Related papers: Singular Vectors and Conservation Laws of Quantum …
A complete classification of low-order conservation laws is obtained for time-dependent generalized Korteweg-de Vries equations. Through the Hamiltonian structure of these equations, a corresponding classification of Hamiltonian symmetries…
The conservation laws of the third order quasilinear scalar evolution equations are considered via differential system and characteristic cohomology. We find a subspace of 2 forms in the infinite prolonged space in which every conservation…
We provide a complete classification of point symmetries and low-order local conservation laws of the generalized quasilinear KdV equation in terms of the arbitrary function. The corresponding interpretation of symmetry transformation…
It is shown that expected values of free scalar and vector quantum fields on graphs satisfy the same conservation laws as the classic fields. It is demonstrated that a modified version of conservation laws is satisfied for Villain action.…
A brief review is given of the author recent achievements in classifying singular points of the Poynting vector patterns in electromagnetic fields of complex configuration. The deep connection between the topological structure of the force…
We investigate conservation laws in the quantum mechanics of closed systems. We review an argument showing that exact decoherence implies the exact conservation of quantities that commute with the Hamiltonian including the total energy and…
We present a fully discrete particle approximation for one-dimensional scalar conservation laws. Under suitable monotonicity assumptions on the macroscopic velocity, we construct a vacuum-compatible family of time-discrete particle…
We examine the accuracy of an intrinsically one-dimensional quantum electrodynamics to predict accurately the forces and charges of a three-dimensional system that has a high degree of symmetry and therefore depends effectively only on a…
We first consider the Lagrangian formulation of general relativity for perturbations with respect to a background spacetime. We show that by combining Noether's method with Belinfante's "symmetrization'' procedure we obtain conserved…
We develop an action principle for those models arising from isotropic loop quantum cosmology, and show that there is a natural conserved quantity $Q$ for the discrete difference equation arising from the Hamiltonian constraint. This…
A quantum scalar field theory with spacetime-dependent coupling is studied. Surprisingly, while translation invariance is explicitly broken in the classical theory, momentum conservation is recovered at the quantum level for some specific…
The notions of generating sets of conservation laws of systems of differential equations with respect to symmetry groups and equivalence groups are introduced and applied. This allows us to generalize essentially the procedure of finding…
It is shown that the Kadanoff-Baym equations at consistent first-order gradient approximation reveal exact rather than approximate conservation laws related to global symmetries of the system. The conserved currents and energy-momentum…
The conservation laws for a class of nonlinear equations with variable coefficients on discrete and noncommutative spaces are derived. For discrete models the conserved charges are constructed explicitly. The applications of the general…
We study a particular deformation of the potential KdV model (pKdV) and construct the quasi-conservation laws by a direct method. The charge densities, differing from their integrable counterpart with homogeneous degree terms, exhibit mixed…
The quasi-integrable KdV equation has been obtained from the corresponding deformation of the Hamiltonian for the usual KdV system. Following suitable gauge-fixing, it has been found that the quasi-conservation condition is satisfied and an…
We discuss the relation between symmetries and conservation laws in the realm of classical field theories based on the Hamiltonian constraint. In this approach, spacetime positions and field values are treated on equal footing, and a…
The connection between supersymmetric quantum mechanics and the Korteweg- de Vries (KdV) equation is discussed, with particular emphasis on the KdV conservation laws. It is shown that supersymmetric quantum mechanics aids in the derivation…
The \nl \cls for the N=1 supersymmetric KdV equation are shown to be related in a simple way to powers of the fourth root of its Lax operator. This provides a direct link between the supersymmetry invariance and the existence of \nl…
This paper is devoted to studying symmetries of certain kinds of k-cosymplectic Hamiltonian systems in first-order classical field theories. Thus, we introduce a particular class of symmetries and study the problem of associating…