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L. Martinez Alonso 《Letters in Mathematical Physics》1979,3(5):419-424
For a wide class of lagrangian systems we show rigorously that the conventional formulation of Noether's theorem provides a bijective map from the set of equivalence classes of Noether's symmetries onto the set of equivalence classes of conserved currents. We further discuss if Noether's theorem is generalized in a significant way by several formulations proposed in this decade.Partially supported by the Junta de Energia Nuclear, Madrid. 相似文献
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SYMMETRIES AND CONSERVED QUANTITIES FOR SYSTEMS OF GENERALIZED CLASSICAL MECHANICS 总被引:4,自引:0,他引:4 下载免费PDF全文
In this paper, the symmetries and the conserved quantities for systems of generalized classical mechanics are studied. First, the generalized Noether's theorem and the generalized Noether's inverse theorem of the systems are given, which are based upon the invariant properties of the canonical action with respect to the action of the infinitesimal transformation of r-parameter finite group of transformation; second, the Lie symmetries and conserved quantities of the systems are studied in accordance with the Lie's theory of the invariance of differential equations under the transformation of infinitesimal groups; and finally, the inner connection between the two kinds of symmetries of systems is discussed. 相似文献
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Noether‘s theory of a rotational relativistic variable mass system is studied.Firstly,Jourdain‘s principle of the rotational relativistic variable mass system is given.Secondly,on the basis of the invariance of the Jourdain‘s principle under the infinitesimal transformations of groups,Noether‘s theorem and its inverse theorem of the rotational relativistic variable mass system are presented.Finally,an example is given to illustrate the application of the result. 相似文献
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Using basic ideas from algebraic geometry, we extend the methods of Lagrangian and symplectic mechanics to treat a large class of discrete mechanical systems, that is, systems such as cellular automata in which time proceeds in integer steps and the configuration space is discrete. In particular, we derive an analog of the Euler-Lagrange equation from a variational principle, and prove an analog of Noether's theorem. We also construct a symplectic structure on the analog of the phase space, and prove that it is preserved by time evolution. 相似文献
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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. 相似文献
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本文导出场论中用奇异拉氏量描述的系统正则形式的广义Noether第一定理(GNFT),导出无限连续群下变更性系统正则形式的广义Noether恒等式(GNI),讨论了它们在Dirac约束理论中的应用。给出一个新的反倒,说明Dirac猜想失效,指出某些变更性系统也具有Dirac约束,讨论了GNI在色动力学中的应用。
关键词: 相似文献
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Generalized Noether theorems in canonical formalism for field theories and their applications 总被引:1,自引:0,他引:1
Zi-ping Li 《International Journal of Theoretical Physics》1993,32(1):201-215
A generalization of Noether's first theorem in phase space for an invariant system with a singular Lagrangian in field theories is derived and a generalization of Noether's second theorem in phase space for a noninvariant system in field theories is deduced. A counterexample is given to show that Dirac's conjecture fails. Some preliminary applications of the generalized Noether second theorem to the gauge field theories are discussed. It is pointed out that for certain systems with a noninvariant Lagrangian in canonical variables for field theories there is also a Dirac constraint. Along the trajectory of motion for a gauge-invariant system some supplementary relations of canonical variables and Lagrange multipliers connected with secondary first-class constraints are obtained. 相似文献
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The aim of this paper is to study the Herglotz variational principle of the fractional Birkhoffian system and its Noether symmetry and conserved quantities. First, the fractional Pfaff-Herglotz action and the fractional PfaffHerglotz principle are presented. Second, based on different definitions of fractional derivatives, four kinds of fractional Birkhoff's equations in terms of the Herglotz variational principle are established. Further, the definition and criterion of Noether symmetry of the fractional Birkhoffian system in terms of the Herglotz variational problem are given. According to the relationship between the symmetry and the conserved quantities, the Noether's theorems within four different fractional derivatives are derived, which can reduce to the Noether's theorem of the Birkhoffian system in terms of the Herglotz variational principle under the classical conditions. As applications of the Noether's t heorems of the fractional Birkhoffian system in terms of the Herglotz variational principle, an example is given at the end of this paper. 相似文献
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We generalize Noether's theorem and the Poincaré invariant to conservative and nonconservative systems with nonlinear nonholonomic constraints. The conservation laws of such systems are illustrated. 相似文献
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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. 相似文献
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研究事件空间中Birkhoff系统的Noether对称性与Noether守恒量.首先,建立了事件空间中Birkhoff系统的参数方程;其次,基于Pfaff作用量在无限小变换下的不变性,给出了事件空间中Birkhoff系统的Noether定理及其逆定理;最后,举例说明结果的应用.
关键词:
事件空间
Birkhoff系统
Pfaff作用量
Noether对称性 相似文献
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Joe Rosen 《International Journal of Theoretical Physics》1971,4(4):287-294
The role of invariance considerations in conventional formulations of Noether's theorem in classical field theory is investigated and found weaker than is usually supposed. It is shown how nonfulfilment of the conventional assumptions going into Noether's theorem brings about nonconservation. 相似文献
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本文导出非不变性作用量系统的广义Noether恒等式并给出它的应用。
关键词: 相似文献
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The conservation laws—precisely speaking, the basis of the conservation laws—are obtained through the use of Noether's theorem, Lie symmetry, and a theorem due to Ibragimov. Though in principle for each generator of Lie symmetry there should be a different conserved vector, due to the closed Lie algebra generated by the generators, some of these vectors become no longer independent. The theorem of Ibragimov is used to construct a basis in the case of the KP equation in three dimensions. It is then shown how the same analysis can be performed through the Hamiltonian formalism. 相似文献
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After an analysis of some types of symplectic bundles, we use seeded fiberbundles to find laws of conservation in relativity from different dynamical groups.By using the concept of dynamical group in a bundle, we obtain an extensionof Noether's theorem to fiber bundle structures. 相似文献
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In this paper, Noether theory of Lagrange systems in discrete case are studied. First, we briefly overview the well-known 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. 相似文献
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A classical field theory for a Schrodinger equation with a non-Hermitian Hamiltonian describing a particle with position-dependent mass has been recently advanced by Nobre and Rego-Monteiro(NR)[Phys.Rev.A 88(2013)032105].This field theory is based on a variational principle involving the wavefunction Ψ(x,t) and an auxiliary fieldΦ{x,t).It is here shown that the relation between the dynamics of the auxiliary field Φ(x,t) and that of the original wavefunction Ψ(x,t) is deeper than suggested by the NR approach.Indeed,we formulate a variational principle for the aforementioned Schrodinger equation which is based solely on the wavefunction Ψ(x,t).A continuity equation for an appropriately defined probability density,and the concomitant preservation of the norm,follows from this variational principle via Noether's theorem.Moreover,the norm-conservation law obtained by NR is reinterpreted as tie preservation of the inner product between pairs of solutions of the variable mass Schrodinger equation. 相似文献
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In this work we study the Lagrangian and the conservation laws for a wave equation with a dissipative source. Using semi-inverse method, we show that the equation possesses a nonlocal Lagrangian with an auxiliary function.As a result, from a modified Noether's theorem and the nonclassical Noether symmetry generators, we construct some conservation laws for this equation, which are different from the ones obtained by Ibragimov's theorem in [Y. Wang and L. Wei, Abstr. App. Anal. 2013(2013) 407908]. The results show that our method work for arbitrary functions f(u)and g(u) rather than special ones. 相似文献