This paper analyses the Noether symmetries and the corresponding conservation laws for Chern-Simons Lagrangians in dimension d = 3. In particular, we find an expression for the superpotential of ChernSimons gravity. As a by-product the general discussion of superpotentials for 3rd order natural and quasi-natural theories is also given. PACS number(s): 04.20.Fy, 11.10Kk, 11.30.-j, 04.20.Cv

One of the difficulties encountered when studying physical theories in discrete space-time is that of describing the underlying continuous symmetries (like Lorentz, or Galilei invariance). One of the ways of addressing this difficulty is to consider point transformations acting simultaneously on difference equations and lattices. In a previous article we have classified ordinary difference sche...

Westervelt's equation is a nonlinear wave that widely used to model the propagation of sound waves in compressible medium, with one important application being ultra-sound human tissue. Two fundamental aspects this -- symmetries and conservation laws are studied present work by modern methods. Numerous results obtained: new conserved integrals; potential systems yielding hidden nonlocal laws; m...

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 No...

The SU(2) collective coordinates expansion of the Born-Infeld Skyrmion Lagrangian is performed. The classical Hamiltonian is computed from this special Lagrangian in approximative way: it is derived from the expansion of this non-polynomial Lagrangian up to secondorder variable in the collective coordinates. This second-class constrained model is quantized by Dirac Hamiltonian method and symple...

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 ⊕sR 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 ≥ ∑kj 1 nj ...

Symmetries, conserved quantities and invariance properties are studied. In the case of Lagrangian systems connection between dynamical symmetries is not too direct, for instance, there always exists an infinite number linearly independent which have no associated Neother constant motion but general possesses invariants symmetry group itself. Now a days crucial renormalizability theory under con...

We deduce the canonical brackets for a two (1 + 1)-dimensional (2D) free Abelian 1-form gauge theory by exploiting the beauty and strength of the continuous symmetries of a Becchi-Rouet-Stora-Tyutin (BRST) invariant Lagrangian density that respects, in totality, six continuous symmetries. All these symmetries lead to the derivation of exactly the same canonical brackets amongst the creation and...

Using approximate symmetry methods for differential equations we have investigated the exact and approximate symmetries of a Lagrangian for the geodesic equations in the Kerr spacetime. Taking Minkowski spacetime as the exact case, it is shown that the symmetry algebra of the Lagrangian is 17 dimensional. This algebra is related to the 15 dimensional Lie algebra of conformal isometries of Minko...