Related papers: Noether's Theorem and its Complement: A Gateway to…
The classical theory of electrodynamics is built upon Maxwell's equations and the concepts of electromagnetic field, force, energy and momentum, which are intimately tied together by Poynting's theorem and the Lorentz force law. Whereas…
We prove that under certain assumptions a partial differential equation can be derived from a variational principle. It is well-known from Noether's theorem that symmetries of a variational functional lead to conservation laws of the…
Invariance theorems in analytical mechanics, such as Noether's theorem, can be adapted to continuum mechanics. For this purpose, it is useful to give a functional representation of the motion and to interpret the groups of invariance with…
We use the Lagrange-Noether methods to derive the conservation laws for models in which matter interacts nonminimally with the gravitational field. The nonminimal coupling function can depend arbitrarily on the gravitational field strength.…
The theorem of Noether dictates that for every continuous symmetry group of an Action the system must possess a conservation law. In this paper we discuss some subgroups of Arnold's labelling symmetry diffeomorphism related to…
Explicit expressions are constructed for a locally conserved vector current associated with a continuous internal symmetry and for energy-momentum and angular-momentum density tensors associated with the Poincar\'e group in field theories…
The Casimir-Polder force is analyzed when an atom is moving at a constant velocity relative to a collection of translationally invariant macroscopic bodies with generic shapes and compositions. The interaction is described within an…
Noether's celebrated theorem associating symmetry and conservation laws in classical field theory is adapted to allow for broken symmetry in geometric mechanics and is shown to play a central role in deriving and understanding the…
Our present understanding of elementary particle interactions is the synergic result of developments of theoretical ideas and of experimental advances that lead to the theory known as the Standard Model of particle physics. Despite the…
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…
How does charge density constrain many-body wavefunctions in nature? The Hohenberg-Kohn theorem for non-relativistic, interacting many-body Schr\"odinger systems is well-known and was proved using \emph{reductio-ad-absurdum}; however, the…
We extend Noether's theorem to the setting of multisymplectic geometry by exhibiting a correspondence between conserved quantities and continuous symmetries on a multi-Hamiltonian system. We show that a homotopy co-momentum map interacts…
In the process of calculating Noether's conservation laws, two sets of integration by parts are performed. Here it is shown why the boundary terms from the first set of integration by parts vanish.
The particles of a classical relativistic gas are supposed to move under the influence of a quasilinear (in the particle four-momenta), self-interacting force inbetween elastic, binary collisions. This force which is completely fixed by the…
Systems of classical continuous particles in the grand canonical ensemble interacting through purely attractive, yet stable, interactions are defined. By a lattice approximation, FKG ferromagnetic inequalities are shown to hold for such…
Quantum entanglement is a concept commonly used with reference to the existence of certain correlations in quantum systems that have no classical interpretation. It is a useful resource to enhance the mutual information of memory channels…
Studying systems where many individual bodies in motion interact with one another is a complex and interesting area. Simple mechanisms that may be determined for biological, chemical, or physical reasons can lead to astonishingly complex…
The quantum dynamics of a subset of interacting bosons in a subspace of fixed particle number is described in terms of symmetrized many-particle states. A suitable partial trace operation over the von Neumann equation of an $N$-particle…
We study the fluctuation electromagnetic interaction in a system of two rotating electrically neutral nonmagnetic particles with allowance for relativistic retardation effect. The particles are assumed to have different temperatures being…
Liquid structure carries deep imprints of an inherent thermal invariance against a spatial transformation of the underlying classical many-body Hamiltonian. At first order in the transformation field the Noether theorem yields the local…