Related papers: Field equations or conservation laws?
These notes have been triggered by physicist's considerations on (1)'Pre-quantized wave equations' for matter fields, (2) Conservation laws, (3) Gauge Field extensions. All starting from variational principles. These notes do not contain…
A general variational principle of classical fields with a Lagrangian containing the field quantity and its derivatives of up to the N-th order is presented. Noether's theorem is derived. The generalized Hamilton-Jacobi's equation for the…
The field equations in the nonsymmetric gravitational theory are derived from a Lagrangian density using a first-order formalism. Using the general covariance of the Lagrangian density, conservation laws and tensor identities are derived.…
A fundamental tenet of gauge theory is that physical quantities should be gauge-invariant. This prompts the question: can gauge symmetries have physical significance? On one hand, the Noether theorems relate conserved charges to symmetries,…
We consider the issue of correspondence between symmetries and conserved quantities in the class of linear relativistic higher-derivative theories of derived type. In this class of models the wave operator is a polynomial in another…
The recently-developed techniques of Noether analysis of the quantum-group spacetime symmetries of some noncommutative field theories rely on the {\it ad hoc} introduction of some peculiar auxiliary transformation parameters, which appear…
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…
A stochastic version of the Noether Theorem is derived for systems under the action of external random forces. The concept of moment generating functional is employed to describe the symmetry of the stochastic forces. The theorem is applied…
This paper mainly contributes to the extension of Noether's theorem to differential-difference equations. For that purpose, we first investigate the prolongation formula for continuous symmetries, which makes a characteristic representation…
We propose a geometrical treatment of symmetries in non-local field theories, where the non-locality is due to a lack of identification of field arguments in the action. We show that the existence of a symmetry of the action leads to a…
The dynamics of nonlinear conservation laws have long posed fascinating problems. With the introduction of some nonlinearity, e.g. Burgers' equation, discontinuous behavior in the solutions is exhibited, even for smooth initial data. The…
Noether's theorem is reviewed with a particular focus on an intermediate step between global and local gauge and coordinate transformations, namely linear transformations. We rederive the well known result that global symmetry leads to…
Noether's first theorem does not establish a one-way explanatory arrow from symmetries to conservation laws, but such an arrow is widely assumed in discussions of the theorem in the physics and philosophy literature. It is argued here that…
Conservation principles establish the primacy of potentials over fields in electrodynamics, both classical and quantum. The contrary conclusion that fields are primary is based on the Newtonian concept that forces completely determine…
Based on the analysis of biquaternion quadratic forms of field, it is shown that Maxwell equations arise as a consequence of the principle of conservation of the energy-momentum flow of field in space-time. It turns out that this principle…
We argue that the variational calculus leading to Euler's equations and Noether's theorem can be replaced by equivariance and invariance conditions avoiding the action integral. We also speculate about the origin of Lagrangian theories in…
Being quantized, conserved Noether symmetry functions are represented by Hermitian operators in the space of solutions of the Schrodinger equation, and their mean values are conserved.
Noether symmetry for higher order gravity theory has been explored, with the introduction of an auxiliary variable which gives the only correct quantum desccription of the theory, as shown in a series of earlier papers. The application of…
A general theorem on conservation laws for arbitrary difference equations is proved. The theorem is based on an introduction of an adjoint system related with a given difference system, and it does not require the existence of a difference…
A certain non-Noetherian connection between symmetry and integrability properties of nonlinear field equations in conservation-law form is studied. It is shown that the symmetry condition alone may lead, in a rather straightforward way, to…