Study of Theory about Large Unified Symmetries for Hamilton Systems

2011 ◽  
Vol 27 (2) ◽  
pp. 245-252
Author(s):  
Y.-P. Luo
Keyword(s):  
Lie Symmetry ◽  
Lie Symmetries ◽  
Noether Symmetry ◽  
Theoretical Physics ◽  
Conserved Quantities ◽  
Noether Symmetries ◽  
Mei Symmetry

ABSTRACTIn this paper, the new concept of theory about Large Unified Symmetries for Hamilton systems are presented. The Large Unified Symmetries and conserved quantities for Hamilton systems are studied by the relation between the three kinds of symmetries and the three kinds of conserved quantities. We worked on the Large Unified Symmetries and conserved quantities by Noether symmetry, Lie symmetry and Mei symmetry, including the definition and criterion of the Large Unified Symmetries and the conserved quantities deduced from them. The Large Unified Symmetries are a intersection set among the Noether symmetries, the Lie symmetries and the Mei symmetries. The theory about Large Unified Symmetries will play an important role in the fields of modern theoretical physics.

Conservation laws corresponding to the Noether symmetries of the geodetic Lagrangian in spherically symmetric spacetimes

2017 ◽  
Vol 26 (05) ◽  
pp. 1741006 ◽  
Author(s):  
Bismah Jamil ◽  
Tooba Feroze
Keyword(s):  
Conservation Laws ◽  
Noether Symmetry ◽  
Complete List ◽  
Spherically Symmetric ◽  
Conserved Quantities ◽  
Noether Symmetries ◽  
Symmetric Spacetimes ◽  
Spherically Symmetric Spacetimes

In this paper, we present a complete list of spherically symmetric nonstatic spacetimes along with the generators of all Noether symmetries of the geodetic Lagrangian for such metrics. Moreover, physical and geometrical interpretations of the conserved quantities (conservation laws) corresponding to each Noether symmetry are also given.

HOJMAN CONSERVED QUANTITIES AND LIE SYMMETRIES OF DISCRETE NON-CONSERVATIVE SYSTEMS

2009 ◽  
Vol 23 (10) ◽  
pp. 1315-1322 ◽  
Author(s):  
JING-LI FU ◽  
BEN-YONG CHEN
Keyword(s):  
Dynamical Systems ◽  
Lie Symmetry ◽  
Lie Symmetries ◽  
Conserved Quantity ◽  
Conserved Quantities ◽  
Conservative Systems ◽  
The Right ◽  
Hojman Conserved Quantity

This letter focuses on studying the theory of Hojman conserved quantity of the discrete non-conservative dynamical systems. The operators of discrete translation and discrete differentiation to the right and left are introduced in discrete non-conservative dynamical systems. The Hojman theorems, the determining equations and Hojman conserved quantities of the Lie symmetry are obtained for discrete non-conservative dynamical systems. Finally, an example is discussed to illustrate the application of the results.

scholarly journals Mei symmetry, Noether symmetry and Lie symmetry of an Emden system

2006 ◽  
Vol 55 (11) ◽  
pp. 5594
Author(s):  
Gu Shu-Long ◽  
Zhang Hong-Bin
Keyword(s):  
Lie Symmetry ◽  
Noether Symmetry ◽  
Mei Symmetry

A cosmological study of Einstein–Skyrme model in anisotropic Kantowski–Sachs spacetime using Lie and Noether symmetries

2018 ◽  
Vol 15 (06) ◽  
pp. 1850089 ◽  
Author(s):  
Santu Mondal ◽  
Sourav Dutta ◽  
Manjusha Tarafdar ◽  
Subenoy Chakraborty
Keyword(s):  
Lie Algebra ◽  
Evolution Equations ◽  
Einstein Gravity ◽  
Lie Symmetry ◽  
Noether Symmetry ◽  
Noether Symmetries ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Unknown Parameters ◽  
Augmented Space

The present work deals with anisotropic (but zero heat flux) Skyrme fluid in a locally rotational Kantowski–Sachs (KS) spacetime in the background of Einstein gravity. The Lie point symmetry is imposed to the system of Einstein field equations and unknown parameters are either determined or interrelated by the imposition of the symmetry. Subsequently, Noether symmetry, a point-like symmetry of the Lagrangian is used and it is found that the Lie algebra of the Noether symmetry is a subalgebra of the corresponding Lie algebra of the Lie symmetry. Then a point transformation in the 2D augmented space is taken in such a manner that one of the variables becomes cyclic and hence the Lagrangian as well as the evolution equations are simplified to a great extent. Finally, solutions to the physical system are presented and are analyzed physically.

scholarly journals Approximate Mei Symmetries and Invariants of the Hamiltonian

Mathematics ◽  
2021 ◽  
Vol 9 (22) ◽  
pp. 2910
Author(s):  
Umara Kausar ◽  
Tooba Feroze
Keyword(s):  
Conserved Quantity ◽  
Noether Symmetry ◽  
Conserved Quantities ◽  
Noether Symmetries ◽  
Fields Of Study

It is known that corresponding to each Noether symmetry there is a conserved quantity. Another class of symmetries that corresponds to conserved quantities is the class of Mei symmetries. However, the two sets of symmetries may give different conserved quantities. In this paper, a procedure of finding approximate Mei symmetries and invariants of the perturbed/approximate Hamiltonian is presented that can be used in different fields of study where approximate Hamiltonians are under consideration. The results are presented in the form of theorems along with their proofs. A simple example of mechanics is considered to elaborate the method of finding these symmetries and the related Mei invariants. At the end, a comparison of approximate Mei symmetries and approximate Noether symmetries is also given. The comparison shows that there is only one common symmetry in both sets of symmetries. Hence, rest of the symmetries in the two sets correspond to two different sets of conserved quantities.

Stellar structures admitting Noether symmetries in f(ℛ,𝒯 ) gravity

2021 ◽  
Author(s):  
M. Sharif ◽  
M. Zeeshan Gul
Keyword(s):  
Specific Model ◽  
Compact Objects ◽  
Noether Symmetry ◽  
Model Parameters ◽  
Conserved Quantities ◽  
Noether Symmetries ◽  
Stellar Objects ◽  
Astrophysical Data ◽  
Symmetry Generators

This paper investigates the geometry of compact stellar objects via Noether symmetry strategy in the framework of curvature-matter coupled gravity. For this purpose, we assume the specific model of this theory to evaluate Noether equations, symmetry generators and corresponding conserved parameters. We use conserved parameters to examine some fascinating attributes of the compact objects for suitable values of the model parameters. It is analyzed that compact objects in this theory depend on the conserved quantities and model parameters. We find that the obtained solutions provide the viability of this process as they are compatible with the astrophysical data.

scholarly journals $$f(\mathcal {R},\varphi ,\chi )$$ cosmology with Noether symmetry

2020 ◽  
Vol 80 (2) ◽  
Author(s):  
M. Farasat Shamir
Keyword(s):  
Scalar Field ◽  
Modified Gravity ◽  
Vital Role ◽  
Gravity Models ◽  
Noether Symmetry ◽  
Accelerated Expansion ◽  
Conserved Quantities ◽  
Noether Symmetries ◽  
Cosmic Evolution ◽  
Friedmann Robertson Walker

Abstract This paper is devoted to explore modified $$f(\mathcal {R})$$f(R) theories of gravity using Noether symmetry approach. For this purpose, Friedmann–Robertson–Walker spacetime is chosen to investigate the cosmic evolution. The study is mainly divided into two parts: Firstly Noether symmetries of metric $$f(\mathcal {R})$$f(R) gravity are revisited and some new class of solutions with the help of conserved quantities are reported. It is shown that different scenarios of cosmic evolution can be discussed using Noether symmetries and one of the case indicates the chances for the existence of Big Rip singularity. Secondly, $$f(\mathcal {R})$$f(R) theory coupled with scalar field has been discussed in detail. The Noether equations of modified gravity are reported with three subcases for flat Friedmann–Robertson–Walker universe. It is concluded that conserved quantities are quite helpful to find some important exact solutions in the cosmological contexts. Moreover, the scalar field involved in the modified gravity plays a vital role in the cosmic evolution and an accelerated expansion phase can be observed for some suitable choices of $$f(\mathcal {R},\varphi ,\chi )$$f(R,φ,χ) gravity models.

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