scholarly journals HIGHER-ORDER NOETHER SYMMETRIES IN k-SYMPLECTIC HAMILTONIAN FIELD THEORY

2013 ◽  
Vol 10 (08) ◽  
pp. 1360013
Author(s):  
NARCISO ROMÁN-ROY ◽  
MODESTO SALGADO ◽  
SILVIA VILARIÑO
Keyword(s):  
Field Theory ◽  
Conservation Laws ◽  
Vector Fields ◽  
Higher Order ◽  
Field Theories ◽  
Noether Symmetries ◽  
Noether’S Theorem ◽  
Noether's Theorem ◽  
Infinitesimal Transformations

For k-symplectic Hamiltonian field theories, we study infinitesimal transformations generated by some kinds of vector fields which are not Noether symmetries, but which allow us to obtain conservation laws by means of suitable generalizations of Noether's theorem.

scholarly journals SYMMETRIES AND CONSERVATION LAWS IN THE GÜNTHER k-SYMPLECTIC FORMALISM OF FIELD THEORY

2007 ◽  
Vol 19 (10) ◽  
pp. 1117-1147 ◽  
Author(s):  
NARCISO ROMÁN-ROY ◽  
MODESTO SALGADO ◽  
SILVIA VILARIÑO
Keyword(s):  
Field Theory ◽  
Conservation Laws ◽  
Classical Field ◽  
Field Theories ◽  
Noether’S Theorem ◽  
Noether's Theorem ◽  
First Order ◽  
Gauge Symmetries ◽  
Classical Field Theories

This paper is devoted to studying symmetries of k-symplectic Hamiltonian and Lagrangian first-order classical field theories. In particular, we define symmetries and Cartan symmetries and study the problem of associating conservation laws to these symmetries, stating and proving Noether's theorem in different situations for the Hamiltonian and Lagrangian cases. We also characterize equivalent Lagrangians, which lead to an introduction of Lagrangian gauge symmetries, as well as analyzing their relation with Cartan symmetries.

scholarly journals SYMMETRIES, NEWTONOID VECTOR FIELDS AND CONSERVATION LAWS IN THE LAGRANGIAN k-SYMPLECTIC FORMALISM

2012 ◽  
Vol 24 (10) ◽  
pp. 1250030 ◽  
Author(s):  
LUCÍA BUA ◽  
IOAN BUCATARU ◽  
MODESTO SALGADO
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Conservation Laws ◽  
Conservation Law ◽  
Vector Fields ◽  
Partial Differential ◽  
Noether’S Theorem ◽  
Dynamical Symmetries ◽  
Noether's Theorem ◽  
Configuration Manifold

In this paper, we study symmetries, Newtonoid vector fields, conservation laws, Noether's theorem and its converse, in the framework of the k-symplectic formalism, using the Frölicher–Nijenhuis formalism on the space of k1-velocities of the configuration manifold.For the case k = 1, it is well known that Cartan symmetries induce and are induced by constants of motions, and these results are known as Noether's theorem and its converse. For the case k > 1, we provide a new proof for Noether's theorem, which shows that, in the k-symplectic formalism, each Cartan symmetry induces a conservation law. We prove that, under some assumptions, the converse of Noether's theorem is also true and we 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.

scholarly journals Positive Energy Condition and Conservation Laws in Kantowski-Sachs Spacetime via Noether Symmetries

Symmetry ◽  
2018 ◽  
Vol 10 (12) ◽  
pp. 712 ◽  
Author(s):  
Sumaira Akhtar ◽  
Tahir Hussain ◽  
Ashfaque Bokhari
Keyword(s):  
Conservation Laws ◽  
Energy Condition ◽  
Positive Energy ◽  
Noether Symmetries ◽  
Noether’S Theorem ◽  
Noether's Theorem ◽  
Metric Functions

In this paper, we have investigated Noether symmetries of the Lagrangian of Kantowski–Sachs spacetime. The associated Lagrangian of the Kantowski–Sachs metric is used to derive the set of determining equations. Solving the determining equations for several values of the metric functions, it is observed that the Kantowski–Sachs spacetime admits the Noether algebra of dimensions 5, 6, 7, 8, 9, and 11. A comparison of the obtained Noether symmetries with Killing and homothetic vectors is also presented. With the help of Noether’s theorem, we have presented the expressions for conservation laws corresponding to all Noether symmetries. It is observed that the positive energy condition is satisfied for most of the obtained metrics.

Introduction

2017 ◽  
Author(s):  
Laurent Baulieu ◽  
John Iliopoulos ◽  
Roland Sénéor
Keyword(s):  
Conservation Laws ◽  
Lagrangian Mechanics ◽  
General Introduction ◽  
Noether’S Theorem ◽  
Noether's Theorem

General introduction with a review of the principles of Hamiltonian and Lagrangian mechanics. The connection between symmetries and conservation laws, with a presentation of Noether’s theorem, is included.

scholarly journals Conservation Laws in Physics – Emmy Noether’s Theorem

2014 ◽  
Vol 29 ◽  
pp. 55-61
Author(s):  
Daniela Manolea
Keyword(s):  
Conservation Laws ◽  
Celestial Body ◽  
Practical Importance ◽  
Microscopic Level ◽  
Human Knowledge ◽  
Noether’S Theorem ◽  
Noether's Theorem ◽  
The World ◽  
Physical Laws ◽  
Practical Impact

The study is explanatory-interpretative and argues the practical character of Physics. It starts from premise that formation of a correct conception of the world begins with the understanding of physics. It is one of the earliest chapters of human knowledge, studying the material world from the microscopic level of the particles to the macroscopic level of the celestial body. As an example for the practical importance of applying the laws of physics take the set of physical laws of conservation, in particular, it explains the practical impact of Emmy Noether's Theorem.

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