相关论文: Noether's Theorem with Momentum and Energy Terms f…

We prove multidimensional integration by parts formulas for generalized fractional derivatives and integrals. The new results allow us to obtain optimality conditions for multidimensional fractional variational problems with Lagrangians…

A simple proof of Noether's first theorem involves the promotion of a constant symmetry parameter $\epsilon$ to an arbitrary function of time, the Noether charge $Q$ is then the coefficient of $\dot\epsilon$ in the variation of the action.…

We give one more proof in two and three space dimensions that the irregular solution of the Schrodinger equation, for zero angular momentum, is in fact the solution of an equation containing an extra 'delta function'. We propose another…

We prove Euler-Lagrange and natural boundary necessary optimality conditions for fractional problems of the calculus of variations which are given by a composition of functionals. Our approach uses the recent notions of Riemann-Liouville…

Noether's theorem provides a powerful link between continuous symmetries and conserved quantities for systems governed by some variational principle. Perhaps unfortunately, most dynamical systems of interest in neuroscience and artificial…

We study, using an optimal control point of view, higher-order variational problems of Herglotz type with time delay. Main results are higher-order Euler-Lagrange and DuBois-Reymond necessary optimality conditions as well as a higher-order…

Using the recent formulation of Noether's theorem for the problems of the calculus of variations with fractional derivatives, the Lagrange multiplier technique, and the fractional Euler-Lagrange equations, we prove a Noether-like theorem to…

We derive the variational principle and Noether's theorem in generally covariant field theory in an explicitly coordinate-independent way by means of the exterior calculus over the space-time manifold. We then focus on the symmetry of…

When discussing consequences of symmetries of dynamical systems based on Noether's first theorem, most standard textbooks on classical or quantum mechanics present a conclusion stating that a global continuous Lie symmetry implies the…

The aim of this paper is to present a new approach to construct constants of motion associated with scaling symmetries of dynamical systems. Scaling maps could be symmetries of the equations of motion but not of its associated Lagrangian…

We apply the principles discussed in an earlier paper to the construction of discrete time field theories. We derive the discrete time field equations of motion and Noether's theorem and apply them to the Schrodinger equation to illustrate…

An exact uncertainty principle, formulated as the assumption that a classical ensemble is subject to random momentum fluctuations of a strength which is determined by and scales inversely with uncertainty in position, leads from the…

We show that for any variational symmetry of the problem of the calculus of variations on time scales there exists a conserved quantity along the respective Euler-Lagrange extremals.

This paper develops a novel approach to necessary optimality conditions for constrained variational problems defined in generally incomplete subspaces of absolutely continuous functions. Our approach involves reducing a variational problem…

We prove higher-order Euler-Lagrange and DuBois-Reymond stationary conditions to fractional action-like variational problems. More general fractional action-like optimal control problems are also considered.

A new derivation is given of the known generalized position-momentum uncertainty relation, which takes into account gravity. The problem of two massive particles, the relative motion of which is described by the Schroedinger equation, is…

The exact momentum conservation laws for the nonlinear gyrokinetic Vlasov-Poisson equations are derived by applying the Noether method on the gyrokinetic variational principle [A. J. Brizard, Phys. Plasmas {\bf 7}, 4816 (2000)]. From the…

The current paper is devoted to the investigation of the general form of the energy-momentum pseudotensor (pEMT) and the corresponding superpotential for the wide class of theories. The only requirement for such a theory is the general…

Noether's theorem on the equivalence of symmetry and conservation laws has applications to geometric problems on symmetric spaces. We remind the reader of the theorem and give an application to a variational problem on hyperbolic surfaces.

The connection between symmetries and conservation laws as made by Noether's theorem is extended to the context of causal variational principles and causal fermion systems. Different notions of continuous symmetries are introduced. It is…