fazle
2014-11-01
First principle based prediction of mean flow quantities of wall-bounded turbulent flows (channel, pipe, and turbulent boundary layer - TBL) remains a great challenge from both physics and engineering standpoints. Physically, a non-equilibrium physical principle governing mean properties in turbulent flows is yet unknown. Here, we outline a recently developed symmetry-based approach which derives analytic expressions governing the mean velocity profile (MVP) from an innovative Lie-group analysis. In analogy to the order parameter in Landau's (1937) mean-field theory, we develop a concept of order functions which are assumed to satisfy a dilation group invariance - representing the effects of the wall on fluctuations - allowing us to construct a set of new invariant solutions of the (unclosed) mean momentum equation (MME). The theory is validated by recent experimental and numerical data, and identifies a universal bulk flow constant 0.45 for all three canonical wall-bounded flows, which asymptotes to the true Karman constant at large Reynolds numbers. The theory equally applies to the quantification of the effects of roughness (She et al. 2012), pressure gradient, compressibility, and buoyancy, and to the study of Reynolds-averaged Navier-Stokes (RANS) models, such as k- ωmodel, with significant improvement of the prediction accuracy. These results affirm that a simple and unified theory of wall-bounded turbulence is viable with appropriate symmetry considerations.
Noether's therorem for local gauge transformations
Energy Technology Data Exchange (ETDEWEB)
Karatas, D.L.; Kowalski, K.L.
1989-05-22
The variational methods of classical field theory may be applied to any theory with an action which is invariant under local gauge transformations. What is the significance of the resulting Noether current. This paper examines such currents for both Abelian and non-Abelian gauge theories and provides an explanation for their form and limited range of physical significance on a level accessible to those with a basic knowledge of classical field theory. Several of the more subtle aspects encountered in the application of the residual local gauge symmetry found by Becchi, Rouet, Stora, and Tyutin are also considered in detail in a self-contained manner. 23 refs.
Boundary Terms and Noether Current of Spherical Black Holes
Ashworth, M C; Ashworth, Michael C.; Hayward, Sean A.
1999-01-01
We consider two proposals for defining black hole entropy in spherical symmetry, where the horizon is defined locally as a trapping horizon. The first case, boundary terms in a dual-null form of the reduced action in two dimensions, gives a result that is proportional to the area. The second case, Wald's Noether current method, is generalized to dynamic black holes, giving an entropy that is just the area of the trapping horizon. These results are compared with a generalized first law of thermodynamics.
Fake Conformal Symmetry in Unimodular Gravity
Oda, Ichiro
2016-01-01
We study Weyl symmetry (local conformal symmetry) in unimodular gravity. It is shown that the Noether currents for both Weyl symmetry and global scale symmetry, identically vanish as in the conformally invariant scalar-tensor gravity. We clearly explain why in the class of conformally invariant gravitational theories, the Noether currents vanish by starting with the conformally invariant scalar-tensor gravity. Moreover, we comment on both classical and quantum-mechanical equivalences among Einstein's general relativity, the conformally invariant scalar-tensor gravity and the Weyl-transverse (WTDiff) gravity. Finally, we discuss the Weyl current in the conformally invariant scalar action and see that it is also vanishing.
Fake conformal symmetry in unimodular gravity
Oda, Ichiro
2016-08-01
We study Weyl symmetry (local conformal symmetry) in unimodular gravity. It is shown that the Noether currents for both Weyl symmetry and global scale symmetry vanish exactly as in conformally invariant scalar-tensor gravity. We clearly explain why in the class of conformally invariant gravitational theories, the Noether currents vanish by starting with conformally invariant scalar-tensor gravity. Moreover, we comment on both classical and quantum-mechanical equivalences in Einstein's general relativity, conformally invariant scalar-tensor gravity, and the Weyl-transverse gravity. Finally, we discuss the Weyl current in the conformally invariant scalar action and see that it is also vanishing.
On the Computation of Noether Normalization
Institute of Scientific and Technical Information of China (English)
朱烨; 张江峰
2004-01-01
This paper considered the Noether normalization of a finitely generated algebra over an algebraically closed field. It gives a necessary and sufficient condition as well as an algorithm for the identification of those algebraically independent variables, then uses these elements to construct the Noether normalization of this algebra.
Physical Theories with Average Symmetry
Alamino, Roberto C.
2013-01-01
This Letter probes the existence of physical laws invariant only in average when subjected to some transformation. The concept of a symmetry transformation is broadened to include corruption by random noise and average symmetry is introduced by considering functions which are invariant only in average under these transformations. It is then shown that actions with average symmetry obey a modified version of Noether's Theorem with dissipative currents. The relation of this with possible violat...
Noether Theorem of Relativistic-Electromagnetic Ideal Hydrodynamics
Elsas, J H Gaspar; Kodama, T
2014-01-01
We present a variational approach for relativistic ideal hydrodynamics interacting with electromagnetic fields. The momentum of fluid is introduced as the canonical conjugate variable of the position of a fluid element, which coincides with the conserved quantity derived from the Noether theorem. We further show that our formulation can reproduce the usual electromagnetic hydrodynamics which is obtained so as to satisfy the conservation of the inertia of fluid motion.
Symmetry analysis for anisotropic field theories
Energy Technology Data Exchange (ETDEWEB)
Parra, Lorena; Vergara, J. David [Instituto de Ciencias Nucleares, UNAM, Circuito Exterior s/n, Ciudad Universitaria. Delg. Coyoacan. C.P. 04510 Mexico DF (Mexico)
2012-08-24
The purpose of this paper is to study with the help of Noether's theorem the symmetries of anisotropic actions for arbitrary fields which generally depend on higher order spatial derivatives, and to find the corresponding current densities and the Noether charges. We study in particular scale invariance and consider the cases of higher derivative extensions of the scalar field, electrodynamics and Chern-Simons theory.
On the notion of gauge symmetries of generic Lagrangian field theory
Giachetta, G; Sardanashvily, G
2008-01-01
Treating gauge theories in a general setting, one meets the following problems: (i) any Lagrangian possesses gauge symmetries which therefore should be separated into the trivial and non-trivial ones, (ii) there is no intrinsic definition of higher-stage gauge symmetries, (iii) gauge and higher-stage gauge symmetries need not form an algebra. We define gauge symmetries as those associated to the Noether identities. Generic Lagrangian theory of even and odd fields on an arbitrary smooth manifold is considered. Under certain conditions, its non-trivial Noether and higher-stage Noether identities are well defined by constructing the antifield Koszul--Tate complex. The inverse second Noether theorem associates to this complex the cochain sequence of ghosts whose ascent operator provides all non-trivial gauge and higher-stage gauge symmetries of Lagrangian theory. This ascent operator, called the gauge operator, is not nilpotent, unless gauge symmetries are abelian. We replace a condition that gauge symmetries for...
Horizontal symmetry in the algebraic approach of genetic code
Godina-Nava, J J
2013-01-01
Using concepts of physics of elementary particles concerning the breaking of symmetry and grannd unified theory we propose to study with the algebraic approximation the degeneracy finded in the genetic code with the incorporation of a horizontal symmetry used in gauge theories to fit the contents of the multiplets of the genetic code. It is used the algebraic approch of Hornos et. al. \\cite{main,PRL71,PRE,MPLB}. We propose an example for the incorporation of horizontal symmetry to study mixtures of elements of the multiplets.
Horizontal symmetry in the algebraic approach of genetic code
Godina-Nava, J. J.
2013-01-01
Using concepts of physics of elementary particles concerning the breaking of symmetry and grannd unified theory we propose to study with the algebraic approximation the degeneracy finded in the genetic code with the incorporation of a horizontal symmetry used in gauge theories to fit the contents of the multiplets of the genetic code. It is used the algebraic approch of Hornos et. al. \\cite{main,PRL71,PRE,MPLB}. We propose an example for the incorporation of horizontal symmetry to study mixtu...
Symmetry algebras in Chern-Simons theories with boundary: canonical approach
Energy Technology Data Exchange (ETDEWEB)
Park, Mu-In. E-mail: mipark@physics.sogang.ac.kr
1999-04-05
I consider the classical Kac-Moody algebra and Virasoro algebra in Chern-Simons theory with boundary within Dirac's canonical method and Noether's procedure. It is shown that the usual (bulk) Gauss law constraint becomes a second-class constraint because of the boundary effect. From this fact, the Dirac bracket can be constructed explicitly without introducing additional gauge conditions and the classical Kac-Moody and Virasoro algebras are obtained within the usual Dirac method. The equivalence to the symplectic reduction method is presented and the connection to the Banados' work is clarified. Also the generalization to the Yang-Mills-Chern-Simons theory is considered where the diffeomorphism symmetry is broken by the (three-dimensional) Yang-Mills term. In this case, the same Kac-Moody algebras are obtained although the two theories are sharply different in the canonical structures. Both models realize the holography principle explicitly and the pure CS theory reveals the correspondence of the Chern-Simons theory with boundary/conformal field theory, which is more fundamental and generalizes the conjectured anti-de Sitter/conformal field theory correspondence.
Approach to Developing Predictive Capability for Hohlraum Drive and Symmetry
Energy Technology Data Exchange (ETDEWEB)
Jones, O. S. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2015-07-22
Currently, we do not have the ability to predict the hohlraum drive and symmetry without requiring ad hoc adjustments to physics models. This document describes a plan for code improvements and focused physics validation experiments.
Teaching "Symmetry" in the Introductory Physics Curriculum
Hill, Christopher T; Hill, Christopher T.; Lederman, Leon M.
2000-01-01
Modern physics is largely defined by fundamental symmetry principles and Noether's Theorem. Yet these are not taught, or rarely mentioned, to beginning students, thus missing an opportunity to reveal that the subject of physics is as lively and contemporary as molecular biology, and as beautiful as the arts. We prescribe a symmetry module to insert into the curriculum, of a week's length.
Symmetries from the solution manifold
Aldaya, Víctor; Guerrero, Julio; Lopez-Ruiz, Francisco F.; Cossío, Francisco
2015-07-01
We face a revision of the role of symmetries of a physical system aiming at characterizing the corresponding Solution Manifold (SM) by means of Noether invariants as a preliminary step towards a proper, non-canonical, quantization. To this end, "point symmetries" of the Lagrangian are generally not enough, and we must resort to the more general concept of contact symmetries. They are defined in terms of the Poincaré-Cartan form, which allows us, in turn, to find the symplectic structure on the SM, through some sort of Hamilton-Jacobi (HJ) transformation. These basic symmetries are realized as Hamiltonian vector fields, associated with (coordinate) functions on the SM, lifted back to the Evolution Manifold through the inverse of this HJ mapping, that constitutes an inverse of the Noether Theorem. The specific examples of a particle moving on S3, at the mechanical level, and nonlinear SU(2)-sigma model in field theory are sketched.
Master formula approach to broken chiral U(3)xU(3) symmetry
Energy Technology Data Exchange (ETDEWEB)
Hiroyuki Kamano
2010-04-01
The master formula approach to chiral symmetry breaking proposed by Yamagishi and Zahed is extended to the U_R(3)xU_L(3) group, in which effects of the U_A(1) anomaly and the flavor symmetry breaking m_u \
Conserved quantities and symmetries related to stochastic Hamiltonian systems
Institute of Scientific and Technical Information of China (English)
Shang Mei; Mei Feng-Xiang
2007-01-01
In this paper symmetries and conservation laws for stochastic dynamical systems are discussed in detail.Determining equations for infinitesimal approximate symmetries of Ito and Stratonovich dynamical systems are derived. It shows how to derive conserved quantities for stochastic dynamical systems by using their symmetries without recourse to Noether's theorem.
A tropical proof of the Brill-Noether Theorem
Cools, Filip; Draisma, Jan; Payne, Sam; Robeva, Elina
2010-01-01
We produce Brill-Noether general graphs in every genus, confirming a conjecture of Baker and giving a new proof of the Brill-Noether Theorem, due to Griffiths and Harris, over any algebraically closed field.
O(D,D) covariant Noether currents and global charges in double field theory
Energy Technology Data Exchange (ETDEWEB)
Park, Jeong-Hyuck [Department of Physics, Sogang University,Seoul, 04107 (Korea, Republic of); Rey, Soo-Jong [School of Physics and Astronomy, Seoul National University,Seoul, 08862 (Korea, Republic of); Fields, Gravity & Strings, Center for Theoretical Physics of the Universe,Institute for Basic Sciences, Daejeon, 34047 (Korea, Republic of); Rim, Woohyun; Sakatani, Yuho [School of Physics and Astronomy, Seoul National University,Seoul, 08862 (Korea, Republic of)
2015-11-20
Double field theory is an approach for massless modes of string theory, unifying and geometrizing all gauge invariance in manifest O(D,D) covariant manner. In this approach, we derive off-shell conserved Noether current and corresponding Noether potential associated with unified gauge invariance. We add Wald-type counter two-form to the Noether potential and define conserved global charges as surface integral. We check our O(D,D) covariant formula against various string backgrounds, both geometric and non-geometric. In all cases we examined, we find perfect agreements with previous results. Our formula facilitates to evaluate momenta along not only ordinary spacetime directions but also dual spacetime directions on equal footing. From this, we confirm recent assertion that null wave in doubled spacetime is the same as macroscopic fundamental string in ordinary spacetime.
Physical Theories with Average Symmetry
Alamino, Roberto C
2013-01-01
This Letter probes the existence of physical laws invariant only in average when subjected to some transformation. The concept of a symmetry transformation is broadened to include corruption by random noise and average symmetry is introduced by considering functions which are invariant only in average under these transformations. It is then shown that actions with average symmetry obey a modified version of Noether's Theorem with dissipative currents. The relation of this with possible violations of physical symmetries, as for instance Lorentz invariance in some quantum gravity theories, is briefly commented.
Loebbert, Florian
2016-01-01
In these introductory lectures we discuss the topic of Yangian symmetry from various perspectives. Forming the classical counterpart of the Yangian and an extension of ordinary Noether symmetries, first the concept of nonlocal charges in classical, two-dimensional field theory is reviewed. We then define the Yangian algebra following Drinfeld's original motivation to construct solutions to the quantum Yang-Baxter equation. Different realizations of the Yangian and its mathematical role as a Hopf algebra and quantum group are discussed. We demonstrate how the Yangian algebra is implemented in quantum, two-dimensional field theories and how its generators are renormalized. Implications of Yangian symmetry on the two-dimensional scattering matrix are investigated. We furthermore consider the important case of discrete Yangian symmetry realized on integrable spin chains. Finally we give a brief introduction to Yangian symmetry in planar, four-dimensional super Yang-Mills theory and indicate its impact on the dila...
Papazoglou, M C
2014-01-01
We employ a variational method to study the effect of the symmetry energy on the neutron skin thickness and the symmetry energy coefficients of various neutron rich nuclei. We concentrate our interest on $^{208}$Pb, $^{124}$Sn, $^{90}$Zr, and $^{48}$Ca, although the method can be applied in the totality of medium and heavy neutron rich nuclei. Our approach has the advantage that the isospin asymmetry function $\\alpha(r)$, which is the key quantity to calculate isovector properties of various nuclei, is directly related with the symmetry energy as a consequence of the variational principle. Moreover, the Coulomb interaction is included in a self-consistent way and its effects can be separated easily from the nucleon-nucleon interaction. We confirm, both qualitatively and quantitatively, the strong dependence of the symmetry energy on the various isovector properties for the relevant nuclei, using possible constraints between the slope and the value of the symmetry energy at the saturation density.
Unified symmetry of Vacco dynamical systems
Institute of Scientific and Technical Information of China (English)
Li Yuan-Cheng; Jing Hong-Xing; Xia Li-Li; Wang Jing; Hou Qi-Bao
2007-01-01
Based on the total time derivative along the trajectory of the time, we study the unified symmetry of Vacco dynamical systems. The definition and the criterion of the unified symmetry for the system are given. Three kinds of conserved quantities, i.e. the Noether conserved quantity, the generalized Hojman conserved quantity and the Mei conserved quantity, are deduced from the unified symmetry. An example is presented to illustrate the results.
Optical zilch and Noether's theorem
Philbin, T G
2013-01-01
A simple conserved quantity for electromagnetic fields in vacuum was discovered by Lipkin in 1964. In recent years this "zilch" has been used as a measure of the chirality of light. The conservation of optical zilch is here shown to be due to a simple symmetry of the standard electromagnetic action. Other investigations of the symmetry underlying zilch conservation have not been based on transformations of the dynamical variables of the standard action (the vector and scalar potentials). The symmetry transformation allows the identification of zilch eigenstates, which are shown to be circularly polarized plane waves. The same symmetry is present for electromagnetism in a homogeneous, dispersive medium, allowing the derivation of the zilch density and flux in such a medium.
Nilpotent Symmetries of a Diffeomorphism Invariant Theory: BRST Approach
Malik, R P
2016-01-01
Within the framework of Becchi-Rouet-Stora-Tyutin (BRST) formalism, we discuss the full set of proper BRST and anti-BRST transformations for a diffeomorphism invariant theory which is described by the Lagrangian density of a standard bosonic string (proposed by Kato and Ogawa). The above (anti-)BRST symmetry transformations are off-shell nilpotent and absolutely anticommuting. The latter property is valid on a constrained hypersurface in the two dimensional spacetime manifold (traced out by the propagation of the bosonic string) where the Curci-Ferrari (CF) type restriction is satisfied. This CF-type restriction is found to be an (anti-)BRST invariant quantity. We derive the precise form of the BRST and anti-BRST invariant Lagrangian densities as well as the exact expressions for the conserved (anti-)BRST and ghost charges of our present theory. The derivation of the proper anti-BRST symmetry transformations and the emergence of the CF-type restriction are completely novel results in our present investigation...
Koreuber, Mechthild
2015-09-01
,,She [Noether] then appeared as the creator of a new direction in algebra and became the leader, the most consistent and brilliant representative, of a particular mathematical doctrine - of all that is characterized by the term ‚Begriffliche Mathematik‘.“ The aim of this paper is to illuminate this "new direction", which can be characterized as a conceptual [begriffliche] perspective in mathematics, and to comprehend its roots and trace its establishment. Field, ring, ideal, the core concepts of this new direction in mathematical images of knowledge, were conceptualized by Richard Dedekind (1831-1916) within the scope of his number theory research and associated with an understanding of a formation of concepts as a "free creation of the human spirit". They thus stand for an abstract perspective of mathematics in their entirety, described as 'modern algebra' in the 1920s and 1930s, leading to an understanding of mathematics as structural sciences. The establishment of this approach to mathematics, which is based on "general mathematical concepts" [allgemein-mathematische Begriffe], was the success of a cultural movement whose most important protagonists included Emmy Noether (1882-1935) and her pupil Bartel L. van der Waerden (1903-1996). With the use of the term 'conceptual', a perspective is taken in the analysis which allows for developing connections between the thinking of Dedekind, the "working and conceptual methods" [Arbeits- und Auffassungsmethoden] of Noether as well as the methodological approach, represented through the thought space of the Noether School as presented under the term "conceptual world" [Begriffswelt] in the Moderne Algebra of van der Waerden. This essay thus makes a contribution to the history of the introduction of a structural perspective in mathematics, a perspective that is inseparable from the mathematical impact of Noether, her reception of the work of Dedekind and the creative strength of the Noether School.
Augmented Superfield Approach to Nilpotent Symmetries of the Modified Version of 2D Proca Theory
Directory of Open Access Journals (Sweden)
A. Shukla
2015-01-01
and absolute anticommutativity of the (anti-BRST and (anti-co-BRST charges within the framework of augmented superfield formalism. This exercise leads to some novel observations which have, hitherto, not been pointed out in the literature within the framework of superfield approach to BRST formalism. For the sake of completeness, we also mention, very briefly, a unique bosonic symmetry, the ghost-scale symmetry, and discrete symmetries of the theory and show that the algebra of conserved charges provides a physical realization of the Hodge algebra (satisfied by the de Rham cohomological operators of differential geometry.
Emmy Noether the mother of modern algebra
Tent, M B W
2008-01-01
This book, written primarily for the young adult reader, tells the life story of Emmy Noether, the most important female mathematician of our time. Because no one expected her to grow into an important scientist, the records of her early life are sketchy. After all, it was assumed that she would grow up to be a wife and mother. Instead, she was a genius who chose a distinctive path. The author has woven this charming story of Emmy Noether's life around the events that appear in the oral and written records, fleshing out the story with details about life in Germany at the time and what we know
Brading, Katherine; Castellani, Elena
2010-01-01
Preface; Copyright acknowledgements; List of contributors; 1. Introduction; Part I. Continuous Symmetries: 2. Classic texts: extracts from Weyl and Wigner; 3. Review paper: On the significance of continuous symmetry to the foundations of physics C. Martin; 4. The philosophical roots of the gauge principle: Weyl and transcendental phenomenological idealism T. Ryckman; 5. Symmetries and Noether's theorems K. A. Brading and H. R. Brown; 6. General covariance, gauge theories, and the Kretschmann objection J. Norton; 7. The interpretation of gauge symmetry M. Redhead; 8. Tracking down gauge: an ode to the constrained Hamiltonian formalism J. Earman; 9. Time-dependent symmetries: the link between gauge symmetries and indeterminism D. Wallace; 10. A fourth way to the Aharanov-Bohm effect A. Nounou; Part II. Discrete Symmetries: 11. Classic texts: extracts from Lebniz, Kant and Black; 12. Review paper: Understanding permutation symmetry S. French and D. Rickles; 13. Quarticles and the identity of discernibles N. Hugget; 14. Review paper: Handedness, parity violation, and the reality of space O. Pooley; 15. Mirror symmetry: what is it for a relational space to be orientable? N. Huggett; 16. Physics and Leibniz's principles S. Saunders; Part III. Symmetry Breaking: 17: Classic texts: extracts from Curie and Weyl; 18. Extract from G. Jona-Lasinio: Cross-fertilization in theoretical physics: the case of condensed matter and particle physics G. Jona-Lasinio; 19. Review paper: On the meaning of symmetry breaking E. Castellani; 20. Rough guide to spontaneous symmetry breaking J. Earman; 21. Spontaneous symmetry breaking: theoretical arguments and philosophical problems M. Morrison; Part IV. General Interpretative Issues: 22. Classic texts: extracts from Wigner; 23. Symmetry as a guide to superfluous theoretical structure J. Ismael and B. van Fraassen; 24. Notes on symmetries G. Belot; 25. Symmetry, objectivity, and design P. Kosso; 26. Symmetry and equivalence E. Castellani.
Hojman Symmetry Approach for Scalar-Tensor Cosmology
Paolella, Mariacristina
2015-01-01
Scalar-tensor Cosmologies can be dealt under the standard of the Hojman conservation theorem that allows to fix the form of the coupling $F(\\phi)$, of the potential $V(\\phi)$ and to find out exact solutions for related cosmological models. Specifically, the existence of a symmetry transformation vector for the equations of motion gives rise to a Hojman conserved quantity on the corresponding minisuperpace and exact solutions for the cosmic scale factor $a$ and the scalar field $\\phi$ can be achieved. In particular, we take advantage of the fact that minimally coupled solutions, previously obtained in the Einstein frame, can be conformally transformed in non-minimally coupled solutions in the Jordan frame. Some physically relevant examples are worked out.
A topological approach unveils system invariances and broken symmetries in the brain.
Tozzi, Arturo; Peters, James F
2016-05-01
Symmetries are widespread invariances underscoring countless systems, including the brain. A symmetry break occurs when the symmetry is present at one level of observation but is hidden at another level. In such a general framework, a concept from algebraic topology, namely, the Borsuk-Ulam theorem (BUT), comes into play and sheds new light on the general mechanisms of nervous symmetries. The BUT tells us that we can find, on an n-dimensional sphere, a pair of opposite points that have the same encoding on an n - 1 sphere. This mapping makes it possible to describe both antipodal points with a single real-valued vector on a lower dimensional sphere. Here we argue that this topological approach is useful for the evaluation of hidden nervous symmetries. This means that symmetries can be found when evaluating the brain in a proper dimension, although they disappear (are hidden or broken) when we evaluate the same brain only one dimension lower. In conclusion, we provide a topological methodology for the evaluation of the most general features of brain activity, i.e., the symmetries, cast in a physical/biological fashion that has the potential to be operationalized. © 2016 Wiley Periodicals, Inc. © 2016 Wiley Periodicals, Inc.
A new type of Lie symmetrical non-Noether conserved quantity for nonholonomic systems
Institute of Scientific and Technical Information of China (English)
Luo Shao-Kai; Huang Fei-Jiang; Lu Yi-Bing
2004-01-01
For a nonholonomic system, a new type of Lie symmetrical non-Noether conserved quantity is given under general infinitesimal transformations of groups in which time is variable. On the basis of the invariance theory of differential equations of motion under infinitesimal transformations for t and qs, we construct the Lie symmetrical determining equations, the constrained restriction equations and the additional restriction equations of the system. And a new type of Lie symmetrical non-Noether conserved quantity is directly obtained from the Lie symmetry of the system, which only depends on the variables t, qs and qs. A series of deductions are inferred for a holonomic nonconservative system,Lagrangian system and other dynamical systems in the case of vanishing of time variation. An example is given to illustrate the application of the results.
Institute of Scientific and Technical Information of China (English)
Zhao Gang-Ling; Chen Li-Qun; Fu Jing-Li; Hong Fang-Yu
2013-01-01
In this paper,Noether symmetry and Mei symmetry of discrete nonholonomic dynamical systems with regular and the irregular lattices are investigated.Firstly,the equations of motion of discrete nonholonomic systems are introduced for regular and irregular lattices.Secondly,for cases of the two lattices,based on the invariance of the Hamiltomian functional under the infinitesimal transformation of time and generalized coordinates,we present the quasi-extremal equation,the discrete analogues of Noether identity,Noether theorems,and the Noether conservation laws of the systems.Thirdly,in cases of the two lattices,we study the Mei symmetry in which we give the discrete analogues of the criterion,the theorem,and the conservative laws of Mei symmetry for the systems.Finally,an example is discussed for the application of the results.
p-systems in local Noether lattices
Directory of Open Access Journals (Sweden)
E. W. Johnson
1994-01-01
Full Text Available In this paper we introduce the concept of a p-system in a local Noether lattice and obtain several characterizations of these elements. We first obtain a topological characterization and then a characterization in terms of the existence of a certain type of decreasing sequence of elements. In addition, p-systems are characterized in quotient lattices and completions.
A non-differentiable Noether's theorem
Cresson, Jacky; Greff, Isabelle
2011-02-01
In the framework of the nondifferentiable embedding of Lagrangian systems, defined by Cresson and Greff [non-dierentiable embedding of lagrangian systems and partial dierential equations. Preprint Max-Plank-Institut für Mathematik in den Naturwissenschaften, Leipzig 16, 26 (2010)], we prove a Noether's theorem based on the lifting of one-parameter groups of diffeomorphisms.
Brill-Noether loci in codimension two
Tarasca, Nicola
2012-01-01
Let us consider the locus in the moduli space of curves of genus 2k defined by curves with a pencil of degree k. Since the Brill-Noether number is equal to -2, such a locus has codimension two. Using the method of test surfaces, we compute the class of its closure in the moduli space of stable curves.
Noether Theorems and Reality of Motion
Palese, M
2016-01-01
We will read, through the Emmy Noether paper and the two concepts of `proper' and `improper' conservation laws, the problem, posed by Hilbert, of the nature of the law of conservation of energy in the theory of General Relativity. Epistemological issues involved with the two kind of conservation laws will be enucleate.
Wardlow, Adam
2011-01-01
We construct infinite dimensional symmetries of a complex, free scalar field on curved space-times generated by isometries of the space-time. We use the Anti de-Sitter backgrounds as an example and check that the boundary terms appearing in the Noether current satisfy the requirement of Noether's theorem that they vanish at the boundary.
Tensor-entanglement-filtering renormalization approach and symmetry-protected topological order
Gu, Zheng-Cheng; Wen, Xiao-Gang
2009-10-01
We study the renormalization group flow of the Lagrangian for statistical and quantum systems by representing their path integral in terms of a tensor network. Using a tensor-entanglement-filtering renormalization approach that removes local entanglement and produces a coarse-grained lattice, we show that the resulting renormalization flow of the tensors in the tensor network has a nice fixed-point structure. The isolated fixed-point tensors Tinv plus the symmetry group Gsym of the tensors (i.e., the symmetry group of the Lagrangian) characterize various phases of the system. Such a characterization can describe both the symmetry breaking phases and topological phases, as illustrated by two-dimensional (2D) statistical Ising model, 2D statistical loop-gas model, and 1+1D quantum spin-1/2 and spin-1 models. In particular, using such a (Gsym,Tinv) characterization, we show that the Haldane phase for a spin-1 chain is a phase protected by the time-reversal, parity, and translation symmetries. Thus the Haldane phase is a symmetry-protected topological phase. The (Gsym,Tinv) characterization is more general than the characterizations based on the boundary spins and string order parameters. The tensor renormalization approach also allows us to study continuous phase transitions between symmetry breaking phases and/or topological phases. The scaling dimensions and the central charges for the critical points that describe those continuous phase transitions can be calculated from the fixed-point tensors at those critical points.
SYMMETRIES AND CONSERVED QUANTITIES FOR SYSTEMS OF GENERALIZED CLASSICAL MECHANICS
Institute of Scientific and Technical Information of China (English)
Zhang Yi; Shang Mei; Mei Feng-xiang
2000-01-01
In this paper, the symmetries and the conserved quantities for systemsof generalized classical mechanics are studied. First, the generalizedNoether's theorem and the generalized Noether's inverse theorem of thesystems are given, which are based upon the invariant properties of thecanonical action with respect to the action of the infinitesimaltransformation of r-parameter finite group of transformation; second,the Lie symmetries and conserved quantities of the systems are studiedin accordance with the Lie's theory of the invariance of differentialequations under the transformation of infinitesimal groups; and finally,the inner connection between the two kinds of symmetries of systems isdiscussed.
Unified symmetry of non-holonomic singular systems
Institute of Scientific and Technical Information of China (English)
2007-01-01
In this paper, the unified symmetry of non-holonomic singular systems is studied. The differential equations of motion of the systems are given. The definition and the criterion of the unified symmetry for the systems are presented. The Noether conserved quantity, the Hojman conserved quantity and the Mei conserved quantity are obtained. An example is given to illustrate the application of the results.
Global Scaling Symmetry, Noether Charge and Universality of Shear Viscosity
Liu, Hai-Shan
2016-01-01
Recently it was established in Einstein-Maxwell-Dilaton gravity that the KSS viscosity/entropy ratio associated with AdS planar black holes can be viewed as the boundary dual to the generalized Smarr relation of the black holes in the bulk. In this paper we establish this relation in Einstein gravity with general minimally-coupled matter, and also in theories with an additional non-minimally coupled scalar field. We consider two examples for explicit demonstrations.
Global scaling symmetry, Noether charge, and universality of shear viscosity
Liu, Hai-Shan
2016-05-01
Recently, it was established in Einstein-Maxwell-Dilaton gravity that the Kovtun-Son-Starinets viscosity/entropy ratio associated with anti-de Sitter planar black holes can be viewed as the boundary dual to the generalized Smarr relation of the black holes in the bulk. In this paper, we establish this relation in Einstein gravity with general minimally coupled matter and also in theories with an additional nonminimally coupled scalar field. We consider two examples for explicit demonstrations.
General Symmetry Approach to Solve Variable-Coefficient Nonlinear Equations
Institute of Scientific and Technical Information of China (English)
RUAN HangYu; CHEN YiXin; LOU SenYue
2001-01-01
After considering the variable coefficient of a nonlinear equation as a new dependent variable, some special types of variable-coefficient equation can be solved from the corresponding constant-coefficient equations by using the general classical Lie approach. Taking the nonlinear Schrodinger equation as a concrete example, the method is recommended in detail.``
Symmetries in Lagrangian Field Theory
Búa, Lucia; Bucataru, Ioan; León, Manuel de; Salgado, Modesto; Vilariño, Silvia
2015-06-01
By generalising the cosymplectic setting for time-dependent Lagrangian mechanics, we propose a geometric framework for the Lagrangian formulation of classical field theories with a Lagrangian depending on the independent variables. For that purpose we consider the first-order jet bundles J1π of a fiber bundle π : E → ℝk where ℝk is the space of independent variables. Generalized symmetries of the Lagrangian are introduced and the corresponding Noether theorem is proved.
Symmetries in Non-Linear Mechanics
Aldaya, Victor; López-Ruiz, Francisco F; Cossío, Francisco
2014-01-01
In this paper we exploit the use of symmetries of a physical system so as to characterize the corresponding solution manifold by means of Noether invariants. This constitutes a necessary preliminary step towards the correct quantisation in non-linear cases, where the success of Canonical Quantisation is not guaranteed in general. To achieve this task "point symmetries" of the Lagrangian are generally not enough, and the notion of contact transformations is in order. The use of the Poincar\\'e-Cartan form permits finding both the symplectic structure on the solution manifold, through the Hamilton-Jacobi transformation, and the required symmetries, realized as Hamiltonian vector fields, associated with functions on the solution manifold (thus constituting an inverse of the Noether Theorem), lifted back to the evolution space through the inverse of this Hamilton-Jacobi mapping. In this framework, solutions and symmetries are somehow identified and this correspondence is also kept at a perturbative level. We prese...
Chen, Alvin Cheng-Hsien
2014-01-01
The present study aims to investigate how conceptual symmetry plays a role in the use of spatial particles in English and to further examine its pedagogical implications via a corpus-based evaluation of the course books in senior high schools in Taiwan. More specifically, we adopt a quantitative corpus-based approach to investigate whether bipolar…
Vacum Black Hole Mass Formula Is a Vanishing Noether Charge
Institute of Scientific and Technical Information of China (English)
WUXiao－Ning; HUANGChao－Guang; 等
2002-01-01
The Noether current and its variation relation with respect to diffeomorphism invariance of gravitational theories have been derived from the horizontal variation and vertical-horizontal bi-variation of the Lagrangian,respectively.For Einstein's GR in the stationary,axisymmetric black holes,the mass formula in vacuum can be derived from this Noether current although it definitely vanishes.This indicates that the mass formula of black holes is a vanishing Noether charge in this case.The first law of black hole thermodynamics can also be derived from the variation relation of this vanishing Noether current.
Noether's theory of Lagrange systems in discrete case
Institute of Scientific and Technical Information of China (English)
Lu Hong-Sheng; Zhang-Hong-Bin; Gu Shu-Long
2011-01-01
In this paper, Noether theory of Lagrange systems in discrete case are studied. First, we briefly overview the wellknown Noether theory of Lagrange system in the continuous case. Then, we introduce some definitions and notations,such as the operators of discrete translation to the right and the left and the operators of discrete differentiation to the right and the left, and give the conditions for the invariance of the difference functional on the uniform lattice and the non-uniform one, respectively. We also deduce the discrete analog of the Noether-type identity. Finally, the discrete analog of Noether's theorem is presented. An example was discussed to illustrate these results.
Vacuum Black Hole Mass Formula Is a Vanishing Noether Charge
Institute of Scientific and Technical Information of China (English)
WU Xiao-Ning; GUO Han-Ying; HUANG Chao-Guang; WU Ke
2002-01-01
The Noether current and its variation relation with respect to diffeomorphism invariance of gravitationaltheories have been derived from the horizontal variation and vertical-horizontal bi-variation of the Lagrangian, respec-tively. For Einstein's GR in the stationary, axisymmetric black holes, the mass formula in vacuum can be derived fromthis Noether current although it definitely vanishes. This indicates that the mass formula of black holes is a vanishingNoether charge in this case. The first law of black hole thermodynamics can also be derived from the variation relationof this vanishing Noether current.
Energy Technology Data Exchange (ETDEWEB)
El Naschie, M.S. [Department of Physics, Alexandria University (Egypt)], E-mail: Chaossf@aol.com
2008-01-15
Noether's theorem relating conservation laws with symmetry is applied in conjunction with the exceptional Lie group hierarchy, the holographic principles and E-infinity theory to calculate the electromagnetic fine structure constant. Various schemes are suggested utilizing the fundamentals of heterotic strings as well as P-Brane theory leading to essentially the same value of 1/{alpha} {approx_equal} 137 in complete agreement with the well-established experimental evidences.
Teaching symmetry in the introductory physics curriculum
Energy Technology Data Exchange (ETDEWEB)
Hill, Christopher T.; Lederman, Leon M.
2000-01-01
Modern physics is largely defined by fundamental symmetry principles and Noether's Theorem. Yet these are not taught, or rarely mentioned, to beginning students, thus missing an opportunity to reveal that the subject of physics is as lively and contemporary as molecular biology, and as beautiful as the arts. We prescribe a symmetry module to insert into the curriculum, of a week's length.
A reciprocal space approach for locating symmetry elements in Patterson superposition maps
Energy Technology Data Exchange (ETDEWEB)
Hendrixson, T.
1990-09-21
A method for determining the location and possible existence of symmetry elements in Patterson superposition maps has been developed. A comparison of the original superposition map and a superposition map operated on by the symmetry element gives possible translations to the location of the symmetry element. A reciprocal space approach using structure factor-like quantities obtained from the Fourier transform of the superposition function is then used to determine the best'' location of the symmetry element. Constraints based upon the space group requirements are also used as a check on the locations. The locations of the symmetry elements are used to modify the Fourier transform coefficients of the superposition function to give an approximation of the structure factors, which are then refined using the EG relation. The analysis of several compounds using this method is presented. Reciprocal space techniques for locating multiple images in the superposition function are also presented, along with methods to remove the effect of multiple images in the Fourier transform coefficients of the superposition map. In addition, crystallographic studies of the extended chain structure of (NHC{sub 5}H{sub 5})SbI{sub 4} and of the twinning method of the orthorhombic form of the high-{Tc} superconductor YBa{sub 2}Cu{sub 3}O{sub 7-x} are presented. 54 refs.
The life and times of Emmy Noether contributions of Emmy Noether to particle physics
Byers, N
1994-01-01
The contributions of Emmy Noether to particle physics fall into two categories. One is given under the rubric of Noether's theorem, and the other may be described as her important contributions to modern mathematics. These will be discussed along with an historical account of her work and what its impact has been. In addition a brief biography is given. (To be published in the Proceedings of the Int'l Conf. on The History of Original Ideas and Basic Discoveries in Particle Physics, Erice, Italy, 29 July-4 Aug., 1994.)
Institute of Scientific and Technical Information of China (English)
Qian Yong-Fen; Li Ren-Jie; Zhao Shu-Hong
2004-01-01
Using a form invariance under special infinitesimal transformations in which time is not variable, the non-Noether conserved quantity of the nonholonomic Vacco dynamical system with variable mass is studied. The differential equations of motion of the systems are established. The definition and criterion of the form invariance of the system under special infinitesimal transformations are studied. The necessary and sufficient condition under which the form invariance is a Lie symmetry is given. The Hojman theorem is established. Finally an example is given to illustrate the application of the result.
Relabeling symmetry in relativistic fluids and plasmas
Kawazura, Yohei; Fukumoto, Yasuhide
2014-01-01
The conservation of the recently formulated relativistic canonical helicity [Yoshida Z, Kawazura Y, and Yokoyama T 2014 J. Math. Phys. 55 043101] is derived from Noether's theorem by constructing an action principle on the relativistic Lagrangian coordinates (we obtain general cross helicities that include the helicity of the canonical vorticity). The conservation law is, then, explained by the relabeling symmetry pertinent to the Lagrangian label of fluid elements. Upon Eulerianizing the Noether current, the purely spatial volume integral on the Lagrangian coordinates is mapped to a space-time mixed three-dimensional integral on the four-dimensional Eulerian coordinates. The relativistic conservation law in the Eulerian coordinates is no longer represented by any divergence-free current; hence, it is not adequate to regard the relativistic helicity (represented by the Eulerian variables) as a Noether charge, and this stands the reason why the "conventional helicity" is no longer a constant of motion. We have...
Scaling symmetries, conservation laws and action principles in one-dimensional gas dynamics
Energy Technology Data Exchange (ETDEWEB)
Webb, G M; Zank, G P [Center for Space Plasma and Aeronomic Research, University of Alabama in Huntsville, Huntsville, AL 35805 (United States)], E-mail: gary.webb@uah.edu
2009-11-27
Scaling symmetries of the planar, one-dimensional gas dynamic equations with adiabatic index {gamma} 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.
From physical symmetries to emergent gauge symmetries
Energy Technology Data Exchange (ETDEWEB)
Barceló, Carlos [Instituto de Astrofísica de Andalucía (IAA-CSIC),Glorieta de la Astronomía, 18008 Granada (Spain); Carballo-Rubio, Raúl [Instituto de Astrofísica de Andalucía (IAA-CSIC), Glorieta de la Astronomía, 18008 Granada (Spain); Laboratory for Quantum Gravity & Strings,Department of Mathematics & Applied Mathematics, University of Cape Town,Private Bag, Rondebosch 7701 (South Africa); Di Filippo, Francesco [Instituto de Astrofísica de Andalucía (IAA-CSIC), Glorieta de la Astronomía, 18008 Granada (Spain); Dipartamento di Scienze Fisiche “E.R. Caianiello”, Università di Salerno,I-84081 Fisciano (Italy); Garay, Luis J. [Departamento de Física Teórica II, Universidad Complutense de Madrid, 28040 Madrid (Spain); Instituto de Estructura de la Materia (IEM-CSIC), Serrano 121, 28006 Madrid (Spain)
2016-10-17
Gauge symmetries indicate redundancies in the description of the relevant degrees of freedom of a given field theory and restrict the nature of observable quantities. One of the problems faced by emergent theories of relativistic fields is to understand how gauge symmetries can show up in systems that contain no trace of these symmetries at a more fundamental level. In this paper we start a systematic study aimed to establish a satisfactory mathematical and physical picture of this issue, dealing first with abelian field theories. We discuss how the trivialization, due to the decoupling and lack of excitation of some degrees of freedom, of the Noether currents associated with physical symmetries leads to emergent gauge symmetries in specific situations. An example of a relativistic field theory of a vector field is worked out in detail in order to make explicit how this mechanism works and to clarify the physics behind it. The interplay of these ideas with well-known results of importance to the emergent gravity program, such as the Weinberg-Witten theorem, are discussed.
From physical symmetries to emergent gauge symmetries
Barceló, Carlos; Carballo-Rubio, Raúl; Di Filippo, Francesco; Garay, Luis J.
2016-10-01
Gauge symmetries indicate redundancies in the description of the relevant degrees of freedom of a given field theory and restrict the nature of observable quantities. One of the problems faced by emergent theories of relativistic fields is to understand how gauge symmetries can show up in systems that contain no trace of these symmetries at a more fundamental level. In this paper we start a systematic study aimed to establish a satisfactory mathematical and physical picture of this issue, dealing first with abelian field theories. We discuss how the trivialization, due to the decoupling and lack of excitation of some degrees of freedom, of the Noether currents associated with physical symmetries leads to emergent gauge symmetries in specific situations. An example of a relativistic field theory of a vector field is worked out in detail in order to make explicit how this mechanism works and to clarify the physics behind it. The interplay of these ideas with well-known results of importance to the emergent gravity program, such as the Weinberg-Witten theorem, are discussed.
From physical symmetries to emergent gauge symmetries
Barceló, Carlos; Di Filippo, Francesco; Garay, Luis J
2016-01-01
Gauge symmetries indicate redundancies in the description of the relevant degrees of freedom of a given field theory and restrict the nature of observable quantities. One of the problems faced by emergent theories of relativistic fields is to understand how gauge symmetries can show up in systems that contain no trace of these symmetries at a more fundamental level. In this paper we start a systematic study aimed to establish a satisfactory mathematical and physical picture of this issue, dealing first with abelian field theories. We discuss how the trivialization, due to the decoupling and lack of excitation of some degrees of freedom, of the Noether currents associated with physical symmetries leads to emergent gauge symmetries in specific situations. An example of a relativistic field theory of a vector field is worked out in detail in order to make explicit how this mechanism works and to clarify the physics behind it. The interplay of these ideas with well-known results of importance to the emergent grav...
Symmetries of geodesic motion in Gödel-type spacetimes
Energy Technology Data Exchange (ETDEWEB)
Camci, U., E-mail: ucamci@akdeniz.edu.tr [Department of Physics, Akdeniz University, 07058 Antalya (Turkey)
2014-07-01
In this paper, we study Noether gauge symmetries of geodesic motion for geodesic Lagrangian of four classes of metrics of Gödel-type spacetimes for which we calculated the Noether gauge symmetries for all classes I-IV, and find the first integrals of corresponding classes to derive a complete characterization of the geodesic motion. Using the obtained expressions for t-dot , r-dot ,φ-dot and ż of each classes I-IV which depends essentially on two independent parameters m and w, we explicitly integrated the geodesic equations of motion for the corresponding Gödel-type spacetimes.
The Noether numbers for cyclic groups of prime order
Shank, R. James; Fleischmann, Peter; Sezer, Müfit; Woodcock, Chris F.
2005-01-01
The Noether number of a representation is the largest degree of an element in a minimal homogeneous generating set for the corresponding ring of invariants. We compute the Noether number for an arbitrary representation of a cyclic group of prime order, and as a consequence prove the "2p−3 conjecture."\\ud \\ud
Noether's theorem of a rotational relativistic variable mass system
Institute of Scientific and Technical Information of China (English)
方建会; 赵嵩卿
2002-01-01
Noether's theory of a rotational relativistic variable mass system is studied. Firstly, Jourdain's principle of therotational relativistic variable mass system is given. Secondly, on the basis of the invariance of the Jourdain's principleunder the infinitesimal transformations of groups, Noether's theorem and its inverse theorem of the rotational relativisticvariable mass system are presented. Finally, an example is given to illustrate the application of the result.
A Birkhoff-Noether method of solving differential equations
Institute of Scientific and Technical Information of China (English)
Shang Mei; Guo Yong-Xin; Mei Feng-Xiang
2007-01-01
In this paper, a Birkhoff-Noether method of solving ordinary differential equations is presented. The differential equations can be expressed in terms of Birkhoff's equations. The first integrals for differential equations can be found by using the Noether theory for Birkhoffian systems. Two examples are given to illustrate the application of the method.
Geometry of Brill-Noether loci on Prym varieties
Hoering, Andreas
2011-01-01
Given the Prym variety of an \\'etale double cover one can define analogues of the classical Brill-Noether loci on Jacobians of curves. Recent work by Lahoz and Naranjo shows that the Brill-Noether locus V^2 completely determines the covering. In this paper we describe the singular locus and the irreducible components of V^2.
Gieseking, Rebecca L.
2016-04-25
Long polymethines are well-known experimentally to symmetry-break, which dramatically modifies their linear and nonlinear optical properties. Computational modeling could be very useful to provide insight into the symmetry-breaking process, which is not readily available experimentally; however, accurately predicting the crossover point from symmetric to symmetry-broken structures has proven challenging. Here, we benchmark the accuracy of several DFT approaches relative to CCSD(T) geometries. In particular, we compare analogous hybrid and long-range corrected (LRC) functionals to clearly show the influence of the functional exchange term. Although both hybrid and LRC functionals can be tuned to reproduce the CCSD(T) geometries, the LRC functionals are better performing at reproducing the geometry evolution with chain length and provide a finite upper limit for the gas-phase crossover point; these methods also provide good agreement with the experimental crossover points for more complex polymethines in polar solvents. Using an approach based on LRC functionals, a reduction in the crossover length is found with increasing medium dielectric constant, which is related to localization of the excess charge on the end groups. Symmetry-breaking is associated with the appearance of an imaginary frequency of b2 symmetry involving a large change in the degree of bond-length alternation. Examination of the IR spectra show that short, isolated streptocyanines have a mode at ~1200 cm-1 involving a large change in bond-length alternation; as the polymethine length or the medium dielectric increases, the frequency of this mode decreases before becoming imaginary at the crossover point.
A spherical parameterization approach based on symmetry analysis of triangular meshes
Institute of Scientific and Technical Information of China (English)
Jian-ping HU; Xiu-ping LIU; Zhi-xun SU; Xi-quan SHI; Feng-shan LIU
2009-01-01
We present an efficient spherical parameterization approach aimed at simultaneously reducing area and angle distortions. We generate the final spherical mapping by independently establishing two hemisphere parameterizations. The essence of the approach is to reduce spherical parameterization to a planar problem using symmetry analysis of 3D meshes. Experiments and comparisons were undertaken with various non-trivial 3D models, which revealed that our approach is efficient and robust. In particular, our method produces almost isometric parameterizations for the objects close to the sphere.
Augmented Superfield Approach to Nilpotent Symmetries of the Modified Version of 2D Proca Theory
Shukla, A; Malik, R P
2013-01-01
We derive the complete set of off-shell nilpotent and absolutely anticommuting Becchi-Rouet-Stora-Tyutin (BRST), anti-BRST and (anti-)co-BRST symmetry transformations for all the fields of the modified version of two (1+1)-dimensional (2D) Proca theory by exploiting the "augmented" superfield formalism where the (dual-)horizontality conditions and (dual-)gauge-invariant restrictions are exploited together. We capture the (anti-)BRST and (anti-)co-BRST invariance of the Lagrangian density in the language of superfield formalism. We also express the nilpotency and absolute anticommutativity of the (anti-)BRST and (anti-)co-BRST charges within the framework of augmented superfield formalism. This exercise leads to some novel observations which have, hitherto, not been pointed out in the literature within the framework of superfield approach to BRST formalism. For the sake of completeness, we also mention, very briefly, a unique bosonic symmetry, the ghost-scale symmetry and discrete symmetries of the theory and ...
Symmetries, Conservation Laws, and Wave Equation on the Milne Metric
Directory of Open Access Journals (Sweden)
Ahmad M. Ahmad
2012-01-01
representing physical systems. For partial differential equation possessing Lagrangians these symmetries are obtained by the invariance of the corresponding action integral. In this paper we provide a systematic procedure for determining Noether symmetries and conserved vectors for a Lagrangian constructed from a Lorentzian metric of interest in mathematical physics. For completeness, we give Lie point symmetries and conservation laws admitted by the wave equation on this Lorentzian metric.
Two-photon annihilation into octet meson pairs. Symmetry relations in the handbag approach
Energy Technology Data Exchange (ETDEWEB)
Diehl, M. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Kroll, P. [Wuppertal Univ. (Gesamthochschule) (Germany). Fachbereich Physik; Regensburg Univ. (Germany). Institut fuer Theoretische Physik
2009-11-15
We explore the implications of SU(3) flavor symmetry in the soft handbag mechanism for two-photon annihilation into pairs of pseudoscalar octet mesons. In this approach we obtain a good description of the experimental results for all measured channels at high energy, with two complex form factors adjusted to the data. We also predict the cross section for {gamma}{gamma}{yields}{eta}{eta}. (orig.)
Lu, Yuan-Ming; Vishwanath, Ashvin
2016-04-01
We study (2+1)-dimensional phases with topological order, such as fractional quantum Hall states and gapped spin liquids, in the presence of global symmetries. Phases that share the same topological order can then differ depending on the action of symmetry, leading to symmetry-enriched topological (SET) phases. Here, we present a K -matrix Chern-Simons approach to identify distinct phases with Abelian topological order, in the presence of unitary or antiunitary global symmetries. A key step is the identification of a smooth edge sewing condition that is used to check if two putative phases are indeed distinct. We illustrate this method by classifying Z2 topological order (Z2 spin liquids) in the presence of an internal Z2 global symmetry for which we find six distinct phases. These include two phases with an unconventional action of symmetry that permutes anyons leading to symmetry-protected Majorana edge modes. Other routes to realizing protected edge states in SET phases are identified. Symmetry-enriched Laughlin states and double-semion theories are also discussed. Somewhat surprisingly, we observe that (i) gauging the global symmetry of distinct SET phases leads to topological orders with the same total quantum dimension, and (ii) a pair of distinct SET phases can yield the same topological order on gauging the symmetry.
Vector-Like Pairs and Brill--Noether Theory
Watari, Taizan
2016-01-01
How likely is it that there are particles in a vector-like pair of representations in low-energy spectrum, when neither symmetry nor anomaly consideration motivates their presence? We address this question in the context of supersymmetric and geometric phase compactification of F-theory and Heterotic dual. Quantisation of the number of generations (or net chiralities in more general term) is also discussed along the way. Self-dual nature of the fourth cohomology of Calabi--Yau fourfolds is essential for the latter issue, while we employ Brill--Noether theory to set upper bounds on the number $\\ell$ of vector-like pairs of chiral multiplets in the SU(5) 5+5bar representations. For typical topological choices of geometry for F-theory compactification for SU(5) unification, the range of $0 \\leq \\ell \\lesssim 4$ for perturbative unification is not in immediate conflict with what is already understood about F-theory compactification at this moment.
Vector-like pairs and Brill-Noether theory
Watari, Taizan
2016-11-01
How likely is it that there are particles in a vector-like pair of representations in low-energy spectrum, when neither symmetry nor anomaly consideration motivates their presence? We address this question in the context of supersymmetric and geometric phase compactification of F-theory and Heterotic dual. Quantisation of the number of generations (or net chiralities in more general term) is also discussed along the way. Self-dual nature of the fourth cohomology of Calabi-Yau fourfolds is essential for the latter issue, while we employ Brill-Noether theory to set upper bounds on the number ℓ of vector-like pairs of chiral multiplets in the SU (5)GUT (5 + 5 bar) representations. For typical topological choices of geometry for F-theory compactification for SU(5) unification, the range of 0 ≤ ℓ ≲ 4 for perturbative unification is not in immediate conflict with what is already understood about F-theory compactification at this moment.
Noether Theory for Hamiltonian System on Time Scales%时间尺度上Hamilton系统的Noether理论
Institute of Scientific and Technical Information of China (English)
张毅
2016-01-01
提出并研究时间尺度上Hamilton系统的Noether对称性与守恒量问题.建立了时间尺度上Hamilton原理,导出了相应的Hamilton正则方程.基于时间尺度上Hamilton作用量在群的无限小变换下的不变性,建立了时间尺度上Hamilton系统的Noether定理.定理的证明分成两步:第一步,在时间不变的无限小变换群下给出证明;第二步,利用时间重新参数化技术得到了一般无限小变换群下的定理.给出了经典和离散两种情况下Hamilton系统的Noether守恒量.文末举例说明结果的应用.%The Noether symmetry and the conserved quantity for a Hamiltonian system on time scales are proposed and studied in this paper.The Hamilton principle on time scales is established,and corresponding Hamilton canonical equations are deduced.Based upon the invariance of the Hamilton action on time scales under the infinitesimal transformations of a group,the Noether theorem for the Hamiltonian system on time scales is established.The proof of the theorem is composed of two steps.First,we prove the Noether theorem under the infinitesimal transformations of a special one-parameter group without varying the time.Second using the technique of time-re-parameterization,we obtain the Noether theorem in its general form.The Noether-type conserved quantities for Hamiltonian system in both the classical and the discrete cases are given.At the end of the paper,two examples are given to illustrate the application of the theorem.
Noether's theorem of relativistic-electromagnetic ideal hydrodynamics
Energy Technology Data Exchange (ETDEWEB)
Elsas, J.H. Gaspar; Koide, T.; Kodama, T., E-mail: jhelsas@gmail.com, E-mail: kodama.takeshi@gmail.com, E-mail: tomoikoide@gmail.com [Universidade Federal do Rio de Janeiro (UFRJ), RJ (Brazil). Instituto de Fisica
2015-06-15
We present a variational approach for relativistic ideal hydrodynamics interacting with electromagnetic fields. The momentum of fluid is introduced as the canonical conjugate variable of the position of a fluid element, which coincides with the conserved quantity derived from Noether's theorem. We further show that our formulation can reproduce the usual electromagnetic hydrodynamics which is obtained so as to satisfy the conservation of the inertia of fluid motion. (author)
Supervariable Approach to the Nilpotent Symmetries for a Toy Model of the Hodge Theory
Directory of Open Access Journals (Sweden)
D. Shukla
2016-01-01
Full Text Available We exploit the standard techniques of the supervariable approach to derive the nilpotent Becchi-Rouet-Stora-Tyutin (BRST and anti-BRST symmetry transformations for a toy model of the Hodge theory (i.e., a rigid rotor and provide the geometrical meaning and interpretation to them. Furthermore, we also derive the nilpotent (anti-co-BRST symmetry transformations for this theory within the framework of the above supervariable approach. We capture the (anti-BRST and (anti-co-BRST invariance of the Lagrangian of our present theory within the framework of augmented supervariable formalism. We also express the (anti-BRST and (anti-co-BRST charges in terms of the supervariables (obtained after the application of the (dual-horizontality conditions and (anti-BRST and (anti-co-BRST invariant restrictions to provide the geometrical interpretations for their nilpotency and anticommutativity properties. The application of the dual-horizontality condition and ensuing proper (i.e., nilpotent and absolutely anticommuting fermionic (anti-co-BRST symmetries are completely novel results in our present investigation.
Symmetries, Symmetry Breaking, Gauge Symmetries
Strocchi, Franco
2015-01-01
The concepts of symmetry, symmetry breaking and gauge symmetries are discussed, their operational meaning being displayed by the observables {\\em and} the (physical) states. For infinitely extended systems the states fall into physically disjoint {\\em phases} characterized by their behavior at infinity or boundary conditions, encoded in the ground state, which provide the cause of symmetry breaking without contradicting Curie Principle. Global gauge symmetries, not seen by the observables, are nevertheless displayed by detectable properties of the states (superselected quantum numbers and parastatistics). Local gauge symmetries are not seen also by the physical states; they appear only in non-positive representations of field algebras. Their role at the Lagrangian level is merely to ensure the validity on the physical states of local Gauss laws, obeyed by the currents which generate the corresponding global gauge symmetries; they are responsible for most distinctive physical properties of gauge quantum field ...
Lagrangian Approach to Dispersionless KdV Hierarchy
Directory of Open Access Journals (Sweden)
Amitava Choudhuri
2007-09-01
Full Text Available We derive a Lagrangian based approach to study the compatible Hamiltonian structure of the dispersionless KdV and supersymmetric KdV hierarchies and claim that our treatment of the problem serves as a very useful supplement of the so-called r-matrix method. We suggest specific ways to construct results for conserved densities and Hamiltonian operators. The Lagrangian formulation, via Noether's theorem, provides a method to make the relation between symmetries and conserved quantities more precise. We have exploited this fact to study the variational symmetries of the dispersionless KdV equation.
Lax Triad Approach to Symmetries of Scalar Modified Kadomtsev–Petviashvili Hierarchy
Deng, Xiao; Chen, Kui; Zhang, Da-Jun
2017-02-01
By means of Lax triads we reconstruct isospectral and nonisospectral scalar modified Kadomtsev–Petviashvili (mKP) hierarchies. In this approach the argument y is treated as an independent variable which is independent of time parameters \\{{t}1,{t}2,\\ldots \\}. Consequently, the isospectral and nonisospectral scalar mKP flows can have clear zero curvature representations, which enables us to handle investigation of symmetries of the scalar isospectral mKP hierarchy as freely as for (1+1)-dimensional systems. As a result, we obtain Lie algebraic structures of the scalar mKP flows and construct symmetries for the scalar isospectral mKP hierarchy. Supported by the National Natural Science Foundation of China under Grant No. 11371241
Predicting the mean fields of compressible turbulent boundary layer via a symmetry approach
Bi, Wei-Tao; Wu, Bin; She, Zhen-Su
2016-11-01
A symmetry approach for canonical wall turbulence is extended to develop mean-field predictions for compressible turbulent boundary layer (CTBL). A stress length and a weighted heat flux length are identified to obey the multilayer dilation symmetry of canonical flows, giving rise to predictions of the mean velocity and temperature profiles for a range of Reynolds number (Re), Mach number (Ma) and wall temperature (Tw). Also predicted are the streamwise developments of the shape factor, the boundary layer edge velocity and the boundary layer thicknesses, etc. Only three parameters are involved in the predictions, which have sound physics and organized behaviors with respect to the Re, Ma and Tw effects. The predictions are extensively validated by direct numerical simulation and experimental data, showing better accuracies than the previous theories. The results provide new quantifications that can be used to assess computations, measurements and turbulence models of CTBL, as well as to provide new insights for the CTBL physics.
Symmetries of Ginsparg-Wilson Chiral Fermions
Mandula, Jeffrey E
2009-01-01
The group structure of the variant chiral symmetry discovered by Luscher in the Ginsparg-Wilson description of lattice chiral fermions is analyzed. It is shown that the group contains an infinite number of linearly independent symmetry generators, and the Lie algebra is given explicitly. CP is an automorphism of this extended chiral group, and the CP transformation properties of the symmetry generators are found. The group has an infinite-parameter subgroup, and the factor group whose elements are its cosets is isomorphic to the continuum chiral symmetry group. Features of the currents associated with these symmetries are discussed, including the fact that some different, non-commuting symmetry generators lead to the same Noether current. These are universal features of lattice chiral fermions based on the Ginsparg-Wilson relation; they occur in the overlap, domain-wall, and perfect-action formulations. In a solvable example - free overlap fermions - these non-canonical elements of lattice chiral symmetry are...
Noether Theorem for Nonholonomic Systems with Time Delay
Directory of Open Access Journals (Sweden)
Shi-Xin Jin
2015-01-01
Full Text Available The paper focuses on studying the Noether theorem for nonholonomic systems with time delay. Firstly, the differential equations of motion for nonholonomic systems with time delay are established, which is based on the Hamilton principle with time delay and the Lagrange multiplier rules. Secondly, based upon the generalized quasi-symmetric transformations for nonconservative systems with time delay, the Noether theorem for corresponding holonomic systems is given. Finally, we obtain the Noether theorem for the nonholonomic nonconservative systems with time delay. At the end of the paper, an example is given to illustrate the application of the results.
A symmetry based approach to quantifying the compressible turbulent boundary layer
Wu, Bin; Bi, Wei-Tao; She, Zhen-Su; Hussain, Fazle
2015-11-01
Developing analytical description of the compressible turbulent boundary layer (CTBL) is of great importance to many technological applications and to the understanding and modeling of compressible turbulence. Here a symmetry-based approach is applied to analyze the CTBL data acquired from DNS, covering a wide range of Reynolds number (Re), Mach number (Ma) and wall temperature. The Reynolds stress length scale displays a four-layer structure in the direction normal to the wall and obeys the dilation group invariance as in the incompressible TBL. A newly-identified turbulent heat flux length scale behaves similarly, which is the classical temperature mixing length weighted by the mean temperature. A significant result is the identification of three physical parameters for each length function to characterize the adiabatic flow: a bulk flow constant, a buffer layer thickness and a boundary layer edge, which vary with Re and Ma. For the diabatic flow, the sublayer thickness and the inner layer scaling exponents vary additionally with the wall temperature. These parameters are modeled empirically, leading to a highly accurate prediction of the mean fields of the CTBL. Thus we reveal that the symmetry principle found in canonical wall-bounded flows holds also for the CTBL, and a quantitative mean field theory is viable with appropriate symmetry considerations.
String-Inspired Gravity through Symmetries
Directory of Open Access Journals (Sweden)
José Antonio Belinchón
2016-02-01
Full Text Available We study a string-inspired cosmological model from the symmetries point of view. We start by deducing the form that each physical quantity must take so that the field equations, in the string frame, admit self-similar solutions. In the same way, we formalize the use of power-law solutions (less restrictive than the self-similar ones by studying the wave equation for the dilaton through the Lie group method. Furthermore, we show how to generate more solutions by using this approach. As examples, we calculate exact solutions to several cosmological models in the four-dimensional NS-NS (Neveu-Schwarz-Neveu-Schwarz sector of low-energy effective string theory coupled to a dilaton and an axion-like H-field within the string frame background, with FRW and the Bianchi Type II metrics. We also study the existence of Noether symmetries, which allow us to determine the form of the physical quantities in the framework of FRW geometry and to find exact cosmological solutions.
Loebbert, Florian
2016-08-01
In these introductory lectures we discuss the topic of Yangian symmetry from various perspectives. Forming the classical counterpart of the Yangian and an extension of ordinary Noether symmetries, first the concept of nonlocal charges in classical, two-dimensional field theory is reviewed. We then define the Yangian algebra following Drinfel’d's original motivation to construct solutions to the quantum Yang-Baxter equation. Different realizations of the Yangian and its mathematical role as a Hopf algebra and quantum group are discussed. We demonstrate how the Yangian algebra is implemented in quantum, two-dimensional field theories and how its generators are renormalized. Implications of Yangian symmetry on the two-dimensional scattering matrix are investigated. We furthermore consider the important case of discrete Yangian symmetry realized on integrable spin chains. Finally we give a brief introduction to Yangian symmetry in planar, four-dimensional super Yang-Mills theory and indicate its impact on the dilatation operator and tree-level scattering amplitudes. These lectures are illustrated by several examples, in particular the two-dimensional chiral Gross-Neveu model, the Heisenberg spin chain and { N }=4 superconformal Yang-Mills theory in four dimensions.
A Unified Symmetry of Mechanical Systems with Variable Mass in Phase Space
Institute of Scientific and Technical Information of China (English)
WANG Peng; FANG Jian-Hui; ZHANG Peng-Yu; DING Ning
2006-01-01
In this paper, the definition and the criterion of a unified symmetry of the mechanical system with variable mass in phase space are given. The Noether conserved quantity, the generalized Hojman conserved quantity, and Mei conserved quantity deduced from the unified symmetry are obtained. An example is given to illustrate the application of the results.
Dynamics-dependent symmetries in Newtonian mechanics
Holland, Peter
2014-01-01
We exhibit two symmetries of one-dimensional Newtonian mechanics whereby a solution is built from the history of another solution via a generally nonlinear and complex potential-dependent transformation of the time. One symmetry intertwines the square roots of the kinetic and potential energies and connects solutions of the same dynamical problem (the potential is an invariant function). The other symmetry connects solutions of different dynamical problems (the potential is a scalar function). The existence of corresponding conserved quantities is examined using Noethers theorem and it is shown that the invariant-potential symmetry is correlated with energy conservation. In the Hamilton-Jacobi picture the invariant-potential transformation provides an example of a field-dependent symmetry in point mechanics. It is shown that this transformation is not a symmetry of the Schroedinger equation.
Symmetries and conservation laws of the damped harmonic oscillator
Indian Academy of Sciences (India)
Amitava Choudhuri; Subrata Ghosh; B Talukdar
2008-04-01
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 variational or Noether symmetries of the damped harmonic oscillator representing it by an explicitly time-dependent Lagrangian and found that a five-parameter group of transformations leaves the action integral invariant. Amongst the associated conserved quantities only two are found to be functionally independent. These two conserved quantities determine the solution of the problem and correspond to a two-parameter Abelian subgroup.
An operational approach to spacetime symmetries: Lorentz transformations from quantum communication
Hoehn, Philipp A
2015-01-01
In most approaches to fundamental physics, spacetime symmetries are postulated a priori and then explicitly implemented in the theory. This includes Lorentz covariance in quantum field theory and diffeomorphism invariance in quantum gravity, which are seen as fundamental principles to which the final theory has to be adjusted. In this paper, we suggest within a much simpler setting that this kind of reasoning can actually be reversed, by taking an operational approach inspired by quantum information theory. We consider observers in distant laboratories, with local physics described by the laws of abstract quantum theory, and without presupposing a particular spacetime structure. We ask what information-theoretic effort the observers have to spend to synchronize their descriptions of local physics. If there are "enough" observables that can be measured jointly on different types of systems, we show that the observers' descriptions are related by an element of the Lorentz group O^+(3,1), together with a global ...
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...
Symbolic computation of variational symmetries in optimal control
2006-01-01
We use a computer algebra system to compute, in an efficient way, optimal control variational symmetries up to a gauge term. The symmetries are then used to obtain families of Noether's first integrals, possibly in the presence of nonconservative external forces. As an application, we obtain eight independent first integrals for a sub-Riemannian nilpotent problem (2, 3, 5, 8). control theory group (cotg) CEOC POCTI/MAT/41683 /2001 PRODEP III/5.3/2003
Theory of symmetry for a rotational relativistic Birkhoff system
Institute of Scientific and Technical Information of China (English)
罗绍凯; 陈向炜; 郭永新
2002-01-01
The theory of symmetry for a rotational relativistic Birkhoff system is studied. In terms of the invariance of therotational relativistic Pfaff-Birkhoff-D'Alembert principle under infinitesimal transformations, the Noether symmetriesand conserved quantities of a rotational relativistic Birkhoff system are given. In terms of the invariance of rotationalrelativistic Birkhoff equations under infinitesimal transformations, the Lie symmetries and conserved quantities of therotational relativistic Birkhoff system are given.
Superfield Approach to Nilpotent Symmetries of the Freedman-Townsend Model: Novel Features
Malik, R. P.
2012-09-01
We perform the Becchi-Rouet-Stora-Tyutin (BRST) analysis of the Freedman-Townsend (FT) model of topologically massive non-Abelian theory by exploiting its (1-form) Yang-Mills (YM) gauge transformations to show the existence of some novel features that are totally different from the results obtained in such a kind of consideration carried out for the dynamical non-Abelian 2-form theory. We tap here the potential and power of the augmented version of Bonora-Tonin's superfield approach to BRST formalism to derive the full set of off-shell nilpotent and absolutely anticommuting (anti-)BRST symmetry transformations where, in addition to the horizontality condition (HC), we are theoretically compelled to exploit the appropriate gauge-invariant restrictions (GIRs) on the (super)fields for the derivation of the appropriate symmetry transformations for all the relevant fields. We compare our key results with that of the other such attempt for the discussion of the present model within the framework of BRST formalism.
BRST approach to Lagrangian formulation for mixed-symmetry fermionic higher-spin fields
Moshin, Pavel Yu.; Reshetnyak, Alexander A.
2007-10-01
We construct a Lagrangian description of irreducible half-integer higher-spin representations of the Poincare group with the corresponding Young tableaux having two rows, on a basis of the BRST approach. Starting with a description of fermionic higher-spin fields in a flat space of any dimension in terms of an auxiliary Fock space, we realize a conversion of the initial operator constraint system (constructed with respect to the relations extracting irreducible Poincare-group representations) into a first-class constraint system. For this purpose, we find auxiliary representations of the constraint subsuperalgebra containing the subsystem of second-class constraints in terms of Verma modules. We propose a universal procedure of constructing gauge-invariant Lagrangians with reducible gauge symmetries describing the dynamics of both massless and massive fermionic fields of any spin. No off-shell constraints for the fields and gauge parameters are used from the very beginning. It is shown that the space of BRST cohomologies with a vanishing ghost number is determined only by the constraints corresponding to an irreducible Poincare-group representation. To illustrate the general construction, we obtain a Lagrangian description of fermionic fields with generalized spin (3/2, 1/2) and (3/2, 3/2) on a flat background containing the complete set of auxiliary fields and gauge symmetries.
Exact cosmological solutions of f(R theories via Hojman symmetry
Directory of Open Access Journals (Sweden)
Hao Wei
2016-02-01
Full Text Available Nowadays, f(R theory has been one of the leading modified gravity theories to explain the current accelerated expansion of the universe, without invoking dark energy. It is of interest to find the exact cosmological solutions of f(R theories. Besides other methods, symmetry has been proved as a powerful tool to find exact solutions. On the other hand, symmetry might hint the deep physical structure of a theory, and hence considering symmetry is also well motivated. As is well known, Noether symmetry has been extensively used in physics. Recently, the so-called Hojman symmetry was also considered in the literature. Hojman symmetry directly deals with the equations of motion, rather than Lagrangian or Hamiltonian, unlike Noether symmetry. In this work, we consider Hojman symmetry in f(R theories in both the metric and Palatini formalisms, and find the corresponding exact cosmological solutions of f(R theories via Hojman symmetry. There exist some new solutions significantly different from the ones obtained by using Noether symmetry in f(R theories. To our knowledge, they also have not been found previously in the literature. This work confirms that Hojman symmetry can bring new features to cosmology and gravity theories.
Two-nucleon scattering in a modified Weinberg approach with a symmetry-preserving regularization
Behrendt, J; Gegelia, J; Meißner, Ulf-G; Nogga, A
2016-01-01
We consider the nucleon-nucleon scattering problem by applying time-ordered perturbation theory to the Lorentz invariant formulation of baryon chiral perturbation theory. Using a symmetry preserving higher derivative form of the effective Lagrangian, we exploit the freedom of the choice of the renormalization condition and obtain an integral equation for the scattering amplitude with an improved ultraviolet behavior. The resulting formulation is used to quantify finite regulator artifacts in two-nucleon phase shifts as well as in the chiral extrapolations of the S-wave scattering lengths and the deuteron binding energy. This approach can be straightforwardly extended to analyze few-nucleon systems and processes involving external electroweak sources.
Two-nucleon scattering in a modified Weinberg approach with a symmetry-preserving regularization
Energy Technology Data Exchange (ETDEWEB)
Behrendt, J.; Epelbaum, E. [Ruhr-Universitaet Bochum, Institut fuer Theoretische Physik II, Bochum (Germany); Gegelia, J. [Forschungszentrum Juelich, Institute for Advanced Simulation, Institut fuer Kernphysik and Juelich Center for Hadron Physics, Juelich (Germany); Tbilisi State University, Tbilisi (Georgia); Meissner, Ulf G. [Universitaet Bonn, Helmholtz Institut fuer Strahlen- und Kernphysik and Bethe Center for Theoretical Physics, Bonn (Germany); Forschungszentrum Juelich, Institute for Advanced Simulation, Institut fuer Kernphysik and Juelich Center for Hadron Physics, Juelich (Germany); Forschungszentrum Juelich, JARA - Forces and Matter Experiments, Juelich (Germany); Forschungszentrum Juelich, JARA - High Performance Computing, Juelich (Germany); Nogga, A. [Forschungszentrum Juelich, Institute for Advanced Simulation, Institut fuer Kernphysik and Juelich Center for Hadron Physics, Juelich (Germany); Forschungszentrum Juelich, JARA - High Performance Computing, Juelich (Germany)
2016-09-15
We consider the nucleon-nucleon scattering problem by applying time-ordered perturbation theory to the Lorentz-invariant formulation of baryon chiral perturbation theory. We employ a higher-derivative symmetry-preserving regularization to obtain an integral equation for the scattering amplitude, which permits a non-perturbative treatment of subleading contributions to the nucleon-nucleon potential. The resulting formulation is used to quantify finite regulator artefacts in two-nucleon phase shifts as well as in the chiral extrapolations of the S-wave scattering lengths and the deuteron binding energy. Our approach can be straightforwardly extended to analyse few-nucleon systems and processes involving external electroweak sources. (orig.)
BRST approach to Lagrangian formulation for mixed-symmetry fermionic higher-spin fields
Moshin, P Yu
2007-01-01
We construct a Lagrangian description for irreducible half-integer higher-spin representations of the Poincare group with the corresponding Young tableaux having two rows, on a basis of the BRST approach. Starting with a formulation for fermionic higher-spin fields in a flat space of any dimension in terms of an auxiliary Fock space, we realize a conversion of the initial operator constraint system (constructed with respect to the relations extracting irreducible Poincare-group representations) into a first-class constraint system. For this purpose, we find auxiliary representations of the constraints subsuperalgebra containing the subsystem of second-class constraints in terms of Verma modules. We propose a universal procedure of constructing gauge-invariant Lagrangians with reducible gauge symmetries describing the dynamics of fermionic fields of any spin. No off-shell constraints for the fields and gauge parameters are used from the very beginning. It is shown that only the constraints corresponding to an ...
Variational Tricomplex, Global Symmetries and Conservation Laws of Gauge Systems
Sharapov, Alexey A.
2016-10-01
Using the concept of variational tricomplex endowed with a presymplectic structure, we formulate the general notion of symmetry. We show that each generalized symmetry of a gauge system gives rise to a sequence of conservation laws that are represented by on-shell closed forms of various degrees. This extends the usual Noether's correspondence between global symmetries and conservation laws to the case of lower-degree conservation laws and not necessarily variational equations of motion. Finally, we equip the space of conservation laws of a given degree with a Lie bracket and establish a homomorphism of the resulting Lie algebra to the Lie algebra of global symmetries.
Variational tricomplex, global symmetries and conservation laws of gauge systems
Sharapov, A A
2016-01-01
Using the concept of variational tricomplex endowed with a presymplectic structure, we formulate the general notion of symmetry. We show that each generalized symmetry of a gauge system gives rise to a sequence of conservation laws that are represented by on-shell closed forms of various degrees. This extends the usual Noether's correspondence between global symmetries and conservation laws to the case of lower-degree conservation laws and not necessarily variational equations of motion. Finally, we equip the space of conservation laws of a given degree with a Lie bracket and establish a homomorphism of the resulting Lie algebra to the Lie algebra of global symmetries.
The gonality theorem of Noether for hypersurfaces
Bastianelli, Francesco; De Poi, Pietro
2011-01-01
It is well known since Noether that the gonality of a smooth plane curve of degree d>3 is d-1. Given a k-dimensional complex projective variety X, the most natural extension of gonality is probably the degree of irrationality, that is the minimum degree of a dominant rational map from X to $\\mathbb{P}^k$. In this paper we are aimed at extending the assertion on plane curves to smooth hypersurfaces in $\\mathbb{P}^n$ in terms of degree of irrationality. We prove that both surfaces in $\\mathbb{P}^3$ and threefolds in $\\mathbb{P}^4$ of sufficiently large degree d have degree of irrationality d-1, except for finitely many cases we classify, whose degree of irrationality is d-2. To this aim we use Mumford's technique of induced differentials and we shift the problem to study first order congruences of lines of $\\mathbb{P}^n$. In particular, we also slightly improve the description of such congruences in $\\mathbb{P}^4$ and we provide a bound on degree of irrationality of hypersurfaces of arbitrary dimension.
Symmetries of geodesic motion in G\\"{o}del-type spacetimes
Camci, U
2014-01-01
In this paper, we study Noether gauge symmetries of geodesic motion for geodesic Lagrangian of four classes of metrics of G\\"{o}del-type spacetimes for which we calculated the Noether gauge symmetries for all classes I-IV, and find the first integrals of corresponding classes to derive a complete characterization of the geodesic motion. Using the obtained expressions for $\\dot{t}, \\dot{r}, \\dot{\\phi}$ and $\\dot{z}$ of each classes I-IV which depends essentially on two independent parameters $m$ and $w$, we explicitly integrated the geodesic equations of motion for the corresponding G\\"{o}del-type spacetimes.
An operational approach to spacetime symmetries: Lorentz transformations from quantum communication
Höhn, Philipp A.; Müller, Markus P.
2016-06-01
In most approaches to fundamental physics, spacetime symmetries are postulated a priori and then explicitly implemented in the theory. This includes Lorentz covariance in quantum field theory and diffeomorphism invariance in quantum gravity, which are seen as fundamental principles to which the final theory has to be adjusted. In this paper, we suggest, within a much simpler setting, that this kind of reasoning can actually be reversed, by taking an operational approach inspired by quantum information theory. We consider observers in distinct laboratories, with local physics described by the laws of abstract quantum theory, and without presupposing a particular spacetime structure. We ask what information-theoretic effort the observers have to spend to synchronize their descriptions of local physics. If there are ‘enough’ observables that can be measured universally on several different quantum systems, we show that the observers’ descriptions are related by an element of the orthochronous Lorentz group {{{O}}}+(3,1), together with a global scaling factor. Not only does this operational approach predict the Lorentz transformations, but it also accurately describes the behavior of relativistic Stern-Gerlach devices in the WKB approximation, and it correctly predicts that quantum systems carry Lorentz group representations of different spin. This result thus hints at a novel information-theoretic perspective on spacetime.
Energy Technology Data Exchange (ETDEWEB)
Bostrem, I.G. [Department of Physics, Ural State University, Ekaterinburg 620083 (Russian Federation); Kishine, J. [Faculty of Engineering, Kyushu Institute of Technology, Kitakyushu 804-8550 (Japan); Lavrov, R.V. [Department of Physics, Ural State University, Ekaterinburg 620083 (Russian Federation); Ovchinnikov, A.S. [Department of Physics, Ural State University, Ekaterinburg 620083 (Russian Federation)], E-mail: alexander.ovchinnikov@usu.ru
2009-01-26
An appearance of the transport spin current in chiral helimagnet is mathematically justified based on the symmetry arguments. Although the starting Lagrangian of the chiral magnet with the Berry phase term and the parity-violating Dzyaloshinskii-Morya coupling is not manifestly Galilean invariant, the Lie point group symmetry analysis and the variational symmetry analysis elucidate the hidden Galilean symmetry and the existence of the linear momentum as a conserved Noether current, respectively.
Institute of Scientific and Technical Information of China (English)
金世欣; 张毅
2014-01-01
The Noether symmetries and the conserved quantities for nonconservative mechanical systems with time delay in phase space are studied .Firstly, the Hamilton canonical equations with time delays for the non-conservative systems are established .Secondly , according to the generalized quasi-invariance of the Hamilton action with time delay in phase space under the infinitesimal transformations of groups , the definitions and criterion of the Noether generalized quasi-symmetric transformations with time delay in phase space are given .Lastly, the relationship between the Noether symmetries and the conserved quanti-ties with time delay in phase space are established .At the end , an example is given to illustrate the ap-plication of the results .%研究相空间中含时滞的非保守力学系统的Noether对称性与守恒量。建立含时滞的非保守系统动力学的Hamilton正则方程；依据相空间中含时滞的Hamilton作用量在无限小群变换下的广义准不变性，给出相空间中含时滞的Noether广义准对称变换的定义和判据；并建立相空间中含时滞的非保守力学系统的Noether对称性与守恒量之间的联系。文末，举例说明结果的应用。
Noether's problem for central extensions of metacyclic $p$-groups
Michailov, Ivo M
2011-01-01
Let $K$ be a field and $G$ be a finite group. Let $G$ act on the rational function field $K(x(g):g\\in G)$ by $K$ automorphisms defined by $g\\cdot x(h)=x(gh)$ for any $g,h\\in G$. Denote by $K(G)$ the fixed field $K(x(g):g\\in G)^G$. Noether's problem then asks whether $K(G)$ is rational over $K$. In [M. Kang, Noether's problem for metacyclic $p$-groups, Adv. Math. 203(2005), 554-567], Kang proves the rationality of $K(G)$ over $K$ if $G$ is any metacyclic $p$-group and $K$ is any field containing enough roots of unity. In this paper, we give a positive answer to the Noether's problem for all central group extensions of the general metacyclic $p$-group, provided that $K$ is infinite and it contains sufficient roots of unity.
Emmy Noether and Linear Evolution Equations
Directory of Open Access Journals (Sweden)
P. G. L. Leach
2013-01-01
Full Text Available Noether’s Theorem relates the Action Integral of a Lagrangian with symmetries which leave it invariant and the first integrals consequent upon the variational principle and the existence of the symmetries. These each have an equivalent in the Schrödinger Equation corresponding to the Lagrangian and by extension to linear evolution equations in general. The implications of these connections are investigated.
Applications of hidden symmetries to black hole physics
Energy Technology Data Exchange (ETDEWEB)
Frolov, Valeri, E-mail: vfrolov@ualberta.ca [Institute of Theoretical Physics, Department of Physics University of Alberta, Edmonton, Alberta, T6G 2G7 (Canada)
2011-02-01
This work is a brief review of applications of hidden symmetries to black hole physics. Symmetry is one of the most important concepts of the science. In physics and mathematics the symmetry allows one to simplify a problem, and often to make it solvable. According to the Noether theorem symmetries are responsible for conservation laws. Besides evident (explicit) spacetime symmetries, responsible for conservation of energy, momentum, and angular momentum of a system, there also exist what is called hidden symmetries, which are connected with higher order in momentum integrals of motion. A remarkable fact is that black holes in four and higher dimensions always possess a set ('tower') of explicit and hidden symmetries which make the equations of motion of particles and light completely integrable. The paper gives a general review of the recently obtained results. The main focus is on understanding why at all black holes have something (symmetry) to hide.
Applications of hidden symmetries to black hole physics
Frolov, Valeri
2010-01-01
This work is a brief review of applications of hidden symmetries to black hole physics. Symmetry is one of the most important concepts of the science. In physics and mathematics the symmetry allows one to simplify a problem, and often to make it solvable. According to the Noether theorem symmetries are responsible for conservation laws. Besides evident (explicit) spacetime symmetries, responsible for conservation of energy, momentum, and angular momentum of a system, there also exist what is called hidden symmetries, which are connected with higher order in momentum integrals of motion. A remarkable fact is that black holes in four and higher dimensions always possess a set (`tower') of explicit and hidden symmetries which make the equations of motion of particles and light completely integrable. The paper gives a general review of the recently obtained results. The main focus is on understanding why at all black holes have something (symmetry) to hide.
Perturbation to Unified Symmetry and Adiabatic Invariants for Relativistic Hamilton Systems
Institute of Scientific and Technical Information of China (English)
ZHANG Ming-Jiang; FANG Jian-Hui; LU Kai; PANG Ting; LIN Peng
2009-01-01
Based on the concept of adiabatic invariant, the perturbation to unified symmetry and adiabatic invariants for relativistic Hamilton systems are studied. The definition of the perturbation to unified symmetry for the system is presented, and the criterion of the perturbation to unified symmetry is given. Meanwhile, the Noether adiabatic invariants, the generalized Hojman adiabatic invariants, and the Mei adiabatic invariants for the perturbed system are obtained.
Munteanu, Florian
2016-01-01
In this paper, we will present Lagrangian and Hamiltonian k-symplectic formalisms, we will recall the notions of symmetry and conservation law and we will define the notion of pseudosymmetry as a natural extension of symmetry. Using symmetries and pseudosymmetries, without the help of a Noether type theorem, we will obtain new kinds of conservation laws for k-symplectic Hamiltonian systems and k-symplectic Lagrangian systems.
Seiler, Christian; Evers, Ferdinand
2016-10-01
A formalism for electronic-structure calculations is presented that is based on the functional renormalization group (FRG). The traditional FRG has been formulated for systems that exhibit a translational symmetry with an associated Fermi surface, which can provide the organization principle for the renormalization group (RG) procedure. We here advance an alternative formulation, where the RG flow is organized in the energy-domain rather than in k space. This has the advantage that it can also be applied to inhomogeneous matter lacking a band structure, such as disordered metals or molecules. The energy-domain FRG (ɛ FRG) presented here accounts for Fermi-liquid corrections to quasiparticle energies and particle-hole excitations. It goes beyond the state of the art G W -BSE , because in ɛ FRG the Bethe-Salpeter equation (BSE) is solved in a self-consistent manner. An efficient implementation of the approach that has been tested against exact diagonalization calculations and calculations based on the density matrix renormalization group is presented. Similar to the conventional FRG, also the ɛ FRG is able to signalize the vicinity of an instability of the Fermi-liquid fixed point via runaway flow of the corresponding interaction vertex. Embarking upon this fact, in an application of ɛ FRG to the spinless disordered Hubbard model we calculate its phase boundary in the plane spanned by the interaction and disorder strength. Finally, an extension of the approach to finite temperatures and spin S =1 /2 is also given.
New approach to the perception of 3D shape based on veridicality, complexity, symmetry and volume.
Pizlo, Zygmunt; Sawada, Tadamasa; Li, Yunfeng; Kropatsch, Walter G; Steinman, Robert M
2010-01-01
This paper reviews recent progress towards understanding 3D shape perception made possible by appreciating the significant role that veridicality and complexity play in the natural visual environment. The ability to see objects as they really are "out there" is derived from the complexity inherent in the 3D object's shape. The importance of both veridicality and complexity was ignored in most prior research. Appreciating their importance made it possible to devise a computational model that recovers the 3D shape of an object from only one of its 2D images. This model uses a simplicity principle consisting of only four a priori constraints representing properties of 3D shapes, primarily their symmetry and volume. The model recovers 3D shapes from a single 2D image as well, and sometimes even better, than a human being. In the rare recoveries in which errors are observed, the errors made by the model and human subjects are very similar. The model makes no use of depth, surfaces or learning. Recent elaborations of this model include: (i) the recovery of the shapes of natural objects, including human and animal bodies with limbs in varying positions (ii) providing the model with two input images that allowed it to achieve virtually perfect shape constancy from almost all viewing directions. The review concludes with a comparison of some of the highlights of our novel, successful approach to the recovery of 3D shape from a 2D image with prior, less successful approaches.
A note on Brill-Noether thoery and rank determining sets for metric graphs
Lim, Chang Mou; Potashnik, Natasha
2011-01-01
We produce open subsets of the moduli space of metric graphs without separating edges where the dimensions of Brill-Noether loci are larger than the corresponding Brill-Noether numbers. These graphs also have minimal rank determining sets that are larger than expected, giving couterexamples to a conjecture of Luo. Furthermore, limits of these graphs have Brill-Noether loci of the expected dimension, so dimensions of Brill-Noether loci of metric graphs do not vary upper semicontinuously in families. Motivated by these examples, we study a notion of rank for the Brill-Noether locus of a metric graph, closely analogous to the Baker-Norine definition of the rank of a divisor. We show that ranks of Brill-Noether loci vary upper semicontinuously in families of metric graphs and are related to dimensions of Brill-Noether loci of algebraic curves by a specialization inequality.
Neutrinos and flavor symmetries
Tanimoto, Morimitsu
2015-07-01
We discuss the recent progress of flavor models with the non-Abelian discrete symmetry in the lepton sector focusing on the θ13 and CP violating phase. In both direct approach and indirect approach of the flavor symmetry, the non-vanishing θ13 is predictable. The flavor symmetry with the generalised CP symmetry can also predicts the CP violating phase. We show the phenomenological analyses of neutrino mixing for the typical flavor models.
Neutrinos and flavor symmetries
Energy Technology Data Exchange (ETDEWEB)
Tanimoto, Morimitsu
2015-07-15
We discuss the recent progress of flavor models with the non-Abelian discrete symmetry in the lepton sector focusing on the θ{sub 13} and CP violating phase. In both direct approach and indirect approach of the flavor symmetry, the non-vanishing θ{sub 13} is predictable. The flavor symmetry with the generalised CP symmetry can also predicts the CP violating phase. We show the phenomenological analyses of neutrino mixing for the typical flavor models.
van Wüllen, Christoph
2009-10-29
Antiferromagnetic coupling in multinuclear transition metal complexes usually leads to electronic ground states that cannot be described by a single Slater determinant and that are therefore difficult to describe by Kohn-Sham density functional methods. Density functional calculations in such cases are usually converged to broken symmetry solutions which break spin and, in many cases, also spatial symmetry. While a procedure exists to extract isotropic Heisenberg (exchange) coupling constants from such calculations, no such approach is yet established for the calculation of magnetic anisotropy energies or zero field splitting parameters. This work proposes such a procedure. The broken symmetry solutions are not only used to extract the exchange couplings but also single-ion D tensors which are then used to construct a (phenomenological) spin Hamiltonian, from which the magnetic anisotropy and the zero-field energy levels can be computed. The procedure is demonstrated for a bi- and a trinuclear Mn(III) model compound.
Nava, Jaime
2015-01-01
This book demonstrates how to describe and analyze a system's behavior and extract the desired prediction and control algorithms from this analysis. A typical prediction is based on observing similar situations in the past, knowing the outcomes of these past situations, and expecting that the future outcome of the current situation will be similar to these past observed outcomes. In mathematical terms, similarity corresponds to symmetry, and similarity of outcomes to invariance. This book shows how symmetries can be used in all classes of algorithmic problems of sciences and engineering: from analysis to prediction to control. Applications cover chemistry, geosciences, intelligent control, neural networks, quantum physics, and thermal physics. Specifically, it is shown how the approach based on symmetry and similarity can be used in the analysis of real-life systems, in the algorithms of prediction, and in the algorithms of control.
Lagrangian approach and dissipative magnetic systems
Energy Technology Data Exchange (ETDEWEB)
Bose, Thomas, E-mail: thomas.bose@physik.uni-halle.de [Martin-Luther-University, Physics Department, Von-Seckendorff-Platz 1, 06114 Halle (Germany); Trimper, Steffen, E-mail: steffen.trimper@physik.uni-halle.de [Martin-Luther-University, Physics Department, Von-Seckendorff-Platz 1, 06114 Halle (Germany)
2011-06-13
A Lagrangian is introduced which includes the coupling between magnetic moments m and the degrees of freedom σ of a reservoir. In case the system-reservoir coupling breaks the time reversal symmetry the magnetic moments perform a damped precession around an effective field which is self-organized by the mutual interaction of the moments. The resulting evolution equation has the form of the Landau-Lifshitz-Gilbert equation. In case the bath variables are constant vector fields the moments m fulfill the reversible Landau-Lifshitz equation. Applying Noether's theorem we find conserved quantities under rotation in space and within the configuration space of the moments. -- Highlights: → We propose a new approach for describing magnetic systems with dissipation on a mesoscopic scale. → The Lagrangian consists of an active magnetic system and a bath. → The coupling between both subsystems breaks the time reversal symmetry. → The suggested Lagrangian leads to the Landau-Lifshitz equation with damping. → We consider symmetry operations by means of Noether's theorem.
Bua, Lucía; Salgado, Modesto
2012-01-01
In this paper we study symmetries, Newtonoid vector fields, conservation laws, Noether Theorem and its converse, in the framework of the $k$-symplectic formalism, using the Fr\\"olicher-Nijenhuis formalism on the space of $k^1$ velocities of the configuration manifold. For the $k=1$ case it is well known that Cartan symmetries induce and are induced by constants of motions, and these results are known as Noether Theorem and its converse. For $k>1$, we provide a new proof that Noether Theorem is true, and hence each Cartan symmetry induces a conservation law. We show that under some assumptions, the converse of Noether Theorem is also true and provide examples when this is not the case. We also study the relations between dynamical symmetries, Newtonoid vector fields, Cartan symmetries and conservation laws, showing when one of them will imply the others. We use several examples of partial differential equations to illustrate when these concepts are related and when they are not.
The decays omega(782), phi(1020) to 5 pi in the hidden local symmetry approach
Achasov, N N
2003-01-01
The decays omega -> 2pi^+ 2pi^- pi^0 and omega -> pi^+ pi^- 3pi^0 are reconsidered in the hidden local symmetry approach (HLS) added with the anomalous terms. The decay amplitudes are analyzed in detail, paying the special attention to the Adler condition of vanishing the whole amplitude at vanishing momentum of any final pion in the chiral limit m_pi -> 0. Combining the Okubo-Zweig-Iizuka (OZI) rule applied to the five pion final state, with the Adler condition, we calculate also the phi -> 2pi^+ 2pi^-pi^0 and phi -> pi^+ pi^- 3pi^0 decay amplitudes. The partial widths of the above decays are evaluated, and the excitation curves in e^+e^- annihilation are obtained, assuming reasonable particular relations among the parameters characterizing the anomalous terms of the HLS Lagrangian. The evaluated branching ratios B(phi -> pi^+ pi^- 3pi^0)~2x10^{-7} and B(phi -> 2pi^+ 2pi^- pi^0)~7x10^{-7} are such that with the luminosity L=500 pb^{-1} attained at DAFNE phi factory, one may already possess about 1685 events ...
Seiler, Christian
2016-01-01
A formalism for electronic-structure calculations is presented that is based on the functional renormalization group (FRG). The traditional FRG has been formulated for systems that exhibit a translational symmetry with an associated Fermi surface, which can provide the organization principle for the renormalization group (RG) procedure. We here advance an alternative formulation, where the RG-flow is organized in the energy-domain rather than in k-space. This has the advantage that it can also be applied to inhomogeneous matter lacking a band-structure, such as disordered metals or molecules. The energy-domain FRG ({\\epsilon}FRG) presented here accounts for Fermi-liquid corrections to quasi-particle energies and particle-hole excitations. It goes beyond the state of the art GW-BSE, because in {\\epsilon}FRG the Bethe-Salpeter equation (BSE) is solved in a self-consistent manner. An efficient implementation of the approach that has been tested against exact diagonalization calculations and calculations based on...
Two Approaches to the Calculation of Approximate Symmetry of Ostrovsky Equation with Small Parameter
Mahdavi, Abolhassan; Nadjafikhah, Mehdi; Toomanian, Megerdich
2015-12-01
In this paper, two methods of approximate symmetries for partial differential equations with a small parameter are applied to a perturbed nonlinear Ostrovsky equation. To compute the first-order approximate symmetry, we have applied two methods which one of them was proposed by Baikov et al. in which the infinitesimal generator is expanded in a perturbation series; whereas the other method by Fushchich and Shtelen [3] is based on the expansion of the dependent variables in perturbation series. Especially, an optimal system of one dimensional subalgebras is constructed and some invariant solutions corresponding to the resulted symmetries are obtained.
Two Approaches to the Calculation of Approximate Symmetry of Ostrovsky Equation with Small Parameter
Energy Technology Data Exchange (ETDEWEB)
Mahdavi, Abolhassan, E-mail: ad.mahdavi@kiau.ac.ir [Karaj Branch Islamic University, Department of Mathematics (Iran, Islamic Republic of); Nadjafikhah, Mehdi, E-mail: mnadjafikhah@iust.ac.ir [Iran University of Science and Technology, School of Mathematics (Iran, Islamic Republic of); Toomanian, Megerdich, E-mail: megerdich.toomanian@kiau.ac.ir [Karaj Branch Islamic University, Department of Mathematics (Iran, Islamic Republic of)
2015-12-15
In this paper, two methods of approximate symmetries for partial differential equations with a small parameter are applied to a perturbed nonlinear Ostrovsky equation. To compute the first-order approximate symmetry, we have applied two methods which one of them was proposed by Baikov et al. in which the infinitesimal generator is expanded in a perturbation series; whereas the other method by Fushchich and Shtelen [3] is based on the expansion of the dependent variables in perturbation series. Especially, an optimal system of one dimensional subalgebras is constructed and some invariant solutions corresponding to the resulted symmetries are obtained.
A short review on Noether’s theorems, gauge symmetries and boundary terms
Bañados, Max; Reyes, Ignacio
2016-06-01
This review is dedicated to some modern applications of the remarkable paper written in 1918 by E. Noether. On a single paper, Noether discovered the crucial relation between symmetries and conserved charges as well as the impact of gauge symmetries on the equations of motion. Almost a century has gone since the publication of this work and its applications have permeated modern physics. Our focus will be on some examples that have appeared recently in the literature. This review aims at students, not researchers. The main three topics discussed are (i) global symmetries and conserved charges (ii) local symmetries and gauge structure of a theory (iii) boundary conditions and algebra of asymptotic symmetries. All three topics are discussed through examples.
LETTERS AND COMMENTS: Reply to 'Noether's theorem once again'
Marinho, Rubens M., Jr.
2009-09-01
This reply answers the issues raised in the comment on my paper (Marinho Jr 2007 Eur. J. Phys. 28 37-43), obtains the Laplace-Runge-Lenz vector (Goldstein 2002 Classical Mechanics 3rd edn (Reading, MA: Addison-Wesley)) using Noether's theorem and includes a Maple program used to derive the results.
Hamiltonian Noether theorem for gauge systems and two time physics
Villanueva, V M; Ruiz, L; Silvas, J
2005-01-01
The Noether theorem for Hamiltonian constrained systems is revisited. In particular, our review presents a novel method to show that the gauge transformations are generated by the conserved quantities associated with the first class constraints. We apply our results to the relativistic point particle, to the Friedberg et al. model and, with special emphasis, to two time physics.
Fractional isoperimetric Noether's theorem in the Riemann-Liouville sense
Frederico, Gastao S F
2012-01-01
We prove Noether-type theorems for fractional isoperimetric variational problems with Riemann-Liouville derivatives. Both Lagrangian and Hamiltonian formulations are obtained. Illustrative examples, in the fractional context of the calculus of variations and optimal control, are discussed in detail.
Symmetry and group theory throughout physics
Directory of Open Access Journals (Sweden)
Villain J.
2012-03-01
Full Text Available As noticed in 1884 by Pierre Curie [1], physical properties of matter are tightly related to the kind of symmetry of the medium. Group theory is a systematic tool, though not always easy to handle, to exploit symmetry properties, for instance to find the eigenvectors and eigenvalues of an operator. Certain properties (optical activity, piezoelectricity are forbidden in molecules or crystals of high symmetry. A few theorems (Noether, Goldstone establish general relations between physical properties and symmetry. Applications of group theory to condensed matter physics, elementary particle physics, quantum mechanics, electromagnetism are reviewed. Group theory is not only a tool, but also a beautiful construction which casts insight into natural phenomena.
Institute of Scientific and Technical Information of China (English)
LUO Shao-Kai
2007-01-01
For a Lagrangian system with the action of small disturbance, the Lie symmetrical perturbation and a new type of non-Noether adiabatic invariant are presented in general infinitesimal transformation groups. On the basis of the invariance of disturbed Lagrangian systems under general infinitesimal transformations, the determining equations of Lie symmetries of the system are constructed. Based on the definition of higher-order adiabatic invariants of a mechanical system, a new type of adiabatic invariant, i.e. generalized Lutzky adiabatic invariants, of a disturbed Lagrangian system are obtained by investigating the perturbation of Lie symmetries for a Lagrangian system with the action of small disturbance. Finally, an example is given to illustrate the application of the method and results.
Energy Technology Data Exchange (ETDEWEB)
Hupin, G; Lacroix, D [Grand Accelerateur National d' Ions Lourds (GANIL), CEA/DSM-CNRS/IN2P3, Bvd Henri Becquerel, 14076 Caen (France); Bender, M, E-mail: hupin@ganil.fr, E-mail: lacroix@ganil.fr, E-mail: bender@ganil.fr [Universite Bordeaux, Centre d' Etudes Nucleaires de Bordeaux Gradignan, UMR5797, F-33175 Gradignan (France)
2011-09-16
The Multi-Reference Energy Density Functional (MR-EDF) approach (also called configuration mixing or Generator Coordinate Method), that is commonly used to treat pairing in finite nuclei and project onto particle number, is re-analyzed. It is shown that, under certain conditions, the MR-EDF energy can be interpreted as a functional of the one-body density matrix of the projected state with good particle number. Based on this observation, we propose a new approach, called Symmetry-Conserving EDF (SC-EDF), where the breaking and restoration of symmetry are accounted for simultaneously. We show, that such an approach is free from pathologies recently observed in MR-EDF and can be used with a large flexibility on the density dependence of the functional.
Augmented Superfield Approach To Exact Nilpotent Symmetries For Matter Fields In Non-Abelian Theory
Malik, R P; Mandal, Bhabani Prasad
2006-01-01
We derive the nilpotent (anti-) BRST symmetry transformations for the Dirac (matter) fields of an interacting four $(3+1)$-dimensional 1-form non-Abelian gauge theory by applying the theoretical arsenal of augmented superfield formalism where (i) the horizontality condition, and (ii) the equality of a gauge invariant quantity, on the six (4, 2)-dimensional supermanifold, are exploited together. The above supermanifold is parameterized by four bosonic spacetime coordinates $x^\\mu$ (with $\\mu = 0,1,2,3)$ and a couple of Grassmannian variables $\\theta $ and $\\bar{\\theta}$. The on-shell nilpotent BRST symmetry transformations for all the fields of the theory are derived by considering the chiral superfields on the five ($4, 1)$-dimensional super sub-manifold and the off-shell nilpotent symmetry transformations emerge from the consideration of the general superfields on the full six (4, 2)-dimensional supermanifold. Geometrical interpretations for all the above nilpotent symmetry transformations are also discussed...
Chaplygin Gas of Tachyon Nature Imposed by Symmetry and Constrained via H(z) Data
Collodel, Lucas Gardai
2015-01-01
An action of general form is proposed for a Universe containing matter, radiation and dark energy. The latter is interpreted as a tachyon field non-minimally coupled to the scalar curvature. The Palatini approach is used when varying the action so the connection is given by a more generic form. Both the self-interaction potential and the non-minimally coupling function are obtained by constraining the system to present invariability under global point transformation of the fields (Noether Symmetry). The only possible solution is shown to be that of minimal coupling and constant potential (Chaplygin gas). The behavior of the dynamical properties of the system is compared to recent observational data, which infers that the tachyon field must indeed be dynamical.
Space-time symmetries and the Yang-Mills gradient flow
Del Debbio, Luigi; Rago, Antonio
2013-01-01
The recent introduction of the gradient flow has provided a new tool to probe the dynamics of quantum field theories. The latest developments have shown how to use the gradient flow for the exploration of symmetries, and the definition of the corresponding renormalized Noether currents. In this paper we introduce infinitesimal translations along the gradient flow for gauge theories, and study the corresponding Ward identities. This approach is readily generalized to the case of gauge theories defined on a lattice, where the regulator breaks translation invariance. The Ward identities in this case lead to a nonperturbative renormalization of the energy-momentum tensor. We discuss an application of this method to the study of dilatations and scale invariance on the lattice.
Hidden beauty baryon states in the local hidden gauge approach with heavy quark spin symmetry
Energy Technology Data Exchange (ETDEWEB)
Xiao, C.W.; Oset, E. [Centro Mixto Universidad de Valencia-CSIC, Institutos de Investigacion de Paterna, Departamento de Fisica Teorica and IFIC, Valencia (Spain)
2013-11-15
Using a coupled-channel unitary approach, combining the heavy quark spin symmetry and the dynamics of the local hidden gauge, we investigate the meson-baryon interaction with hidden beauty and obtain several new states of N around 11 GeV. We consider the basis of states {eta}{sub b} N, {Upsilon};N, B {Lambda}{sub b}, B {Sigma}{sub b}, B{sup *}{Lambda}{sub b}, B{sup *}{Sigma}{sub b}, B{sup *}{Sigma}{sub b}{sup *} and find four basic bound states which correspond to B {Sigma}{sub b}, B {Sigma}{sub b}{sup *}, B{sup *}{Sigma}{sub b} and B{sup *}{Sigma}{sub b}{sup *}, decaying mostly into {eta}{sub b} N and {Upsilon}N and with a binding energy about 50-130 MeV with respect to the thresholds of the corresponding channel. All of them have isospin I = 1/2, and we find no bound states or resonances in I = 3/2. The B {Sigma}{sub b} state appears in J = 1/2, the B {Sigma}{sub b}{sup *} in J = 3/2, the B{sup *}{Sigma}{sub b} appears nearly degenerate in J = 1/2, 3/2 and the B{sup *}{Sigma}{sub b}{sup *} appears nearly degenerate in J = 1/2, 3/2, 5/2. These states have a width from 2-110 MeV, with conservative estimates of uncertainties, except for the one in J = 5/2 which has zero width since it cannot decay into any of the states of the basis chosen. We make generous estimates of the uncertainties and find that within very large margins these states appear bound. (orig.)
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.
Symmetries, conservation laws, and time reversibility for Hamiltonian systems with external forces
Schaft, A.J. van der
1983-01-01
A system theoretic framework is given for the description of Hamiltonian systems with external forces and partial observations of the state. It is shown how symmetries and conservation laws can be defined within this framework. A generalization of Noether's theorem is obtained. Finally a precise def
Many conserved quantities induced by Lie symmetries of a Lagrangian system
Energy Technology Data Exchange (ETDEWEB)
Nucci, M.C., E-mail: nucci@unipg.i [Dipartimento di Matematica e Informatica and INFN Sezione Perugia, Universita di Perugia, 06123 Perugia (Italy)
2011-03-14
Lie symmetries along with either Noether theorem or Jacobi Last Multiplier yield all the conserved quantities that one may seek and even more. We show that three new conserved quantities derived in Jian-Hui Fang, Ming-Jiang Zhang, Wei-Wei Zhang (2010) can be algorithmically obtained by these old methods. Even more than three.
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.
Itoh, K; Sawanaka, H; So, H; Ukita, N
2003-01-01
We present a lattice theory with an exact fermionic symmetry, which mixes the link and the fermionic variables. The staggered fermionic variables may be reconstructed into a Majorana fermion in the continuum limit. The gauge action has a novel structure. Though it is the ordinary plaquette action, two different couplings are assigned in the ``Ichimatsu pattern'' or the checkered pattern. In the naive continuum limit, the fermionic symmetry survives as a continuum (or an $O(a^0)$) symmetry. The transformation of the fermion is proportional to the field strength multiplied by the difference of the two gauge couplings in this limit. This work is an extension of our recently proposed cell model toward the realization of supersymmetric Yang-Mills theory on lattice.
Jiménez-Hoyos, Carlos A; Scuseria, Gustavo E
2013-01-01
Recent work from our research group has demonstrated that symmetry-projected Hartree--Fock (HF) methods provide a compact representation of molecular ground state wavefunctions based on a superposition of non-orthogonal Slater determinants. The symmetry-projected ansatz can account for static correlations in a computationally efficient way. Here we present a variational extension of this methodology applicable to excited states of the same symmetry as the ground state. Benchmark calculations on the C$_2$ dimer with a modest basis set, which allows comparison with full configuration interaction results, indicate that this extension provides a high quality description of the low-lying spectrum for the entire dissociation profile. We apply the same methodology to obtain the full low-lying vertical excitation spectrum of formaldehyde, in good agreement with available theoretical and experimental data, as well as to a challenging model $C_{2v}$ insertion pathway for BeH$_2$. The variational excited state methodolo...
Mishra, H; Mishra, Hiranmaya; Parikh, Jitendra C.
2001-01-01
We discuss in this note simultaneous existence of chiral symmetry breakingand color superconductivity at finite temperature and density in aNambu-Jona-Lasinio type model. The methodology involves an explicitconstruction of a variational ground state and minimisation of thethermodynamic potential. There appears to be a phase at finite densities withboth quark antiquark as well as diquark condensates for the "ground" state.Chiral symmetry breaking phase appear to catalyse the threshold for the diquarkcondensates to appear. We also compute the equation of state in this model.
Symmetry analysis of the Klein-Gordon equation in Bianchi I spacetimes
Paliathanasis, A.; Tsamparlis, M.; Mustafa, M. T.
2015-02-01
In this work we perform the symmetry classification of the Klein-Gordon equation in Bianchi I spacetime. We apply a geometric method which relates the Lie symmetries of the Klein-Gordon equation with the conformal algebra of the underlying geometry. Furthermore, we prove that the Lie symmetries which follow from the conformal algebra are also Noether symmetries for the Klein-Gordon equation. We use these results in order to determine all the potentials in which the Klein-Gordon admits Lie and Noether symmetries. Due to the large number of cases and for easy reference the results are presented in the form of tables. For some of the potentials we use the Lie admitted symmetries to determine the corresponding invariant solution of the Klein-Gordon equation. Finally, we show that the results also solve the problem of classification of Lie/Noether point symmetries of the wave equation in Bianchi I spacetime and can be used for the determination of invariant solutions of the wave equation.
Symmetry analysis of the Klein-Gordon equation in Bianchi I spacetimes
Paliathanasis, A; Mustafa, M T
2014-01-01
In this work we perform the symmetry classification of the Klein Gordon equation in Bianchi I spacetime. We apply a geometric method which relates the Lie symmetries of the Klein Gordon equation with the conformal algebra of the underlying geometry. Furthermore, we prove that the Lie symmetries which follow from the conformal algebra are also and Noether symmetries for the Klein Gordon equation. We use these resutls in order to determine all the potentials in which the Klein Gordon admits Lie and Noether symmetries. Due to the large number of cases and for easy reference the results are presented in the form of tables. For some of the potentials we use the Lie admitted symmetries to determine the corresponding invariant solution of the Klein Gordon equation. Finally, we show that the results also solve the problem of classification of Lie/Noether point symmetries of the wave equation in Bianchi I spacetime and can be used for the determination of invariant solutions of the wave equation.
Time Solutions and Symmetries in Extended Gravity Quantum Cosmology
Directory of Open Access Journals (Sweden)
Capozziello Salvatore
2013-09-01
Full Text Available Minisuperspace models are taken into account searching for Noether symmetries. The existence of conserved quantities gives selection rule to recover classical behaviors in cosmic evolution according to the so called Hartle criterion, that allows to select correlated regions in the configuration space of dynamical variables. We show that such a statement works for general classes of gravity theories. Examples for nonminimally coupled and higher-order models are discussed.
Canonical symmetry properties of the constrained singular generalized mechanical system
Institute of Scientific and Technical Information of China (English)
李爱民; 江金环; 李子平
2003-01-01
Based on generalized Apell-Chetaev constraint conditions and to take the inherent constrains for singular Lagrangian into account, the generalized canonical equations for a general mechanical system with a singular higher-order Lagrangian and subsidiary constrains are formulated. The canonical symmetries in phase space for such a system are studied and Noether theorem and its inversion theorem in the generalized canonical formalism have been established.
Canonical symmetry properties of the constrained singular generalized mechanical system
Institute of Scientific and Technical Information of China (English)
LiAi-Min; JiangJin-Huan; LiZi-Ping
2003-01-01
Based on generalized Apell-Chetaev constraint conditions and to take the inherent constrains for singular Lagrangian into account,the generalized canonical equations for a general mechanical system with a singular higher-order Lagrangian and subsidiary constrains are formulated. The canonical symmetries in phase space for such a system are studied and Noether theorem and its inversion theorem in the generalized canonical formalism have been established.
Emergent symmetry in a thermal pure state path integral
Sasa, Shin-ichi; Yokokura, Yuki
2016-01-01
We study a thermally isolated quantum many-body system with an external control represented by a time-dependent parameter. By formulating a thermal pure state path integral, we derive an effective action for trajectories in a thermodynamic state space, where the entropy appears with its conjugate variable. In particular, when operations are quasi-static, the symmetry for the uniform translation of the conjugate variable emerges in the path integral. This leads to the entropy as a Noether invariant.
Noether-Form Invariance of Nonholonomic Controllable Mechanical Systems in Phase Space
Institute of Scientific and Technical Information of China (English)
XIA Li-Li; LI Yuan-Cheng
2007-01-01
In this paper, we study the Noether-form invariance of nonholonomic mechanical controllable systems in phase space. Equations of motion of the controllable mechanical systems in phase space are presented. The definition and the criterion for this system are presented. A new conserved quantity and the Noether conserved quantity deduced from the Noether-form invariance are obtained. An example is given to illustrate the application of the results.
Curved Spacetimes and Curved Graphene: a status report of the Weyl-symmetry approach
Iorio, Alfredo
2014-01-01
This is a status report about the ongoing work on the realization of quantum field theory on curved graphene spacetimes that uses Weyl symmetry. The programme is actively pursued from many different perspectives. Here we point to what has been done, and to what needs to be done.
Structure of Symmetry Groups via Cartan's Method: Survey of Four Approaches
Directory of Open Access Journals (Sweden)
Oleg I. Morozov
2005-10-01
Full Text Available In this review article we discuss four recent methods for computing Maurer-Cartan structure equations of symmetry groups of differential equations. Examples include solution of the contact equivalence problem for linear hyperbolic equations and finding a contact transformation between the generalized Hunter-Saxton equation and the Euler-Poisson equation.
A Variational Approach to an Inhomogeneous Second-Order Ordinary Differential System
Directory of Open Access Journals (Sweden)
B. Muatjetjeja
2013-01-01
Full Text Available This paper studies the coupled inhomogeneous Lane-Emden system from the Lagrangian formulation point of view. The existence of multiple positive solutions has been discussed in the literature. Here we aim to classify the system with respect to a first-order Lagrangian according to the Noether point symmetries it admits. We then obtain first integrals of the various cases which admit Noether point symmetries.
Lapierre, David; Kochanov, Roman; Kokoouline, Viatcheslav; Tyuterev, Vladimir
2016-01-01
Energies and lifetimes (widths) of vibrational states above the lowest dissociation limit of $^{16}$O$_3$ were determined using a previously-developed efficient approach, which combines hyperspherical coordinates and a complex absorbing potential. The calculations are based on a recently-computed potential energy surface of ozone determined with a spectroscopic accuracy [J. Chem. Phys. {\\bf 139}, 134307 (2013)]. The effect of permutational symmetry on rovibrational dynamics and the density of resonance states in O$_3$ is discussed in detail. Correspondence between quantum numbers appropriate for short- and long-range parts of wave functions of the rovibrational continuum is established. It is shown, by symmetry arguments, that the allowed purely vibrational ($J=0$) levels of $^{16}$O$_3$ and $^{18}$O$_3$, both made of bosons with zero nuclear spin, cannot dissociate on the ground state potential energy surface. Energies and wave functions of bound states of the ozone isotopologue $^{16}$O$_3$ with rotational ...
Multivector field formulation of Hamiltonian field theories: equations and symmetries
Energy Technology Data Exchange (ETDEWEB)
Echeverria-Enriquez, A.; Munoz-Lecanda, M.C.; Roman-Roy, N. [Departamento de Matematica Aplicada y Telematica, Edificio C-3, Campus Norte UPC, Barcelona (Spain)
1999-12-03
We state the intrinsic form of the Hamiltonian equations of first-order classical field theories in three equivalent geometrical ways: using multivector fields, jet fields and connections. Thus, these equations are given in a form similar to that in which the Hamiltonian equations of mechanics are usually given. Then, using multivector fields, we study several aspects of these equations, such as the existence and non-uniqueness of solutions, and the integrability problem. In particular, these problems are analysed for the case of Hamiltonian systems defined in a submanifold of the multimomentum bundle. Furthermore, the existence of first integrals of these Hamiltonian equations is considered, and the relation between Cartan-Noether symmetries and general symmetries of the system is discussed. Noether's theorem is also stated in this context, both the 'classical' version and its generalization to include higher-order Cartan-Noether symmetries. Finally, the equivalence between the Lagrangian and Hamiltonian formalisms is also discussed. (author)
Noether's theorems applications in mechanics and field theory
Sardanashvily, Gennadi
2016-01-01
The book provides a detailed exposition of the calculus of variations on fibre bundles and graded manifolds. It presents applications in such area's as non-relativistic mechanics, gauge theory, gravitation theory and topological field theory with emphasis on energy and energy-momentum conservation laws. Within this general context the first and second Noether theorems are treated in the very general setting of reducible degenerate graded Lagrangian theory.
On the Equivalence of Euler-Lagrange and Noether Equations
Energy Technology Data Exchange (ETDEWEB)
Faliagas, A. C., E-mail: apostol.faliagas@gmail.com [University of Athens, Department of Mathematics (Greece)
2016-03-15
We prove that, under the condition of nontriviality, the Euler-Lagrange and Noether equations are equivalent for a general class of scalar variational problems. Examples are position independent Lagrangians, Lagrangians of p-Laplacian type, and Lagrangians leading to nonlinear Poisson equations. As applications we prove certain propositions concerning the nonlinear Poisson equation and its generalisations, and the equivalence of admissible and inner variations for the systems under consideration.
Noether theorem for Birkhoffian systems on time scales
Song, Chuan-Jing; Zhang, Yi
2015-10-01
Birkhoff equations on time scales and Noether theorem for Birkhoffian system on time scales are studied. First, some necessary knowledge of calculus on time scales are reviewed. Second, Birkhoff equations on time scales are obtained. Third, the conditions for invariance of Pfaff action and conserved quantities are presented under the special infinitesimal transformations and general infinitesimal transformations, respectively. Fourth, some special cases are given. And finally, an example is given to illustrate the method and results.
The Brill-Noether curve and Prym-Tyurin varieties
Ortega, Angela
2012-01-01
We prove that the Jacobian of a general curve C of genus g=2a+1, with g>4, can be realized as a Prym-Tyurin variety for the Brill-Noether curve W^1_{a+2}(C). As a consequence of this result we are able to compute the class of the sum of the secant divisors for the curve C, embedded with a complete linear series g^{a-1}_{3a-2}
Rowlands' Duality Principle: A Generalization of Noether's Theorem?
Karam, Sabah E.
This paper will examine a physical principle that has been used in making valid predictions and generalizes established conservation laws. In a previous paper it was shown how Rowlands' zero-totality condition could be viewed as a generalization of Newton's third law of motion. In this paper it will be argued that Rowlands' Duality Principle is a generalization of Noether's Theorem and that the two principles taken together are truly foundational principles that have tamed Metaphysics.
Anabalón, Andrés; Deruelle, Nathalie; Julié, Félix-Louis
2016-08-01
In this paper we describe 4-dimensional gravity coupled to scalar and Maxwell fields by the Einstein-Katz action, that is, the covariant version of the "Gamma-Gamma -Gamma-Gamma" part of the Hilbert action supplemented by the divergence of a generalized "Katz vector". We consider static solutions of Einstein's equations, parametrized by some integration constants, which describe an ensemble of asymptotically AdS black holes. Instead of the usual Dirichlet boundary conditions, which aim at singling out a specific solution within the ensemble, we impose that the variation of the action vanishes on shell for the broadest possible class of solutions. We will see that, when a long-range scalar "hair" is present, only sub-families of the solutions can obey that criterion. The Katz-Bicak-Lynden-Bell ("KBL") superpotential built on this (generalized) vector will then give straightforwardly the Noether charges associated with the spacetime symmetries (that is, in the static case, the mass). Computing the action on shell, we will see next that the solutions which obey the imposed variational principle, and with Noether charges given by the KBL superpotential, satisfy the Gibbs relation, the Katz vectors playing the role of "counterterms". Finally, we show on the specific example of dyonic black holes that the sub-class selected by our variational principle satisfies the first law of thermodynamics when their mass is defined by the KBL superpotential.
Energy Technology Data Exchange (ETDEWEB)
Anabalón, Andrés [Departamento de Ciencias, Facultad de Artes Liberales y Facultad de Ingeniería y Ciencias,Universidad Adolfo Ibáñez, Viña del Mar (Chile); Deruelle, Nathalie; Julié, Félix-Louis [APC, Université Paris Diderot, CNRS, CEA, Observatoire de Paris,Sorbonne Paris Cité, 10, rue Alice Domon et Léonie Duquet,F-75205 Paris CEDEX 13 (France)
2016-08-08
In this paper we describe 4-dimensional gravity coupled to scalar and Maxwell fields by the Einstein-Katz action, that is, the covariant version of the “Gamma-Gamma − Gamma-Gamma' part of the Hilbert action supplemented by the divergence of a generalized “Katz vector'. We consider static solutions of Einstein’s equations, parametrized by some integration constants, which describe an ensemble of asymptotically AdS black holes. Instead of the usual Dirichlet boundary conditions, which aim at singling out a specific solution within the ensemble, we impose that the variation of the action vanishes on shell for the broadest possible class of solutions. We will see that, when a long-range scalar “hair' is present, only sub-families of the solutions can obey that criterion. The Katz-Bicak-Lynden-Bell (“KBL') superpotential built on this (generalized) vector will then give straightforwardly the Noether charges associated with the spacetime symmetries (that is, in the static case, the mass). Computing the action on shell, we will see next that the solutions which obey the imposed variational principle, and with Noether charges given by the KBL superpotential, satisfy the Gibbs relation, the Katz vectors playing the role of “counterterms'. Finally, we show on the specific example of dyonic black holes that the sub-class selected by our variational principle satisfies the first law of thermodynamics when their mass is defined by the KBL superpotential.
A New Type of Conserved Quantity of Mei Symmetry for Lagrange Systems
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
A new type of conserved quantity, which is induced from the Mei symmetry of Lagrange systems, is studied.The conditions for that the new type of conserved quantity exists and the form of the new type of conserved quantity are obtained. An illustrated example is given. The Noether conserved quantity induced from the Mei symmetry of Lagrange systems is a special case of the new type of conserved quantity given in this paper.
Isospin-symmetry-breaking effects in A∼70 nuclei within beyond-mean-field approach
Energy Technology Data Exchange (ETDEWEB)
Petrovici, A.; Andrei, O. [National Institute for Physics and Nuclear Engineering, R-077125 Bucharest (Romania)
2015-02-24
Particular isospin-symmetry-breaking probes including Coulomb energy differences (CED), mirror energy differences (MED), and triplet energy differences (TED) manifest anomalies in the A∼70 isovector triplets of nuclei. The structure of proton-rich nuclei in the A∼70 mass region suggests shape coexistence and competition between pairing correlations in different channels. Recent results concerning the interplay between isospin-mixing and shape-coexistence effects on exotic phenomena in A∼70 nuclei obtained within the beyond-mean-field complex Excited Vampir variational model with symmetry projection before variation using a realistic effective interaction in a relatively large model space are presented. Excited Vampir predictions concerning the Gamow-Teller β decay to the odd-odd N=Z {sup 66}As and {sup 70}Br nuclei correlated with the pair structure analysis in the T=1 and T=0 channel of the involved wave functions are discussed.
Noether Current of the Surface Term of Einstein-Hilbert Action, Virasoro Algebra, and Entropy
Directory of Open Access Journals (Sweden)
Bibhas Ranjan Majhi
2013-01-01
Full Text Available A derivation of Noether current from the surface term of Einstein-Hilbert action is given. We show that the corresponding charge, calculated on the horizon, is related to the Bekenstein-Hawking entropy. Also using the charge, the same entropy is found based on the Virasoro algebra and Cardy formula approach. In this approach, the relevant diffeomorphisms are found by imposing a very simple physical argument: diffeomorphisms keep the horizon structure invariant. This complements similar earlier results (Majhi and Padmanabhan (2012 (arXiv:1204.1422 obtained from York-Gibbons-Hawking surface term. Finally we discuss the technical simplicities and improvements over the earlier attempts and also various important physical implications.
Einstein's Equations for Spin 2 Mass 0 from Noether's Converse Hilbertian Assertion
Pitts, J. Brian
2016-11-01
An overlap between the general relativist and particle physicist views of Einstein gravity is uncovered. Noether's 1918 paper developed Hilbert's and Klein's reflections on the conservation laws. Energy-momentum is just a term proportional to the field equations and a 'curl' term with identically zero divergence. Noether proved a converse "Hilbertian assertion": such "improper" conservation laws imply a generally covariant action.
Invariants of broken discrete symmetries
Kalozoumis, P; Diakonos, F K; Schmelcher, P
2014-01-01
The parity and Bloch theorems are generalized to the case of broken global symmetry. Local inversion or translation symmetries are shown to yield invariant currents that characterize wave propagation. These currents map the wave function from an arbitrary spatial domain to any symmetry-related domain. Our approach addresses any combination of local symmetries, thus applying in particular to acoustic, optical and matter waves. Nonvanishing values of the invariant currents provide a systematic pathway to the breaking of discrete global symmetries.
Extended Galilean symmetries of non-relativistic strings
Batlle, Carles; Gomis, Joaquim; Not, Daniel
2017-02-01
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.
From physics to biology by extending criticality and symmetry breakings.
Longo, G; Montévil, M
2011-08-01
Symmetries play a major role in physics, in particular since the work by E. Noether and H. Weyl in the first half of last century. Herein, we briefly review their role by recalling how symmetry changes allow to conceptually move from classical to relativistic and quantum physics. We then introduce our ongoing theoretical analysis in biology and show that symmetries play a radically different role in this discipline, when compared to those in current physics. By this comparison, we stress that symmetries must be understood in relation to conservation and stability properties, as represented in the theories. We posit that the dynamics of biological organisms, in their various levels of organization, are not "just" processes, but permanent (extended, in our terminology) critical transitions and, thus, symmetry changes. Within the limits of a relative structural stability (or interval of viability), variability is at the core of these transitions.
Extended Galilean symmetries of non-relativistic strings
Batlle, Carles; Not, Daniel
2016-01-01
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.
The origin of order in random matrices with symmetries
Johnson, Calvin W
2012-01-01
From Noether's theorem we know symmetries lead to conservation laws. What is left to nature is the ordering of conserved quantities; for example, the quantum numbers of the ground state. In physical systems the ground state is generally associated with `low' quantum numbers and symmetric, low-dimensional irreps, but there is no \\textit{a priori} reason to expect this. By constructing random matrices with nontrivial point-group symmetries, I find the ground state is always dominated by extremal low-dimensional irreps. Going further, I suggest this explains the dominance of J=0 g.s. even for random two-body interactions.
Energy Technology Data Exchange (ETDEWEB)
Krishna, S., E-mail: skrishna.bhu@gmail.com [Physics Department, Centre of Advanced Studies, Banaras Hindu University (BHU), Varanasi-221 005 (India); Shukla, A., E-mail: ashukla038@gmail.com [Physics Department, Centre of Advanced Studies, Banaras Hindu University (BHU), Varanasi-221 005 (India); Malik, R.P., E-mail: rpmalik1995@gmail.com [Physics Department, Centre of Advanced Studies, Banaras Hindu University (BHU), Varanasi-221 005 (India); DST-CIMS, Faculty of Science, BHU-Varanasi-221 005 (India)
2014-12-15
Using the supersymmetric (SUSY) invariant restrictions on the (anti-)chiral supervariables, we derive the off-shell nilpotent symmetries of the general one (0+1)-dimensional N=2 SUSY quantum mechanical (QM) model which is considered on a (1, 2)-dimensional supermanifold (parametrized by a bosonic variable t and a pair of Grassmannian variables θ and θ-bar with θ{sup 2}=(θ-bar){sup 2}=0,θ(θ-bar)+(θ-bar)θ=0). We provide the geometrical meanings to the two SUSY transformations of our present theory which are valid for any arbitrary type of superpotential. We express the conserved charges and Lagrangian of the theory in terms of the supervariables (that are obtained after the application of SUSY invariant restrictions) and provide the geometrical interpretation for the nilpotency property and SUSY invariance of the Lagrangian for the general N=2 SUSY quantum theory. We also comment on the mathematical interpretation of the above symmetry transformations. - Highlights: • A novel method has been proposed for the derivation of N=2 SUSY transformations. • General N=2 SUSY quantum mechanical (QM) model with a general superpotential, is considered. • The above SUSY QM model is generalized onto a (1, 2)-dimensional supermanifold. • SUSY invariant restrictions are imposed on the (anti-)chiral supervariables. • Geometrical meaning of the nilpotency property is provided.
Dense baryonic matter in the hidden local symmetry approach: Half-skyrmions and nucleon mass
Ma, Yong-Liang; Harada, Masayasu; Lee, Hyun Kyu; Oh, Yongseok; Park, Byung-Yoon; Rho, Mannque
2013-07-01
Hadron properties in dense medium are treated in a unified way in a skyrmion model constructed with an effective Lagrangian, in which the ρ and ω vector mesons are introduced as hidden gauge bosons, valid up to O(p4) terms in chiral expansion including the homogeneous Wess-Zumino terms. All the low energy constants of the Lagrangian—apart from the pion decay constant and the vector meson mass—are fixed by the master formula derived from the relation between the five-dimensional holographic QCD and the four-dimensional hidden local symmetry Lagrangian. This Lagrangian allows one to pin down the density n1/2 at which the skyrmions in medium fractionize into half-skyrmions, bringing in a drastic change in the equation of state of dense baryonic matter. We find that the U(1) field that figures in the Chern-Simons term in the five-dimensional holographic QCD action or equivalently the ω field in the homogeneous Wess-Zumino term in the dimensionally reduced hidden local symmetry action plays a crucial role in the half-skyrmion phase. The importance of the ω degree of freedom may be connected to what happens in the instanton structure of elementary baryon noticed in holographic QCD. The most striking and intriguing in what is found in the model is that the pion decay constant that smoothly drops with increasing density in the skyrmion phase stops decreasing at n1/2 and remains nearly constant in the half-skyrmion phase. In accordance with the large Nc consideration, the baryon mass also stays nonscaling in the half-skyrmion phase. This feature which is reminiscent of the parity-doublet baryon model with a chirally invariant mass m0 is supported by the nuclear effective field theory with the parameters of the Lagrangian scaling modified at the skyrmion-half-skyrmion phase transition. It also matches with one-loop renormalization group analysis based on hidden local symmetry. A link between a nonvanishing m0 and the origin of nucleon mass distinctive from
Three-dimensional organic Dirac-line materials due to nonsymmorphic symmetry: A data mining approach
Geilhufe, R. Matthias; Bouhon, Adrien; Borysov, Stanislav S.; Balatsky, Alexander V.
2017-01-01
A data mining study of electronic Kohn-Sham band structures was performed to identify Dirac materials within the Organic Materials Database. Out of that, the three-dimensional organic crystal 5,6-bis(trifluoromethyl)-2-methoxy-1 H -1,3-diazepine was found to host different Dirac-line nodes within the band structure. From a group theoretical analysis, it is possible to distinguish between Dirac-line nodes occurring due to twofold degenerate energy levels protected by the monoclinic crystalline symmetry and twofold degenerate accidental crossings protected by the topology of the electronic band structure. The obtained results can be generalized to all materials having the space group P 21/c (No. 14, C2h 5) by introducing three distinct topological classes.
Quantum Local Symmetry of the D-Dimensional Non-Linear Sigma Model: A Functional Approach
Directory of Open Access Journals (Sweden)
Andrea Quadri
2014-04-01
Full Text Available We summarize recent progress on the symmetric subtraction of the Non-Linear Sigma Model in D dimensions, based on the validity of a certain Local Functional Equation (LFE encoding the invariance of the SU(2 Haar measure under local left transformations. The deformation of the classical non-linearly realized symmetry at the quantum level is analyzed by cohomological tools. It is shown that all the divergences of the one-particle irreducible (1-PI amplitudes (both on-shell and off-shell can be classified according to the solutions of the LFE. Applications to the non-linearly realized Yang-Mills theory and to the electroweak theory, which is directly relevant to the model-independent analysis of LHC data, are briefly addressed.
Noether's Theorem and its complement in many-particle systems
Smilga, Walter
2016-01-01
Noether's Theorem has gained outstanding importance in theoretical particle physics, because it leads to strong conservation laws, such as the conservation of momentum and of angular momentum. Closely related to this theorem, but unnoticed so far, is a law that requires the exchange of momentum between two particles that are described by an irreducible two-particle representation of the Poincare group. The exchange of momentum determines an interaction. On closer inspection, this interaction is identified as the electromagnetic interaction. This sheds new light on the particle interactions described by the Standard Model and, in particular, on the perturbation algorithm of quantum electrodynamics.
The unknown sister of Noether's theorem
Energy Technology Data Exchange (ETDEWEB)
Smilga, Walter
2016-07-01
Noether's theorem has gained outstanding importance in theoretical particle physics, because it leads to strong conservation laws, such as the conservation of momentum and of angular momentum. Closely related to this theorem is another law that has an opposite effect: it requires the exchange of momentum between two particles that are described by an irreducible two-particle representation of the Poincare group. Exchange of momentum determines an interaction. On closer inspection, this interaction is uniquely identified as the electromagnetic interaction. This finding sheds new light on the phenomenon of particle interaction in general and, in particular, on the perturbation algorithm of quantum electrodynamics.
Symmetries in atmospheric sciences
Bihlo, Alexander
2009-01-01
Selected applications of symmetry methods in the atmospheric sciences are reviewed briefly. In particular, focus is put on the utilisation of the classical Lie symmetry approach to derive classes of exact solutions from atmospheric models. This is illustrated with the barotropic vorticity equation. Moreover, the possibility for construction of partially-invariant solutions is discussed for this model. A further point is a discussion of using symmetries for relating different classes of differential equations. This is illustrated with the spherical and the potential vorticity equation. Finally, discrete symmetries are used to derive the minimal finite-mode version of the vorticity equation first discussed by E. Lorenz (1960) in a sound mathematical fashion.
Institute of Scientific and Technical Information of China (English)
丁金凤; 金世欣; 张毅
2016-01-01
The fractional Noether symmetries and fractional conserved quantities for Hamilton system with time delay based on Caputo derivatives are discussed.The fractional Hamilton canonical equations of the corresconding system with time delay are established base upon the fractional Hamilton principle of the Hamilton systems with time delay.Then,the fractional Noether symmetries of the Hamilton system with time delay are obtained,which based on the invariance of the fractional Hamilton action with time delay under the infinitesimal transformations of group.Finally,fractional Noether theorems with time delay of the Hamilton system are established.At the end,one example is given to illustrate the application of the results.%提出并讨论了Caputo导数定义下的含时滞的Hamilton系统的分数阶Noether对称性与守恒量。根据含时滞的Hamilton系统的分数阶Hamilton原理，建立了相应的含时滞的分数阶Hamilton 正则方程；依据分数阶Hamilton作用量在无限小变换下的不变性，得到了含时滞的Hamilton系统的分数阶Noether对称性；最后，建立了系统的含时滞的分数阶Noether理论，并举例说明结果的应用。
Symmetry breaking in non conservative systems
Martínez-Pérez, N E
2016-01-01
We apply Noether's theorem to show how the invariances of conservative systems are broken for nonconservative systems, in the variational formulation of Galley. This formulation considers a conservative action, extended by the inclusion of a time reversed sector and a nonconservative generalized potential. We assume that this potential is invariant under the symmetries of the initial conservative system. The breaking occurs because the time reversed sector requires inverse symmetry transformations, under which the nonconservative potential is not invariant. The resulting violation of the conservation laws is consistent with the equations of motion. We generalize this formulation for fermionic and sypersymmetric systems. In the case of a supersymmetric oscillator, the effect of damping is that the bosonic and fermionic components become different frequencies. Considering that initially the nonconservative action is invariant under supersymmetry, and that the breaking is associated to an instability, this resul...
Superfield Approach To Nilpotent Symmetries For QED With A Single Restriction On Supermanifold
Malik, R P
2005-01-01
We derive together the exact local, covariant, continuous and off-shell nilpotent Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry transformations for the U(1) gauge field (A_\\mu), the (anti-)ghost fields ((\\bar C)C) and the Dirac fields (\\psi, \\bar\\psi) of the Lagrangian density of a four (3 + 1)-dimensional QED by exploiting a single restriction on the six (4 + 2)-dimensional supermanifold. A set of four even spacetime coordinates x^\\mu (\\mu = 0, 1, 2, 3) and two odd Grassmannian variables \\theta and \\bar\\theta parametrize this six dimensional supermanifold. The new gauge invariant restriction on the above supermanifold, due to the augmented superfield formalism, owes its origin to the (super) covariant derivatives and their intimate relation with the (super) 2-form curvatures (\\tilde F^{(2)})F^{(2)} constructed from the (super) 1-form gauge connections (\\tilde A^{(1)})A^{(1)}. The results obtained separately by exploiting (i) the horizontality condition, and (ii) one of its consistent extensions, ar...
Symmetry breaking: A heuristic approach to chaotic scattering in many dimensions
Benet, L.; Broch, J.; Merlo, O.; Seligman, T. H.
2005-03-01
As the theory of chaotic scattering in high-dimensional systems is poorly developed, it is very difficult to determine initial conditions for which interesting scattering events, such as long delay times, occur. We propose to use symmetry breaking as a way to gain the insight necessary to determine low-dimensional subspaces of initial conditions in which we can find such events easily. We study numerically the planar scattering off a disk moving on an elliptic Kepler orbit, as a simplified model of the elliptic restricted three-body problem. When the motion of the disk is circular, the system has an integral of motion, the Jacobi integral, which is no longer conserved for nonvanishing eccentricity. In the latter case, the system has an effective five-dimensional phase space and is therefore not amenable for study with the usual methods. Using the symmetric problem as a starting point we define an appropriate two-dimensional subspace of initial conditions by fixing some coordinates. This subspace proves to be useful to define scattering experiments where the rich and nontrivial dynamics of the problem is illustrated. We consider in particular trajectories which take very long before escaping or are trapped by consecutive collisions with the disk.
Brill-Noether loci for divisors on irregular varieties
Lopes, Margarida Mendes; Pirola, Gian Pietro
2011-01-01
For a projective variety X, a line bundle L on X and r a natural number we consider the r-th Brill-Noether locus W^r(L,X):={\\eta\\in Pic^0(X)|h^0(L+\\eta)\\geq r+1}: we describe its natural scheme structure and compute the Zariski tangent space. If X is a smooth surface of maximal Albanese dimension and C is a curve on X, we define a Brill-Noether number \\rho(C, r) and we prove, under some mild additional assumptions, that if \\rho(C, r) is non negative then W^r(C,X) is nonempty of dimension bigger or equal to \\rho(C,r). As an application, we derive lower bounds for h^0(K_D) for a divisor D that moves linearly on a smooth projective variety X of maximal Albanese dimension and inequalities for the numerical invariants of curves that do not move linearly on a surface of maximal Albanese dimension.
Unified Symmetry of Nonholonomic System of Non-Chetaev's Type with Variable Mass in Event Space
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
The unified symmetry of a nonholonomic system of non-Chetaev's type with variable mass in event space is studied. The differential equations of motion of the system are given. Then the definition and tie criterion of the unified symmetry for the system are obtained. Finally, the Noether conserved quantity, the Hojman conserved quantity, and a new type of conserved quantity are deduced horn the united symmetry of the nonholonomic system of non-Chetaev's type with variable mass in event space at one time. An example is given to illustrate the application of the results.
Unified Symmetry of Nonholonomic System of Non-Chetaev's Type in Event Space
Institute of Scientific and Technical Information of China (English)
HOU Qi-Bao; LI Yuan-Cheng; WANG Jing; XIA Li-Li
2007-01-01
The unified symmetry of a nonholonomic system of non-Chetaev's type in event space under infinitesimal transformations of group is studied.Firstly,the differential equations of motion of the system are given.Secondly,the definition and the criterion of the unified symmetry for the system are obtained.Thirdly,a new conserved quantity,besides the Noether conserved quantity and the Hojman conserved quantity,is deduced from the unified symmetry of a nonholonomic system of non-Chetaev's type.Finally,an example is given to illustrate the application of the result.
Invariants of broken discrete symmetries
Kalozoumis, P.; Morfonios, C.; Diakonos, F. K.; Schmelcher, P.
2014-01-01
The parity and Bloch theorems are generalized to the case of broken global symmetry. Local inversion or translation symmetries are shown to yield invariant currents that characterize wave propagation. These currents map the wave function from an arbitrary spatial domain to any symmetry-related domain. Our approach addresses any combination of local symmetries, thus applying in particular to acoustic, optical and matter waves. Nonvanishing values of the invariant currents provide a systematic ...
On Noether's Theorem for the Invariant of the Time-Dependent Harmonic Oscillator
Abe, Sumiyoshi; Itto, Yuichi; Matsunaga, Mamoru
2009-01-01
The time-dependent oscillator describing parametric oscillation, the concept of invariant and Noether's theorem are important issues in physics education. Here, it is shown how they can be interconnected in a simple and unified manner.
On Noether's theorem for the invariant of the time-dependent harmonic oscillator
Energy Technology Data Exchange (ETDEWEB)
Abe, Sumiyoshi; Itto, Yuichi; Matsunaga, Mamoru [Department of Physical Engineering, Mie University, Mie 514-8507 (Japan)
2009-11-15
The time-dependent oscillator describing parametric oscillation, the concept of invariant and Noether's theorem are important issues in physics education. Here, it is shown how they can be interconnected in a simple and unified manner.
Weakly Noether Symmetry of a Lagrange System%Lagrange系统的弱Noether对称性
Institute of Scientific and Technical Information of China (English)
梅凤翔; 水小平
2006-01-01
研究Lagrange系统的一类对称性,称为弱Noether对称性.给出弱Noether对称性的判据,证明由这种对称性也可以求得Noether守恒量.弱Noether对称性比Noether对称性有更广泛的应用.
Lagrange-Noether method for solving second-order differential equations
Institute of Scientific and Technical Information of China (English)
Wu Hui-Bin; Wu Run-Heng
2009-01-01
The purpose of this paper is to provide a new method called the Lagrange-Noether method for solving second-order differential equations. The method is,firstly,to write the second-order differential equations completely or partially in the form of Lagrange equations,and secondly,to obtain the integrals of the equations by using the Noether theory of the Lagrange system. An example is given to illustrate the application of the result.
NOETHER'S THEOREM OF NONHOLONOMIC SYSTEMS OF NON-CHETAEV'S TYPE WITH UNILATERAL CONSTRAINTS
Institute of Scientific and Technical Information of China (English)
LI YUAN-CHENG; ZHANG YI; LIANG JING-HUI; MEI FENG-XIANG
2001-01-01
In this paper, we present Noether's theorem and its inverse theorem for nonholonomic systems of non-Chetaev's type with unilateral constraints. We present first the principle of Jourdain for the system and, on the basis of the invariance of the differential variational principle under the infinitesimal transformations of groups, we have established Noether's theory for the above systems. An example is given to illustrate the application of the result.
Logarithmic correction to BH entropy as Noether charge
Aros, R; Montecinos, A
2010-01-01
We consider the role of the type-A trace anomaly in static black hole solutions to semiclassical Einstein equation in four dimensions. Via Wald's Noether charge formalism, we compute the contribution to the entropy coming from the anomaly induced effective action and unveil a logarithmic correction to the Bekenstein-Hawking area law. The corrected entropy is given by a seemingly universal formula involving the coefficient of the type-A trace anomaly, the Euler characteristic of the horizon and the value at the horizon of the solution to the uniformization problem for Q-curvature. Two instances are examined in detail: Schwarzschild and a four-dimensional massless topological black hole. We also find agreement with the logarithmic correction due to one-loop contribution of conformal fields in the Schwarzschild background.
Anomalous effective action, Noether current, Virasoro algebra and Horizon entropy
Energy Technology Data Exchange (ETDEWEB)
Majhi, Bibhas Ranjan [IUCAA, Ganeshkhind, Pune University Campus, Post Bag 4, Pune (India); Hebrew University of Jerusalem, Racah Institute of Physics, Jerusalem (Israel); Chakraborty, Sumanta [IUCAA, Ganeshkhind, Pune University Campus, Post Bag 4, Pune (India)
2014-05-15
Several investigations show that in a very small length scale there exist corrections to the entropy of black hole horizon. Due to fluctuations of the background metric and the external fields the action incorporates corrections. In the low energy regime, the one-loop effective action in four dimensions leads to trace anomaly. We start from the Noether current corresponding to the Einstein-Hilbert plus the one-loop effective action to calculate the charge for the diffeomorphisms which preserve the Killing horizon structure. Then a bracket for the charges is calculated. We show that the Fourier modes of the bracket are exactly similar to the Virasoro algebra. Then using the Cardy formula the entropy is evaluated. Finally, the explicit terms of the entropy expression is calculated for a classical background. It turns out that the usual expression for the entropy; i.e. the Bekenstein-Hawking form, is not modified. (orig.)
Special determinants in higher-rank Brill-Noether theory
Osserman, Brian
2011-01-01
Continuing our previous study of modified expected dimensions for rank-2 Brill-Noether loci with prescribed special determinants, we introduce a general framework which applies a priori for arbitrary rank, and use it to prove modified expected dimension bounds in several new cases, applying both to rank 2 and to higher rank. The main tool is the introduction of generalized alternating Grassmannians, which are the loci inside Grassmannians corresponding to subspaces which are simultaneously isotropic for a family of multilinear alternating forms on the ambient vector space. In the case of rank 2 with 2-dimensional spaces of sections, we adapt arguments due to Teixidor i Bigas to show that our new modified expected dimensions are in fact sharp.
Nilpotent Symmetries of a Specific N = 2 Supersymmetric Quantum Mechanical Model: A Novel Approach
Krishna, S; Malik, R P
2013-01-01
We derive the on-shell nilpotent supersymmetric (SUSY) transformations for the N = 2 SUSY quantum mechanical model of a one (0 + 1)-dimensional free particle by exploiting the SUSY invariant restrictions on the (anti-)chiral supervariables of the SUSY theory that is defined on a (1, 2)-dimensional supermanifold (parametrized by a bosonic variable t and a pair of Grassmannian variables \\theta and \\bar \\theta with \\theta^2 = \\bar \\theta^2 = 0,\\theta \\bar \\theta + \\bar \\theta \\theta = 0). Within the framework of our novel approach, we express the Lagrangian and conserved SUSY charges in terms of the (anti-)chiral supervariables to demonstrate the SUSY invariance of the Lagrangian and nilpotency of the conserved charges in a simple manner. Our approach has the potential to be generalized to the description of other N = 2 SUSY quantum mechanical systems with physically interesting potential functions.
Qiu, Wu; Yuan, Jing; Ukwatta, Eranga; Sun, Yue; Rajchl, Martin; Fenster, Aaron
2014-04-01
We propose a novel global optimization-based approach to segmentation of 3-D prostate transrectal ultrasound (TRUS) and T2 weighted magnetic resonance (MR) images, enforcing inherent axial symmetry of prostate shapes to simultaneously adjust a series of 2-D slice-wise segmentations in a "global" 3-D sense. We show that the introduced challenging combinatorial optimization problem can be solved globally and exactly by means of convex relaxation. In this regard, we propose a novel coherent continuous max-flow model (CCMFM), which derives a new and efficient duality-based algorithm, leading to a GPU-based implementation to achieve high computational speeds. Experiments with 25 3-D TRUS images and 30 3-D T2w MR images from our dataset, and 50 3-D T2w MR images from a public dataset, demonstrate that the proposed approach can segment a 3-D prostate TRUS/MR image within 5-6 s including 4-5 s for initialization, yielding a mean Dice similarity coefficient of 93.2%±2.0% for 3-D TRUS images and 88.5%±3.5% for 3-D MR images. The proposed method also yields relatively low intra- and inter-observer variability introduced by user manual initialization, suggesting a high reproducibility, independent of observers.
Behera, Amiya; Wang, Anbo
2016-06-01
This paper offers a simple, practical strategy to implement wavelength modulation spectroscopy (WMS) with a tunable diode laser. It eliminates the need to pre-characterize the laser intensity parameters or make any design changes to a conventional WMS system. Consequently, sensitivity and signal strength remain the same as what can be obtained from a traditional WMS setup at low modulation amplitude. Like previously proposed calibration-free approaches, this new method also yields an absolute absorption line shape function. To recover residual amplitude modulation (RAM) contributions present in the first and second harmonic signals of WMS, we exploited their even or odd symmetric nature. We then used these isolated RAM signals to estimate the absolute line shape function, thus removing the impact of optical intensity fluctuations on measurement. We have also discussed uncertainties and noises associated with the estimated absolute line shape function and the applicability of this new method to detect several gases in the near infrared region. We used measurements of the 1650.96 nm absorption line for 1% and 8% methane concentration in the 60-100 kPa pressure range to validate the efficacy of this new RAM recovery technique and demonstrated a calibration-free system. Because this approach has minimal dependency on diode laser operating conditions, it is more robust and suitable for harsh industrial environments.
Ground-state properties of even and odd Magnesium isotopes in a symmetry-conserving approach
Directory of Open Access Journals (Sweden)
Marta Borrajo
2017-01-01
Full Text Available We present a self-consistent theory for odd nuclei with exact blocking and particle number and angular momentum projection. The demanding treatment of the pairing correlations in a variation-after-projection approach as well as the explicit consideration of the triaxial deformation parameters in a projection after variation method, together with the use of the finite-range density-dependent Gogny force, provides an excellent tool for the description of odd–even and even–even nuclei. We apply the theory to the Magnesium isotopic chain and obtain an outstanding description of the ground-state properties, in particular binding energies, odd–even mass differences, mass radii and electromagnetic moments among others.
Ground-state properties of even and odd Magnesium isotopes in a symmetry-conserving approach
Borrajo, Marta
2016-01-01
We present a self-consistent theory for odd nuclei with exact blocking and particle number and angular momentum projection. The demanding treatment of the pairing correlations in a variation-after-projection approach as well as the explicit consideration of the triaxial deformation parameters in a projection after variation method, together with the use of the finite-range density-dependent Gogny force, provides an excellent tool for the description of odd-even and even-even nuclei. We apply the theory to the Magnesium isotopic chain and obtain an outstanding description of the ground-state properties, in particular binding energies, odd-even mass differences, mass radii and electromagnetic moments among others.
Ground-state properties of even and odd Magnesium isotopes in a symmetry-conserving approach
Borrajo, Marta; Egido, J. Luis
2017-01-01
We present a self-consistent theory for odd nuclei with exact blocking and particle number and angular momentum projection. The demanding treatment of the pairing correlations in a variation-after-projection approach as well as the explicit consideration of the triaxial deformation parameters in a projection after variation method, together with the use of the finite-range density-dependent Gogny force, provides an excellent tool for the description of odd-even and even-even nuclei. We apply the theory to the Magnesium isotopic chain and obtain an outstanding description of the ground-state properties, in particular binding energies, odd-even mass differences, mass radii and electromagnetic moments among others.
Lie symmetries and conservation laws for the time fractional Derrida-Lebowitz-Speer-Spohn equation
Rui, Wenjuan; Zhang, Xiangzhi
2016-05-01
This paper investigates the invariance properties of the time fractional Derrida-Lebowitz-Speer-Spohn (FDLSS) equation with Riemann-Liouville derivative. By using the Lie group analysis method of fractional differential equations, we derive Lie symmetries for the FDLSS equation. In a particular case of scaling transformations, we transform the FDLSS equation into a nonlinear ordinary fractional differential equation. Conservation laws for this equation are obtained with the aid of the new conservation theorem and the fractional generalization of the Noether operators.
Symmetries and conservation laws for the wave equations of scalar statistical optics
Energy Technology Data Exchange (ETDEWEB)
Mitofsky, A M; Carney, P S [Department of Electrical and Computer Engineering and the Beckman Institute for Science and Technology, University of Illinois at Urbana-Champaign, 405 N Mathews Avenue, Urbana, IL 61801 (United States)
2008-10-17
The Lie method and Noether's theorem are applied to the double wave equations for the correlation functions of statistical optics. Generalizations of the deterministic conservation laws are found and seen to correspond to the usual laws in the deterministic limit. The statistically stationary wave equations are shown to contain fewer symmetries than for the nonstationary case, so the corresponding conservation laws differ from the conservation laws of the nonstationary, two-time, wave equations.
Symmetry Analysis and Conservation Laws for the Hunter-Saxton Equation
Institute of Scientific and Technical Information of China (English)
Mehdi Nadjafikhah; Fatemeh Ahangari
2013-01-01
In this paper,the problem of determining the most generalLie point symmetries group and conservation laws of a well known nonlinear hyperbolic PDE in mathematical physics called the Hunter-Saxton equation (HSE) is analyzed.By applying the basic Lie symmetry method for the HSE,the classical Lie point symmetry operators are obtained.Also,the algebraic structure of the Lie algebra of symmetries is discussed and an optimal system of one-dimensional subalgebras of the HSE symmetry algebra which creates the preliminary classification of group invariant solutions is constructed.Particularly,the Lie invariants as well as similarity reduced equations corresponding to infinitesimal symmetries are obtained.Mainly,the conservation laws of the HSE are computed via three different methods including Boyer's generalization of Noether's theorem,first homotopy method and second homotopy method.
Energy Technology Data Exchange (ETDEWEB)
Strocchi, F. [Scuola Normale Superiore, Classe di Scienze, Pisa (Italy)
2008-07-01
This new edition of Prof. Strocchi's well received primer on rigorous aspects of symmetry breaking presents a more detailed and thorough discussion of the mechanism of symmetry breaking in classical field theory in relation with the Noether theorem. Moreover, the link between symmetry breaking without massless Goldstone bosons in Coulomb systems and in gauge theories is made more explicit in terms of the delocalized Coulomb dynamics. Furthermore, the chapter on the Higgs mechanism has been significantly expanded with a non-perturbative treatment of the Higgs phenomenon, at the basis of the standard model of particle physics, in the local and in the Coulomb gauges. Last but not least, a subject index has been added and a number of misprints have been corrected. From the reviews of the first edition: The notion of spontaneous symmetry breaking has proven extremely valuable, the problem is that most derivations are perturbative and heuristic. Yet mathematically precise versions do exist, but are not widely known. It is precisely the aim of his book to correct this unbalance. - It is remarkable to see how much material can actually be presented in a rigorous way (incidentally, many of the results presented are due to Strocchi himself), yet this is largely ignored, the original heuristic derivations being, as a rule, more popular. - At each step he strongly emphasizes the physical meaning and motivation of the various notions introduced, a book that fills a conspicuous gap in the literature, and does it rather well. It could also be a good basis for a graduate course in mathematical physics. It can be recommended to physicists as well and, of course, for physics/mathematics libraries. J.-P. Antoine, Physicalia 28/2, 2006 Strocchi's main emphasis is on the fact that the loss of symmetric behaviour requires both the non-symmetric ground states and the infinite extension of the system. It is written in a pleasant style at a level suitable for graduate students in
Energy Technology Data Exchange (ETDEWEB)
Barbosa, Gabriel Duarte; Ferreira, Renata Rosa; Thibes, Ronaldo [Universidade Estadual do Sudoeste da Bahia (UESB), BA (Brazil)
2011-07-01
Full text: We consider a classical particle minimally coupled to an external electromagnetic field, in both non-relativistic and relativistic regimes. The coupling is constructed via the electromagnetic potential which is assumed to satisfy the classical Maxwell equations. We review Noether's theorem at classical level associating infinitesimal symmetries to conserved quantities. The fundamental space-time symmetries are investigated considering a non-relativistic action, a relativistic action in a particular reference frame and an explicitly Lorentz invariant Lagrangian. We work out in detail the corresponding conserved quantities for each case. The well-known Noether's theorem establishes a connection between continuous infinitesimal symmetries of the action and conserved quantities - given a particular action, for each infinitesimal symmetry there exists an explicit conserved quantity. In particular, a single particle subjected to an external electromagnetic field gives rise to an action which may enjoy space-time symmetries. For the non-relativistic particle, we analyze translations in space and time and spatial rotations, calculating the conserved quantities - linear momentum, energy and angular momentum. The relativistic particle enjoys space-time Lorentz symmetry. Thus we check the six symmetries of the homogeneous Lorentz group, corresponding to three spatial rotations and three boosts, and the four space-time translations extending to the non-homogeneous Lorentz group (Poincare group). We consider two distinct actions describing the relativistic particle minimally coupled to an external electromagnetic field - the first one describes the particle in a particular frame of reference enforcing the relativistic generalization of Newton's second law with the Lorentz force while the second one is obtained from a Lorentz scalar Lagrangian. In all cases the conserved quantities are explicitly calculated via Noether's theorem. (author)
Canonical charges and asymptotic symmetry algebra of conformal gravity
Irakleidou, Maria; Preis, Florian
2014-01-01
We study canonical conformal gravity in four dimensions and construct the gauge generators and the associated charges. Using slightly generalized boundary conditions compared to those in \\cite{Grumiller:2013mxa} we find that the charges associated with space-time diffeomorphisms are finite and conserved in time. They are also shown to agree with the Noether charges found in \\cite{Grumiller:2013mxa}. However, there exists no charge associated with Weyl transformations. Consequently the asymptotic symmetry algebra is isomorphic to the Lie algebra of the boundary condition preserving diffeomorphisms. For illustrative purposes we apply the results to the Mannheim--Kazanas--Riegert solution of conformal gravity.
On systems having Poincaré and Galileo symmetry
Energy Technology Data Exchange (ETDEWEB)
Holland, Peter, E-mail: peter.holland@gtc.ox.ac.uk
2014-12-15
Using the wave equation in d≥1 space dimensions it is illustrated how dynamical equations may be simultaneously Poincaré and Galileo covariant with respect to different sets of independent variables. This provides a method to obtain dynamics-dependent representations of the kinematical symmetries. When the field is a displacement function both symmetries have a physical interpretation. For d=1 the Lorentz structure is utilized to reveal hitherto unnoticed features of the non-relativistic Chaplygin gas including a relativistic structure with a limiting case that exhibits the Carroll group, and field-dependent symmetries and associated Noether charges. The Lorentz transformations of the potentials naturally associated with the Chaplygin system are given. These results prompt the search for further symmetries and it is shown that the Chaplygin equations support a nonlinear superposition principle. A known spacetime mixing symmetry is shown to decompose into label-time and superposition symmetries. It is shown that a quantum mechanical system in a stationary state behaves as a Chaplygin gas. The extension to d>1 is used to illustrate how the physical significance of the dual symmetries is contingent on the context by showing that Maxwell’s equations exhibit an exact Galileo covariant formulation where Lorentz and gauge transformations are represented by field-dependent symmetries. A natural conceptual and formal framework is provided by the Lagrangian and Eulerian pictures of continuum mechanics.
Invariants of Broken Discrete Symmetries
Kalozoumis, P. A.; Morfonios, C.; Diakonos, F. K.; Schmelcher, P.
2014-08-01
The parity and Bloch theorems are generalized to the case of broken global symmetry. Local inversion or translation symmetries in one dimension are shown to yield invariant currents that characterize wave propagation. These currents map the wave function from an arbitrary spatial domain to any symmetry-related domain. Our approach addresses any combination of local symmetries, thus applying, in particular, to acoustic, optical, and matter waves. Nonvanishing values of the invariant currents provide a systematic pathway to the breaking of discrete global symmetries.
Symmetries and singularities of the Szekeres system
Energy Technology Data Exchange (ETDEWEB)
Paliathanasis, Andronikos, E-mail: anpaliat@phys.uoa.gr [Instituto de Ciencias Físicas y Matemáticas, Universidad Austral de Chile, Valdivia (Chile); Institute of Systems Science, Durban University of Technology, POB 1334, Durban 4000 (South Africa); Leach, P.G.L., E-mail: leach.peter@ucy.ac.cy [Department of Mathematics and Institute of Systems Science, Research and Postgraduate Support, Durban University of Technology, POB 1334, Durban 4000 (South Africa); School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Private Bag X54001, Durban 4000 (South Africa)
2017-04-18
Highlights: • Lagrangian formalism of the Szekeres system. • Symmetries and conservation laws for the silent universe. • Comparison of stability analysis of special solutions with the Laurent expansion provided by the singularity analysis. - Abstract: The Szekeres system is studied with two methods for the determination of conservation laws. Specifically we apply the theory of group invariant transformations and the method of singularity analysis. We show that the Szekeres system admits a Lagrangian and the conservation laws that we find can be derived by the application of Noether's theorem. The stability for the special solutions of the Szekeres system is studied and it is related with the Left or Right Painlevé Series which describes the expansions.
Voisin, Claire
1999-01-01
This is the English translation of Professor Voisin's book reflecting the discovery of the mirror symmetry phenomenon. The first chapter is devoted to the geometry of Calabi-Yau manifolds, and the second describes, as motivation, the ideas from quantum field theory that led to the discovery of mirror symmetry. The other chapters deal with more specialized aspects of the subject: the work of Candelas, de la Ossa, Greene, and Parkes, based on the fact that under the mirror symmetry hypothesis, the variation of Hodge structure of a Calabi-Yau threefold determines the Gromov-Witten invariants of its mirror; Batyrev's construction, which exhibits the mirror symmetry phenomenon between hypersurfaces of toric Fano varieties, after a combinatorial classification of the latter; the mathematical construction of the Gromov-Witten potential, and the proof of its crucial property (that it satisfies the WDVV equation), which makes it possible to construct a flat connection underlying a variation of Hodge structure in the ...
Häring, Reto Andreas
1993-01-01
The representations of the observable algebra of a low dimensional quantum field theory form the objects of a braided tensor category. The search for gauge symmetry in the theory amounts to finding an algebra which has the same representation category. In this paper we try to establish that every quantum field theory satisfying some basic axioms posseses a weak quasi Hopf algebra as gauge symmetry. The first step is to construct a functor from the representation category to the category of finite dimensional vector spaces. Given such a functor we can use a generalized reconstruction theorem to find the symmetry algebra. It is shown how this symmetry algebra is used to build a gauge covariant field algebra and we investigate the question why this generality is necessary.
Verbovetsky, A.V.; Kersten, P.H.M.; Krasil'shchik, I.
2005-01-01
Using new methods of analysis of integrable systems,based on a general geometric approach to nonlinear PDE,we discuss the Dispersionless Boussinesq Equation, which is equivalent to the Benney-Lax equation,being a system of equations of hydrodynamical type. The results include: a description of local
Directory of Open Access Journals (Sweden)
Ristić Vladimir M.
2014-01-01
Full Text Available The theories that combine two different approaches in dealing with interacting objects, for instance, treating electromagnetic laser field classically, and the interacting atom as a quantum object, have some ambiguities and, as such, they should be labeled as “mixed”. From the Noether's Theorem Corollary, which we proved earlier, about the conservation laws of energy, momentum and angular momentum in mixed theories, follows that the aforementioned theories do not support the law of angular momentum/spin conservation (to be precise, the obtained result does not imply that the law of conservation of angular momentum and spin is not valid generally, but rather that mixed theories can produce the results which might violate this law. In present paper, an additional explanation following our Corollary is given to why the calculation of the stopping power in the fully quantized theory gives better results than those that were obtained in mixed theories, which further confirms the predictions of our Corollary. [Projekat Ministarstva nauke Republike Srbije, br. 171021: The experimental and theoretical research in radiation physics and radioecology
Institute of Scientific and Technical Information of China (English)
Hou Qi-Bao; Li Yuan-Cheng; Wang Jing; Xia Li-Li
2007-01-01
This paper studies the unified symmetry of a nonholonomic system of non-Chetaev type with unilateral constraints in event space under infinitesimal transformations of group. Firstly, it gives the differential equations of motion of the system. Secondly, it obtains the definition and the criterion of the unified symmetry for the system. Thirdly, a new conserved quantity, besides the Noether conserved quantity and the Hojman conserved quantity, is deduced from the unified symmetry of a nonholonomic system of non-Chetaev type with unilateral constraints. Finally, an example is given to illustrate the application of the results.
BRILL-NOETHER MATRIX FOR RANK TWO VECTOR BUNDLES
Institute of Scientific and Technical Information of China (English)
谭小江
2002-01-01
Let X be an arbitrary smooth irreducible complex projective curve, E → X a rank two vector bundle generated by its sections. The author first represents E as a triple {D1,D2, f},where D1, D2 are two effective divisors with d = deg(D1) + deg(D2), and f ∈ Ho (X, [D1] |D2)is a collection of polynomials. E is the extension of [D2] by [D1] which is determined by f. By using f and the Brill-Noether matrix of D1 + D2, the author constructs a 29 × d matrix WE whose zero space gives Im{Ho(X, [D1]) → Ho(X, [D1] |D1 )} Im{Ho(X, E) → Ho(X, [D2]) →H0(X, [D2] |D2)}. From this and Ho(X, E) = Ho(X, [D1]) Im{Ho(X, E) → Ho(X, [D2])},it is got in particular that dimHo(X, E) = deg(E) - rank(WE) + 2.
Velocity-dependent symmetries and conserved quantities of the constrained dynamical systems
Institute of Scientific and Technical Information of China (English)
Fu Jing-Li; Chen Li-Qun; Yang Xiao-Dong
2004-01-01
In this paper, we have exterided the theorem of the velocity-dependent symmetries to nonholonomic dynamical systems. Based on the infinitesimal transformations with respect to the coordinates, we establish the determining equations and restrictive equation of the velocity-dependent system before the structure equation is obtained. The direct and the inverse issues of the velocity-dependent symmetries for the nonholonomic dynamical system is studied and the non-Noether type conserved quantity is found as the result. Finally, we give an example to illustrate the conclusion.
Noether's theorem in non-local field theories
Krivoruchenko, M I
2016-01-01
Explicit expressions are constructed for a locally conserved vector current associated with a continuous internal symmetry and for energy-momentum and angular-momentum density tensors associated with the Poincar\\'e group in field theories with higher-order derivatives and in non-local field theories. An example of non-local charged scalar field equations with broken C and CPT symmetries is considered. For this case, we find simple analytical expressions for the conserved currents.
Anabalón, Andrés; Julié, Félix
2016-01-01
In this paper we describe 4-dimensional gravity coupled to scalar and Maxwell fields by the Einstein-Katz action, that is, the covariant version of the "Gamma-Gamma $-$ Gamma-Gamma" part of the Hilbert action supplemented by the divergence of a generalized "Katz vector". We consider static solutions of Einstein's equations, parametrized by some integration constants, which describe an ensemble of asymptotically AdS black holes. Instead of the usual Dirichlet boundary conditions, which aim at singling out a specific solution within the ensemble, we impose that the variation of the action vanishes on shell for the broadest possible class of solutions. We will see that, when a long-range scalar "hair" is present, only sub-families of the solutions can obey that criterion. The Katz superpotential built on his (generalized) vector will then give straightforwardly the Noether charges associated with the spacetime symmetries (that is, in the static case, the mass). Computing the action on shell, we will see next tha...
Off-shell Noether current and conserved charge in Horndeski theory
Directory of Open Access Journals (Sweden)
Jun-Jin Peng
2016-01-01
Full Text Available We derive the off-shell Noether current and potential in the context of Horndeski theory, which is the most general scalar–tensor theory with a Lagrangian containing derivatives up to second order while yielding at most to second-order equations of motion in four dimensions. Then the formulation of conserved charges is proposed on basis of the off-shell Noether potential and the surface term got from the variation of the Lagrangian. As an application, we calculate the conserved charges of black holes in a scalar–tensor theory with non-minimal coupling between derivatives of the scalar field and the Einstein tensor.
Noether theorem for nonholonomic nonconservative mechanical systems in phase space on time scales
Zu, Qi-hang; Zhu, Jian-qing
2016-08-01
The paper focuses on studying the Noether theorem for nonholonomic nonconservative mechanical systems in phase space on time scales. First, the Hamilton equations of nonholonomic nonconservative systems on time scales are established, which is based on the Lagrange equations for nonholonomic systems on time scales. Then, based upon the quasi-invariance of Hamilton action of systems under the infinitesimal transformations with respect to the time and generalized coordinate on time scale, the Noether identity and the conserved quantity of nonholonomic nonconservative systems on time scales are obtained. Finally, an example is presented to illustrate the application of the results.
Off-shell Noether current and conserved charge in Horndeski theory
Energy Technology Data Exchange (ETDEWEB)
Peng, Jun-Jin, E-mail: pengjjph@163.com [School of Physics and Electronic Science, Guizhou Normal University, Guiyang, Guizhou 550001 (China); Institute of Technical Physics, SEEE, Wuhan Textile University, Wuhan, Hubei 430073 (China)
2016-01-10
We derive the off-shell Noether current and potential in the context of Horndeski theory, which is the most general scalar–tensor theory with a Lagrangian containing derivatives up to second order while yielding at most to second-order equations of motion in four dimensions. Then the formulation of conserved charges is proposed on basis of the off-shell Noether potential and the surface term got from the variation of the Lagrangian. As an application, we calculate the conserved charges of black holes in a scalar–tensor theory with non-minimal coupling between derivatives of the scalar field and the Einstein tensor.
Brill-Noether locus of rank 1 and degree g-1 on a nodal curve
Coelho, Juliana
2011-01-01
In this paper we consider the Brill-Noether locus $W_{\\underline d}(C)$ of line bundles of multidegree $\\underline d$ of total degree $g-1$ having a nonzero section on a nodal reducible curve $C$ of genus $g\\geq2$. We give an explicit description of the irreducible components of $W_{\\underline d}(C)$ for a semistable multidegre $\\underline d$. As a consequence we show that, if two semistable multidegrees of total degre $g-1$ on a curve with no rational components differ by a twister, then the respective Brill-Noether loci have isomorphic components.
The Noether Theorems Invariance and Conservation Laws in the 20th Century
Kosmann-Schwarzbach, Yvette
2011-01-01
In 1915 and 1916 Emmy Noether was asked by Felix Klein and David Hilbert to assist them in understanding issues involved in any attempt to formulate a general theory of relativity, in particular the new ideas of Einstein. She was consulted particularly over the difficult issue of the form a law of conservation of energy could take in the new theory, and she succeeded brilliantly, finding two deep theorems. But between 1916 and 1950, the theorem was poorly understood and Noether's name disappeared almost entirely. People like Klein and Einstein did little more then mention her name in the vario
Johnson, Adam R.
2013-01-01
A molecular orbital (MO) diagram, especially its frontier orbitals, explains the bonding and reactivity for a chemical compound. It is therefore important for students to learn how to construct one. The traditional methods used to derive these diagrams rely on linear algebra techniques to combine ligand orbitals into symmetry-adapted linear…
Attanucci, Frank J.; Losse, John
2008-01-01
In a first calculus course, it is not unusual for students to encounter the theorems which state: If f is an even (odd) differentiable function, then its derivative is odd (even). In our paper, we prove some theorems which show how the symmetry of a continuous function f with respect to (i) the vertical line: x = a or (ii) with respect to the…
Symmetry 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.
Flavour from accidental symmetries
Energy Technology Data Exchange (ETDEWEB)
Ferretti, Luca [SISSA/ISAS and INFN, I-34013 Trieste (Italy); King, Stephen F. [School of Physics and Astronomy, University of Southampton, Southampton, SO17 1BJ (United Kingdom); Romanino, Andrea [SISSA/ISAS and INFN, I-34013 Trieste (Italy)
2006-11-15
We consider a new approach to fermion masses and mixings in which no special 'horizontal' dynamics is invoked to account for the hierarchical pattern of charged fermion masses and for the peculiar features of neutrino masses. The hierarchy follows from the vertical, family-independent structure of the model, in particular from the breaking pattern of the Pati-Salam group. The lightness of the first two fermion families can be related to two family symmetries emerging in this context as accidental symmetries.
Arzano, Michele; Kowalski-Glikman, Jerzy
2016-09-01
We construct discrete symmetry transformations for deformed relativistic kinematics based on group valued momenta. We focus on the specific example of κ-deformations of the Poincaré algebra with associated momenta living on (a sub-manifold of) de Sitter space. Our approach relies on the description of quantum states constructed from deformed kinematics and the observable charges associated with them. The results we present provide the first step towards the analysis of experimental bounds on the deformation parameter κ to be derived via precision measurements of discrete symmetries and CPT.
Hernández-Pastora, J L; Ruiz, E
1998-01-01
The FHP algorithm allows to obtain the relativistic multipole moments of a vacuum stationary axisymmetric solution in terms of coefficients which appear in the expansion of its Ernst's potential on the symmetry axis. First of all, we will use this result in order to determine, at a certain approximation degree, the Ernst's potential on the symmetry axis of the metric whose only multipole moments are mass and angular momentum. By using Sibgatullin's method we analyse a series of exacts solutions with the afore mentioned multipole characteristic. Besides, we present an approximate solution whose Ernst's potential is introduced as a power series of a dimensionless parameter. The calculation of its multipole moments allows us to understand the existing differences between both approximations to the proposed pure multipole solution.
Oberlack, Martin; Nold, Andreas; Sanjon, Cedric Wilfried; Wang, Yongqi; Hau, Jan
2016-11-01
Classical hydrodynamic stability theory for laminar shear flows, no matter if considering long-term stability or transient growth, is based on the normal-mode ansatz, or, in other words, on an exponential function in space (stream-wise direction) and time. Recently, it became clear that the normal mode ansatz and the resulting Orr-Sommerfeld equation is based on essentially three fundamental symmetries of the linearized Euler and Navier-Stokes equations: translation in space and time and scaling of the dependent variable. Further, Kelvin-mode of linear shear flows seemed to be an exception in this context as it admits a fourth symmetry resulting in the classical Kelvin mode which is rather different from normal-mode. However, very recently it was discovered that most of the classical canonical shear flows such as linear shear, Couette, plane and round Poiseuille, Taylor-Couette, Lamb-Ossen vortex or asymptotic suction boundary layer admit more symmetries. This, in turn, led to new problem specific non-modal ansatz functions. In contrast to the exponential growth rate in time of the modal-ansatz, the new non-modal ansatz functions usually lead to an algebraic growth or decay rate, while for the asymptotic suction boundary layer a double-exponential growth or decay is observed.
Variational derivatives in locally Lagrangian field theories and Noether-Bessel-Hagen currents
Cattafi, Francesco; Palese, Marcella; Winterroth, Ekkehart
2016-01-01
The variational Lie derivative of classes of forms in the Krupka's variational sequence is defined as a variational Cartan formula at any degree, in particular for degrees lesser than the dimension of the basis manifold. As an example of application, we determine the condition for a Noether-Bessel-H
Reply to 'Noether's theorem once again'
Energy Technology Data Exchange (ETDEWEB)
Marinho, Rubens M Jr [Departamento de Fisica, Instituto Tecnologico de Aeronautica (Brazil)], E-mail: marinho@ita.br
2009-09-15
This reply answers the issues raised in the comment on my paper (Marinho Jr 2007 Eur. J. Phys. 28 37-43), obtains the Laplace-Runge-Lenz vector (Goldstein 2002 Classical Mechanics 3rd edn (Reading, MA: Addison-Wesley)) using Noether's theorem and includes a Maple program used to derive the results. (letters and comments)
Brill--Noether loci of stable rank--two vector bundles on a general curve
Ciliberto, Ciro
2011-01-01
In this note we give an easy proof of the existence of generically smooth components of the expected dimension of certain Brill--Noether loci of stable rank 2 vector bundles on a curve with general moduli, with related applications to Hilbert scheme of scrolls.
Directory of Open Access Journals (Sweden)
Kirstin Peters
2010-11-01
Full Text Available A well-known result by Palamidessi tells us that πmix (the π-calculus with mixed choice is more expressive than πsep (its subset with only separate choice. The proof of this result argues with their different expressive power concerning leader election in symmetric networks. Later on, Gorla offered an arguably simpler proof that, instead of leader election in symmetric networks, employed the reducibility of incestual processes (mixed choices that include both enabled senders and receivers for the same channel when running two copies in parallel. In both proofs, the role of breaking (initial symmetries is more or less apparent. In this paper, we shed more light on this role by re-proving the above result - based on a proper formalization of what it means to break symmetries without referring to another layer of the distinguishing problem domain of leader election. Both Palamidessi and Gorla rephrased their results by stating that there is no uniform and reasonable encoding from πmix into πsep. We indicate how the respective proofs can be adapted and exhibit the consequences of varying notions of uniformity and reasonableness. In each case, the ability to break initial symmetries turns out to be essential.
Spontaneously Broken Asymptotic Symmetries and an Effective Action for Horizon Dynamics
Eling, Christopher
2016-01-01
Asymptotic spacetime symmetries have been conjectured to play an important role in quantum gravity. In this paper we study the breaking of asymptotic symmetries associated with a null horizon boundary. In two-dimensions, these symmetries are reparametrizations of the time parameter on the horizon. We show how this horizon reparametrization symmetry is explicitly and spontaneously broken in dilaton gravity and construct an effective action for these pseudo-Goldstone modes using the on-shell gravitational action for a null boundary. The variation of this action yields the horizon constraint equation. This action is invariant under a 2 parameter subgroup of $SL(2)$ transformations, whose Noether charges we interpret via the membrane paradigm. We place these results in the context of recent work on the near $AdS_2$/ near $CFT_1$ correspondence. In this setting the horizon action characterizes the infrared regime near the horizon and has a hydrodynamical sigma model form. We also discuss our construction in Genera...
Ahangari, Fatemeh
2017-01-01
Scalar-field cosmology can be regarded as one of the significant fields of research in recent years. This paper is dedicated to a thorough investigation of the symmetries and conservation laws of the geodesic equations associated to a specific exact cosmological solution of a scalar-field potential which was originally motivated by six-dimensional Einstein-Maxwell theory. The mentioned string inspired Friedmann-Robertson-Lamai ^tre-Walker (FRLW) solution is one of the noteworthy solutions of Einstein field equations. For this purpose, first of all the Christoffel symbols and the corresponding system of geodesic equations are computed and then the associated Lie symmetries are totally analyzed. Moreover, the algebraic structure of the Lie algebra of local symmetries is briefly investigated and a complete classification of the symmetry subalgebras is presented. Besides by applying the resulted symmetry operators the invariant solutions of the system of geodesic equations are discussed. In addition, the Noether symmetries and the Killing vector fields of the geodesic Lagrangian are determined and the corresponding optimal system of one-dimensional subalgebras is constructed. Mainly, an entire set of local conservation laws is computed for our analyzed scalar-field cosmological solution. For this purpose, two distinct procedures are applied: the celebrated Noether's theorem and the direct method which is fundamentally based on a systematic application of Euler differential operators which annihilate any divergence expression identically.
Mishra, H
2001-01-01
We discuss in this note simultaneous existence of chiral symmetry breaking and color superconductivity at finite temperature and density in a Nambu-Jona-Lasinio type model. The methodology involves an explicit construction of a variational ground state and minimisation of the thermodynamic potential. There exist nontrivial solutions to the gap equations at finite densities with both quark-antiquark as well as diquark condensates for the 'ground' state. However, such a phase is thermodynamically unstable with the pressure being negative in this region. We also compute the equation of state, and obtain the structure of the phase diagram in the model.
Neutrino mass, mixing and discrete symmetries
Smirnov, Alexei Y
2013-01-01
Status of the discrete symmetry approach to explanation of the lepton masses and mixing is summarized in view of recent experimental results, in particular, establishing relatively large 1-3 mixing. The lepton mixing can originate from breaking of discrete flavor symmetry $G_f$ to different residual symmetries $G_{\\ell}$ and $G_\
Mudie, M H; Winzeler-Mercay, U; Radwan, S; Lee, L
2002-09-01
To determine (1) the most effective of three treatment approaches to retrain seated weight distribution long-term after stroke and (2) whether improvements could be generalized to weight distribution in standing. Inpatient rehabilitation unit. Forty asymmetrical acute stroke subjects were randomly allocated to one of four groups in this pilot study. Changes in weight distribution were compared between the 10 subjects of each of three treatment groups (task-specific reach, Bobath, or Balance Performance Monitor [BPM] feedback training) and a no specific treatment control group. One week of measurement only was followed by two weeks of daily training sessions with the treatment to which the subject was randomly allocated. Measurements were performed using the BPM daily before treatment sessions, two weeks after cessation of treatment and 12 weeks post study. Weight distribution was calculated in terms of mean balance (percentage of total body weight) or the mean of 300 balance points over a 30-s data run. In the short term, the Bobath approach was the most effective treatment for retraining sitting symmetry after stroke (p = 0.004). Training with the BPM and no training were also significant (p = 0.038 and p = 0.035 respectively) and task-specific reach training failed to reach significance (p = 0.26). At 12 weeks post study 83% of the BPM training group, 38% of the task-specific reach group, 29% of the Bobath group and 0% of the untrained group were found to be distributing their weight to both sides. Some generalization of symmetry training in sitting to standing was noted in the BPM training group which appeared to persist long term. Results should be treated with caution due to the small group sizes. However, these preliminary findings suggest that it might be possible to restore postural symmetry in sitting in the early stages of rehabilitation with therapy that focuses on creating an awareness of body position.
Symmetry-improved 2PI approach to the Goldstone-boson IR problem of the SM effective potential
Pilaftsis, Apostolos; Teresi, Daniele
2016-05-01
The effective potential of the Standard Model (SM), from three loop order and higher, suffers from infrared (IR) divergences arising from quantum effects due to massless would-be Goldstone bosons associated with the longitudinal polarizations of the W± and Z bosons. Such IR pathologies also hinder accurate evaluation of the two-loop threshold corrections to electroweak quantities, such as the vacuum expectation value of the Higgs field. However, these divergences are an artifact of perturbation theory, and therefore need to be consistently resummed in order to obtain an IR-safe effective potential. The so-called Two-Particle-Irreducible (2PI) effective action provides a rigorous framework to consistently perform such resummations, without the need to resort to ad hoc subtractions or running into the risk of over-counting contributions. By considering the recently proposed symmetry-improved 2PI formalism, we address the problem of the Goldstone-boson IR divergences of the SM effective potential in the gaugeless limit of the theory. In the same limit, we evaluate the IR-safe symmetry-improved 2PI effective potential, after taking into account quantum loops of chiral fermions, as well as the renormalization of spurious custodially breaking effects triggered by fermionic Yukawa interactions. Finally, we compare our results with those obtained with other methods presented in the literature.
Symmetry-improved 2PI approach to the Goldstone-boson IR problem of the SM effective potential
Directory of Open Access Journals (Sweden)
Apostolos Pilaftsis
2016-05-01
Full Text Available The effective potential of the Standard Model (SM, from three loop order and higher, suffers from infrared (IR divergences arising from quantum effects due to massless would-be Goldstone bosons associated with the longitudinal polarizations of the W± and Z bosons. Such IR pathologies also hinder accurate evaluation of the two-loop threshold corrections to electroweak quantities, such as the vacuum expectation value of the Higgs field. However, these divergences are an artifact of perturbation theory, and therefore need to be consistently resummed in order to obtain an IR-safe effective potential. The so-called Two-Particle-Irreducible (2PI effective action provides a rigorous framework to consistently perform such resummations, without the need to resort to ad hoc subtractions or running into the risk of over-counting contributions. By considering the recently proposed symmetry-improved 2PI formalism, we address the problem of the Goldstone-boson IR divergences of the SM effective potential in the gaugeless limit of the theory. In the same limit, we evaluate the IR-safe symmetry-improved 2PI effective potential, after taking into account quantum loops of chiral fermions, as well as the renormalization of spurious custodially breaking effects triggered by fermionic Yukawa interactions. Finally, we compare our results with those obtained with other methods presented in the literature.
Horizontal Symmetry: Bottom Up and Top Down
Lam, C S
2011-01-01
A group-theoretical connection between horizontal symmetry $\\G$ and fermion mixing is established, and applied to neutrino mixing. The group-theoretical approach is consistent with a dynamical theory based on $U(1)\\times \\G$, but the dynamical theory can be used to pick out the most stable mixing that purely group-theoretical considerations cannot. A symmetry common to leptons and quarks is also discussed. This higher symmetry picks $A_4$ over $S_4$ to be the preferred symmetry for leptons.
Peters, Kirstin
2010-01-01
A well-known result by Palamidessi tells us that {\\pi}mix (the {\\pi}-calculus with mixed choice) is more expressive than {\\pi}sep (its subset with only separate choice). The proof of this result argues with their different expressive power concerning leader election in symmetric networks. Later on, Gorla of- fered an arguably simpler proof that, instead of leader election in symmetric networks, employed the reducibility of "incestual" processes (mixed choices that include both enabled senders and receivers for the same channel) when running two copies in parallel. In both proofs, the role of breaking (ini- tial) symmetries is more or less apparent. In this paper, we shed more light on this role by re-proving the above result-based on a proper formalization of what it means to break symmetries-without referring to another layer of the distinguishing problem domain of leader election. Both Palamidessi and Gorla rephrased their results by stating that there is no uniform and reason- able encoding from {\\pi}mix i...
Peters, Kirstin; 10.4204/EPTCS.41.10
2010-01-01
A well-known result by Palamidessi tells us that \\pimix (the \\pi-calculus with mixed choice) is more expressive than \\pisep (its subset with only separate choice). The proof of this result argues with their different expressive power concerning leader election in symmetric networks. Later on, Gorla offered an arguably simpler proof that, instead of leader election in symmetric networks, employed the reducibility of incestual processes (mixed choices that include both enabled senders and receivers for the same channel) when running two copies in parallel. In both proofs, the role of breaking (initial) symmetries is more or less apparent. In this paper, we shed more light on this role by re-proving the above result - based on a proper formalization of what it means to break symmetries without referring to another layer of the distinguishing problem domain of leader election. Both Palamidessi and Gorla rephrased their results by stating that there is no uniform and reasonable encoding from \\pimix into \\pisep. We...
Asymptotic Symmetries from finite boxes
Andrade, Tomas
2015-01-01
It is natural to regulate an infinite-sized system by imposing a boundary condition at finite distance, placing the system in a "box." This breaks symmetries, though the breaking is small when the box is large. One should thus be able to obtain the asymptotic symmetries of the infinite system by studying regulated systems. We provide concrete examples in the context of Einstein-Hilbert gravity (with negative or zero cosmological constant) by showing in 4 or more dimensions how the Anti-de Sitter and Poincar\\'e asymptotic symmetries can be extracted from gravity in a spherical box with Dirichlet boundary conditions. In 2+1 dimensions we obtain the full double-Virasoro algebra of asymptotic symmetries for AdS$_3$ and, correspondingly, the full Bondi-Metzner-Sachs (BMS) algebra for asymptotically flat space. In higher dimensions, a related approach may continue to be useful for constructing a good asymptotically flat phase space with BMS asymptotic symmetries.
Discrete symmetries in the MSSM
Energy Technology Data Exchange (ETDEWEB)
Schieren, Roland
2010-12-02
The use of discrete symmetries, especially abelian ones, in physics beyond the standard model of particle physics is discussed. A method is developed how a general, abelian, discrete symmetry can be obtained via spontaneous symmetry breaking. In addition, anomalies are treated in the path integral approach with special attention to anomaly cancellation via the Green-Schwarz mechanism. All this is applied to the minimal supersymmetric standard model. A unique Z{sup R}{sub 4} symmetry is discovered which solves the {mu}-problem as well as problems with proton decay and allows to embed the standard model gauge group into a simple group, i.e. the Z{sup R}{sub 4} is compatible with grand unification. Also the flavor problem in the context of minimal flavor violation is addressed. Finally, a string theory model is presented which exhibits the mentioned Z{sup R}{sub 4} symmetry and other desirable features. (orig.)
Shape analysis with subspace symmetries
Berner, Alexander
2011-04-01
We address the problem of partial symmetry detection, i.e., the identification of building blocks a complex shape is composed of. Previous techniques identify parts that relate to each other by simple rigid mappings, similarity transforms, or, more recently, intrinsic isometries. Our approach generalizes the notion of partial symmetries to more general deformations. We introduce subspace symmetries whereby we characterize similarity by requiring the set of symmetric parts to form a low dimensional shape space. We present an algorithm to discover subspace symmetries based on detecting linearly correlated correspondences among graphs of invariant features. We evaluate our technique on various data sets. We show that for models with pronounced surface features, subspace symmetries can be found fully automatically. For complicated cases, a small amount of user input is used to resolve ambiguities. Our technique computes dense correspondences that can subsequently be used in various applications, such as model repair and denoising. © 2010 The Author(s).
Pramanik, Souvik; Ghosh, Subir
2013-10-01
We have developed a unified scheme for studying noncommutative algebras based on generalized uncertainty principle (GUP) and Snyder form in a relativistically covariant point particle Lagrangian (or symplectic) framework. Even though the GUP-based algebra and Snyder algebra are very distinct, the more involved latter algebra emerges from an approximation of the Lagrangian model of the former algebra. Deformed Poincaré generators for the systems that keep space-time symmetries of the relativistic particle models have been studied thoroughly. From a purely constrained dynamical analysis perspective the models studied here are very rich and provide insights on how to consistently construct approximate models from the exact ones when nonlinear constraints are present in the system. We also study dynamics of the GUP particle in presence of external electromagnetic field.
3-dimensional organic Dirac-line material due to non-symmorphic symmetry: a data mining approach
Geilhufe, R Matthias; Borysov, Stanislav S; Balatsky, Alexander V
2016-01-01
A data mining study of electronic Kohn-Sham band structures was performed to identify Dirac materials within the Organic Materials Database (OMDB). Out of that, the 3-dimensional organic crystal 5,6-Bis(trifluoromethyl)-2-methoxy-1H-1,3-diazepine was found to host different Dirac line-nodes within the band structure. From a group theoretical analysis, it is possible to distinguish between Dirac line-nodes occurring due to 2-fold degenerate energy levels protected by the monoclinic crystalline symmetry and 2-fold degenerate accidental crossings protected by the topology of the electronic band structure. The obtained results can be generalized to all materials having the space group $P2_1/c$ ($\\#14$, $C^5_{2h}$) by introducing three distinct topological classes.
Directory of Open Access Journals (Sweden)
Morteza Ordobazari
2013-11-01
Full Text Available Please cite this article as: Ordobazari M, Naqavi Al-Hosseini AA, Zafarmand H. A novel approach for craniofacial symmetry evaluation: Using the midsagittal Reference line drawn from “Crista Gali” with NHP technique. Novel Biomed 2013;1(2:48-53.Background and objective: The purpose of this study was the determination of midsagittal reference line (MSL for craniofacial asymmetry assessment by drawing a line from Crista gali parallel to the true vertical line in PA cephalometry, using Natural Head Position (NHP technique.Method and Materials: 60 Iranian subjects within the age range of 9-13 years old were selected for this prospective study. Patients referred for orthodontic treatment and ghad no supernumerary or missing teeth, no skeletal anomaly, or any history of orthodontic and jaw surgery with normal occlusion. Posteroanterior cephalometric radiographs (PA Ceph were taken of all subjects with NHP technique. The midsagittal line was also traced parallel to the hanging chain from Crista gali. True horizontal line (THL and true vertical line (TVL were also traced from Crista gali (Cg. Using Cartesian system based upon Cg point (0~0, the craniofacial symmetry was assessed with linear, angular and proportional measurements in PA cephalogam, related to TVL and THL lines, for 10 bilateral (R&L anatomical landmarks. The mean differences of the above measurements in left and right sides were analyzed by T- test.Results: The proportional ratios for all left and right measurements were not statistically significant. This was true for both vertical and horizontal distances. The significant level for MSL drawn from Cg as referred to ANS (0±0.255 and Me points (0.007±0.527 was 0.002 and 0.004, respectively.Conclusion: In posteroanterior cephalometry radiographs taken with NHP method, the MSL drawn from Crista gali is reproducible and reliable up to 96% of the times for facial symmetry diagnosis.
Directory of Open Access Journals (Sweden)
Sandra Beaufaÿs
2016-04-01
Full Text Available Dieses Buch bietet eine sorgfältige Analyse der Arbeitsweise Emmy Noethers und ihrer Wirkung auf die zeitgenössische mathematische Disziplin bis zur Herausbildung der modernen Algebra. Mechthild Koreuber zeigt, auf welche Weise sich von der Mathematikerin ausgehend eine wissenschaftliche Schule bildete, obgleich sie nie die institutionellen Voraussetzungen dazu aufwies. Insbesondere werden die sozialen Voraussetzungen und Wirkungsweisen in den Blick genommen, die bei der Verfertigung mathematischer Forschung als auch bei der Bildung von und dem Bruch mit Denktraditionen bedeutsam sind.
Reta, Daniel; Moreira, Ibério de P R; Illas, Francesc
2016-07-12
In the most general case of three electrons in three symmetry unrelated centers with Ŝ1 = Ŝ2 = Ŝ3 = 1/2 localized magnetic moments, the low energy spectrum consists of one quartet (Q) and two doublet (D1, D2) pure spin states. The energy splitting between these spin states can be described with the well-known Heisenberg-Dirac-Van Vleck (HDVV) model spin Hamiltonian, and their corresponding energy expressions are expressed in terms of the three different two-body magnetic coupling constants J12, J23, and J13. However, the values of all three magnetic coupling constants cannot be extracted using the calculated energy of the three spin-adapted states since only two linearly independent energy differences between pure spin states exist. This problem has been recently investigated by Reta et al. (J. Chem. Theory Comput. 2015, 11, 3650), resulting in an alternative proposal to the original Noodleman's broken symmetry mapping approach. In the present work, this proposal is validated by means of ab initio effective Hamiltonian theory, which allows a direct extraction of all three J values from the one-to-one correspondence between the matrix elements of both effective and HDVV Hamiltonian. The effective Hamiltonian matrix representation has been constructed from configuration interaction wave functions for the three spin states obtained for two model systems showing a different degree of delocalization of the unpaired electrons. These encompass a trinuclear Cu(II) complex and a π-conjugated purely organic triradical.
Spectral theorem and partial symmetries
Energy Technology Data Exchange (ETDEWEB)
Gozdz, A. [University of Maria Curie-Sklodowska, Department of Mathematical Physics, Institute of Physics (Poland); Gozdz, M. [University of Maria Curie-Sklodowska, Department of Complex Systems and Neurodynamics, Institute of Informatics (Poland)
2012-10-15
A novel method of the decompositon of a quantum system's Hamiltonian is presented. In this approach the criterion of the decomposition is determined by the symmetries possessed by the sub-Hamiltonians. This procedure is rather generic and independent of the actual global symmetry, or the lack of it, of the full Hamilton operator. A detailed investigation of the time evolution of the various sub-Hamiltonians, therefore the change in time of the symmetry of the physical object, is presented for the case of a vibrator-plus-rotor model. Analytical results are illustrated by direct numerical calculations.
Petrov, Alexander N
2013-01-01
A construction of conservation laws and conserved quantities for perturbations in arbitrary metric theories of gravity is developed. In an arbitrary field theory, with the use of incorporating an auxiliary metric into the initial Lagrangian covariantized Noether identities are carried out. Identically conserved currents with corresponding superpotentials are united into a family. Such a generalized formalism of the covariantized identities gives a natural basis for constructing conserved quantities for perturbations. A new family of conserved currents and correspondent superpotentials for perturbations on arbitrary curved backgrounds in metric theories is suggested. The conserved quantities are both of pure canonical Noether and of Belinfante corrected types. To test the results each of the superpotentials of the family is applied to calculate the mass of the Schwarzschild-anti-de Sitter black hole in the Einstein-Gauss-Bonnet gravity. Using all the superpotentials of the family gives the standard accepted ma...
Einstein's Equations for Spin $2$ Mass $0$ from Noether's Converse Hilbertian Assertion
Pitts, J Brian
2016-01-01
An overlap between the general relativist and particle physicist views of Einstein gravity is uncovered. Noether's 1918 paper developed Hilbert's and Klein's reflections on the conservation laws. Energy-momentum is just a term proportional to the field equations and a 'curl' term with identically zero divergence. Noether proved a \\emph{converse} "Hilbertian assertion": such "improper" conservation laws imply a generally covariant action. Later and independently, particle physicists derived the nonlinear Einstein equations assuming the absence of negative-energy degrees of freedom ("ghosts") for stability, along with universal coupling: all energy-momentum including gravity's serves as a source for gravity. Those assumptions (all but) imply (for 0 graviton mass) that the energy-momentum is only a term proportional to the field equations and a symmetric "curl," which implies the coalescence of the flat background geometry and the gravitational potential into an effective curved geometry. The flat metric, though...
Higher rank Brill-Noether theory on sections of K3 surfaces
Farkas, Gavril
2011-01-01
We discuss the role of K3 surfaces in the context of Mercat's conjecture in higher rank Brill-Noether theory. Using liftings of Koszul classes, we show that Mercat's conjecture in rank 2 fails for any number of sections and for any gonality stratum along a Noether-Lefschetz divisor inside the locus of curves lying on K3 surfaces. Then we show that Mercat's conjecture in rank 3 fails even for curves lying on K3 surfaces with Picard number 1. Finally, we provide a detailed proof of Mercat's conjecture in rank 2 for general curves of genus 11, and describe explicitly the action of the Fourier-Mukai involution on the moduli space M_{11}.
Noether's problem for $p$-groups with an abelian subgroup of index $p$
Michailov, Ivo M
2012-01-01
Let $K$ be a field and $G$ be a finite group. Let $G$ act on the rational function field $K(x(g):g\\in G)$ by $K$ automorphisms defined by $g\\cdot x(h)=x(gh)$ for any $g,h\\in G$. Denote by $K(G)$ the fixed field $K(x(g):g\\in G)^G$. Noether's problem then asks whether $K(G)$ is rational over $K$. In this paper, we give a positive answer to the Noether's problem for all $p$-groups with an abelian subgroup of index $p$ and with a trivial $p$-th lower central subgroup, provided that $K$ contains sufficient roots of unity.
Solving the Noether procedure for cubic interactions of higher spins in (A)dS
Joung, Euihun; Lopez, Luca; Taronna, Massimo
2013-05-01
The Noether procedure represents a perturbative scheme to construct all possible consistent interactions starting from a given free theory. In this paper we describe how cubic interactions involving higher spins in any constant-curvature background can be systematically derived within this framework. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Higher spin theories and holography’.
RENEWAL OF BASIC LAWS AND PRINCIPLES FOR POLAR CONTINUUM THEORIES (Ⅲ)-NOETHER'S THEOREM
Institute of Scientific and Technical Information of China (English)
戴天民
2003-01-01
The existing various couple stress theories have been carefully restudied. Thepurpose is to propose a coupled Noether's theorem and to reestablish rather completeconservation laws and balance equations for couple stress elastodynamics. The new concreteforms of various conservation laws of couple stress elasticity are derived. The precise natureof these conservation laws which result from the given invariance requirements areestablished. Various special cases are reduced and the results of micropolar continua may benaturally transited from the results presented in this paper.
Comments on the Gauge Fixed BRST Cohomology and the Quantum Noether Method
Barnich, G; Skenderis, K; Barnich, Glenn; Hurth, Tobias; Skenderis, Kostas
2004-01-01
We discuss in detail the relation between the gauge fixed and gauge invariant BRST cohomology. In particular in certain gauges some cohomology classes of the gauge fixed BRST differential do not correspond to gauge invariant observables, and in addition ``accidental'' conserved currents may appear. These correspond 1-1 to observables that become trivial in this gauge. We explicitly show how the gauge fixed BRST cohomology appears in the context of the Quantum Noether Method.
Twisted Grosse-Wulkenhaar $\\phi^{\\star 4}$ model: dynamical noncommutativity and Noether currents
Hounkonnou, Mahouton Norbert
2009-01-01
This paper addresses the computation of Noether currrents for the renormalizable Grosse-Wulkenhaar (GW) $\\phi^{\\star 4}$ model subjected to a dynamical noncomutativity realized through a twisted Moyal product. The noncommutative (NC) energy-momentum tensor (EMT), angular momentum tensor (AMT) and the dilatation current (DC) are explicitly derived. The breaking of translation and rotation invariances has been avoided via a constraint equation.
Symmetry-Improved 2PI Approach to the Goldstone-Boson IR Problem of the SM Effective Potential
Pilaftsis, Apostolos
2015-01-01
The effective potential of the Standard Model (SM), from three loop order and higher, suffers from infra-red (IR) divergences arising from quantum effects due to massless would-be Goldstone bosons associated with the longitudinal polarizations of the W and Z bosons. Such IR pathologies also hinder accurate evaluation of the two-loop threshold corrections to electroweak quantities, such as the vacuum expectation value of the Higgs field. However, these divergences are an artifact of perturbation theory, and therefore need to be consistently resummed in order to obtain a IR-safe effective potential. The so-called Two-Particle-Irreducible (2PI) effective action provides a rigorous framework to consistently perform such resummations, without the need to resort to ad hoc subtractions or running into the risk of over-counting contributions. By considering the recently proposed symmetry-improved 2PI formalism, we address the problem of the Goldstone-boson IR divergences of the SM effective potential in the gaugeless...
Lie point symmetries of a general class of PDEs: The heat equation
Paliathanasis, Andronikos; Tsamparlis, Michael
2012-01-01
We give two theorems which show that the Lie point and the Noether symmetries of a second-order ordinary differential equation of the form (D/(Ds))(((Dx^{i}(s))/(Ds)))=F(x^{i}(s),x^{j}(s)) are subalgebras of the special projective and the homothetic algebra of the space respectively. We examine the possible extension of this result to partial differential equations (PDE) of the form A^{ij}u_{ij}-F(x^{i},u,u_{i})=0 where u(x^{i}) and u_{ij} stands for the second partial derivative. We find tha...
CP and other Symmetries of Symmetries
Trautner, Andreas
2016-01-01
Outer automorphisms of symmetries ("symmetries of symmetries") in relativistic quantum field theories are studied, including charge conjugation (C), space-reflection (P) , and time-reversal (T) transformations. The group theory of outer automorphisms is pedagogically introduced and it is shown that CP transformations are special outer automorphisms of the global, local, and space-time symmetries of a theory. It is shown that certain discrete groups allow for a group theoretical prediction of parameter independent CP violating complex phases with fixed geometrical values. The remainder of this thesis pioneers the study of outer automorphisms which are not related to C, P, or T. It is shown how outer automorphisms, in general, relate symmetry invariants and, in theories with spontaneous symmetry breaking, imply relations between different vacuum expectation values. Thereby, outer automorphisms can give rise to emergent symmetries. An example model with a discrete symmetry and three copies of the Standard Model ...
Assessing symmetry of financial returns series
Coronel-Brizio, H F; Rodriguez-Achach, M
2007-01-01
Testing symmetry of a probability distribution is a common question arising from applications in several fields. Particularly, in the study of observables used in the analysis of stock market index variations, the question of symmetry has not been fully investigated by means of statistical procedures. In this work a distribution-free test statistic Tn for testing symmetry, derived by Einmahl and McKeague, based on the empirical likelihood approach, is used to address the study of symmetry of financial returns. The asymptotic points of the test statistic Tn are also calculated and a procedure for assessing symmetry for the analysis of the returns of stock market indices is presented.
Ordóñez, Carlos R.
2016-03-01
We derive anomalous equations of state for nonrelativistic 2D complex bosonic fields with contact interactions, using Fujikawa's path-integral approach to anomalies and scaling arguments. In the process, we derive an anomalous virial theorem for such systems. The methods used are easily generalizable for other 2D systems, including fermionic ones, and of different spatial dimensionality, all of which share a classical SO(2 , 1) Schrödinger symmetry. The discussion is of a more formal nature and is intended mainly to shed light on the structure of anomalies in 2D many-body systems. The anomaly corrections to the virial theorem and equation of state-pressure relationship-may be identified as the Tan contact term. The practicality of these ideas rests upon being able to compute in detail the Fujikawa Jacobian that contains the anomaly. This and other conceptual issues, as well as some recent developments, are discussed at the end of the paper.
Clemente-Juan, Juan Modesto; Palii, Andrew; Coronado, Eugenio; Tsukerblat, Boris
2016-08-09
In this article, we focus on the electron-vibrational problem of the tetrameric mixed-valence (MV) complexes proposed for implementation as four-dot molecular quantum cellular automata (mQCA).1 Although the adiabatic approximation explored in ref 2 is an appropriate tool for the qualitative analysis of the basic characteristics of mQCA, like vibronic trapping of the electrons encoding binary information and cell-cell response, it loses its accuracy providing moderate vibronic coupling and fails in the description of the discrete pattern of the vibronic levels. Therefore, a precise solution of the quantum-mechanical vibronic problem is of primary importance for the evaluation of the shapes of the electron transfer optical absorption bands and quantitative analysis of the main parameters of tetrameric quantum cells. Here, we go beyond the Born-Oppenheimer paradigm and present a solution of the quantum-mechanical pseudo Jahn-Teller (JT) vibronic problem in bielectronic MV species (exemplified by the tetra-ruthenium complexes) based on the recently developed symmetry-assisted approach.3,4 The mathematical approach to the vibronic eigenproblem takes into consideration the point symmetry basis, and therefore, the total matrix of the JT Hamiltonian is blocked to the maximum extent. The submatrices correspond to the irreducible representations (irreps) of the point group. With this tool, we also extend the theory of the mQCA cell beyond the limit of prevailing Coulomb repulsion in the electronic pair (adopted in ref 2), and therefore, the general pseudo-JT problems for spin-singlet ((1)B1g, 2(1)A1g, (1)B2g, (1)Eu) ⊗ (b1g + eu) and spin-triplet states ((3)A2g, (3)B1g, 2(3)Eu) ⊗ (b1g + eu) in a square-planar bielectronic system are solved. The obtained symmetry-adapted electron-vibrational functions are employed for the calculation of the profiles (shape functions) of the charge transfer absorption bands in the tetrameric MV complexes and for the discussion of the
Energy Technology Data Exchange (ETDEWEB)
Henley, E.M.
1981-09-01
Internal and space-time symmetries are discussed in this group of lectures. The first of the lectures deals with an internal symmetry, or rather two related symmetries called charge independence and charge symmetry. The next two discuss space-time symmetries which also hold approximately, but are broken only by the weak forces; that is, these symmetries hold for both the hadronic and electromagnetic forces. (GHT)
Symmetry and symmetry breaking in particle physics
Tsou, ST
1998-01-01
Symmetry, in particular gauge symmetry, is a fundamental principle in theoretical physics. It is intimately connected to the geometry of fibre bundles. A refinement to the gauge principle, known as ``spontaneous symmetry breaking'', leads to one of the most successful theories in modern particle physics. In this short talk, I shall try to give a taste of this beautiful and exciting concept.