相关论文: Symmetries, conservation laws, and cohomology of M…
We carry out an extensive investigation of conservation laws and potential symmetries for the class of linear (1+1)-dimensional second-order parabolic equations. The group classification of this class is revised by employing admissible…
Noether's theorem connects symmetries to invariants in continuous systems, however its extension to discrete systems has remained elusive. Recognizing the lowest-order finite difference as the foundation of local continuity, a viable method…
Symmetries and conservation laws are studied for two classes of physically and analytically interesting radial wave equations with power nonlinearities in multi-dimensions. The results consist of two main classifications: all symmetries of…
Classifications of symmetries and conservation laws are presented for a variety of physically and analytically interesting wave equations with power onlinearities in n spatial dimensions: a radial hyperbolic equation, a radial Schrodinger…
A complete and explicit classification of all independent local conservation laws of Maxwell's equations in four dimensional Minkowski space is given. Besides the elementary linear conservation laws, and the well-known quadratic…
Modern physics is largely devoted to study conservation laws, such as charge, energy, linear momentum or angular momentum, because they give us information about the symmetries of our universe. Here, we propose to add the relationship…
It has been proposed that any coupling constant in a covariant action can be treated as a conserved charge by promoting the coupling constant to auxiliary fields, typically realized by a scalar field paired with a higher-form gauge field.…
The conservation laws of electromagnetism, and implicitly all theories built from quadratic Lagrangians, are extended to a continuum of nonlocal versions. These are associated with symmetries of a class of equal time field correlation…
This paper presents recent work on connections between symmetries and conservation laws. After reviewing Noether's theorem and its limitations, we present the Direct Construction Method to show how to find directly the conservation laws for…
We show that the so-called hidden potential symmetries considered in a recent paper [Gandarias M., Physica A, 2008, V.387, 2234-2242] are ordinary potential symmetries that can be obtained using the method introduced by Bluman and…
It's well known that Noether symmetries lead to the conservation laws. Conserved quantities are constructed out of generator of the symmetry - invariant Hamiltonian vector field. Considering more general class of vector fields -…
In the present work, using the recently introduced framework of local geometric deformations, special types of vector fields - so-called hidden Killing vector fields - are constructed, which solve the Killing equation not globally, but only…
We discuss nonlocal symmetries and nonlocal conservation laws that follow from the systematic potentialisation of evolution equations. Those are the Lie point symmetries of the auxiliary systems, also known as potential symmetries. We…
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…
Symmetries and conservation laws are studied for a generalized Westervelt equation which is a nonlinear partial differential equation modelling the propagation of sound waves in a compressible medium. This nonlinear wave equation is widely…
The dual symmetry between electric and magnetic fields is an important intrinsic property of Maxwell equations in free space. This symmetry underlies the conservation of optical helicity, and, as we show here, is closely related to the…
Einstein-Maxwell theory is not only covariant under diffeomorphisms but also is under $U(1)$ gauge transformations. We introduce a combined transformation constructed out of diffeomorphism and $U(1)$ gauge transformation. We show that…
Symmetry, which describes invariance, is an eternal concern in mathematics and physics, especially in the investigation of solutions to the partial differential equation (PDE). A PDE's nonlocally related PDE systems provide excellent…
The construction of a theory of quantum gravity is an outstanding problem that can benefit from better understanding the laws of nature that are expected to hold in regimes currently inaccessible to experiment. Such fundamental laws can be…
Maxwell's equations are considered in metric-free form, with a local but otherwise arbitrary constitutive law. After splitting Maxwell's equations into evolution equations and constraints, we derive the characteristic equation and we…