Related papers: Noether conservation laws in quantum mechanics
Hamiltonian and Lagrangian formulations for the two-dimensional quasi-geostrophic equations linearized about a zonally-symmetric basic flow are presented. The Lagrangian and Hamiltonian exhibit an infinite U(1) symmetry due to the absence…
This paper expounds the relations between continuous symmetries and conserved quantities, i.e. Noether's ``first theorem'', in both the Lagrangian and Hamiltonian frameworks for classical mechanics. This illustrates one of mechanics' grand…
Symmetries are defined in histories-based theories paying special attention to the class of history theories admitting quasitemporal structure (a generalization of the concept of `temporal sequences' of `events' using partial semigroups)…
Quasi-Noether differential systems are more general than variational systems and are quite common in mathematical physics. They include practically all differential systems of interest, at least those that have conservation laws. In this…
We discuss the Hamiltonian dynamics for cosmologies coming from Extended Theories of Gravity. In particular, minisuperspace models are taken into account searching for Noether symmetries. The existence of conserved quantities gives…
This study investigates pseudo-Hermitian quantum mechanics, where the Hamiltonian satisfies a modified Hermiticity condition. We extend the uncertainty relation for such systems, demonstrating its equivalence to the standard Hermitian case…
We extend Noether's theorem to dynamical optimal control systems being under the action of nonconservative forces. A systematic way of calculating conservation laws for nonconservative optimal control problems is given. As a corollary, the…
We derive the Noether identities and the conservation laws for general gravitational models with arbitrarily interacting matter and gravitational fields. These conservation laws are used for the construction of the covariant equations of…
The Noether symmetry of a generic $f(R)$ cosmological model is investigated by utilizing the behavior of the corresponding Lagrangian under the infinitesimal generators of the desired symmetry. We explicitly calculate the form of $f(R)$ for…
Quantum mechanics is one of the basic theories of modern physics. Here, the famous Schr\"odinger equation and the differential operators representing mechanical quantities in quantum mechanics are derived, just based on the principle that…
Regular perturbative Lagrangians that admit approximate Noether symmetries and approximate conservation laws are studied. Specifically, we investigate the connection between approximate Noether symmetries and collineations of the underlying…
The existence of a Noether symmetry for a given minisuperspace cosmological model is a sort of selection rule to recover classical behaviours in cosmic evolution since oscillatory regimes for the wave function of the universe come out. The…
The Noether symmetry issue for Horndeski Lagrangian has been studied. We have been proven a series of theorems about the form of Noether conserved charge (current) for irregular (not quadratic) dynamical systems. Special attentions have…
A generalized Noether's theorem and the operational determination of a physical geometry in quantum physics are used to motivate a quantum geometry consisting of relations between quantum states that are defined by a universal group. Making…
In a way paralleling the recently accepted non-Hermitian version of quantum mechanics in its Schr\"{o}dinger representation (working often with the innovative and heuristically productive concept of ${\cal PT}-$symmetry), it is demonstrated…
Using the Noether Charge formulation, we study a perturbation of the conserved gravitating system. By requiring the boundary term in the variation of the Hamiltonian to depend only on the symplectic structure, we propose a general…
The present work deals with Einstein-aether Scalar tensor gravity in the background of homogeneous and isotropic flat FLRW space-time model. The Noether symmetry vector identifies a transformation in the augmented space so that the field…
We prove a theorem concerning the Noether symmetries for the area minimizing Lagrangian under the constraint of a constant volume in an n-dimensional Riemannian space. We illustrate the application of the theorem by a number of examples.
We formulate symmetries in semiclassical Gaussian wave packet dynamics and find the corresponding conserved quantities, particularly the semiclassical angular momentum, via Noether's theorem. We consider two slightly different formulations…
An infinite sequence of commuting nonpolynomial contact symmetries of the two-dimensional minimal surface equation is constructed. Local and nonlocal conservation laws for $n$-dimensional minimal area surface equation are obtained by using…