Related papers: Invariant relationships deriving from classical sc…
Symmetry is key in classical and modern physics. A striking example is conservation of energy as a consequence of time-shift invariance from Noether's theorem. Symmetry is likewise a key element in statistics, which, as also physics,…
We study the existence and stability of cosmological scaling solutions of a non-minimally coupled scalar field evolving in either an exponential or inverse power law potential. We show that for inverse power law potentials there exist…
We analyze the relationship of generalized conditional symmetries of evolution equations to the formal compatibility and passivity of systems of differential equations as well as to systems of vector fields in involution. Earlier results on…
We consider the second variational derivative of a given gauge-natural invariant Lagrangian taken with respect to (prolongations of) vertical parts of gauge-natural lifts of infinitesimal principal automorphisms. By requiring such a second…
This paper is purposed to exploit prevalent premises for determining analytical solutions to differential equations formulated from the calculus of variations. we realize this premises from the statement of Emmy Noether's theorem; that…
Scaling symmetries have previously been examined for classical field theories described by singular Lagrangians; in this article, we apply these results to the first-order formulation of General Relativity. It is shown that the dynamical…
Taking into account the characteristics of a free scalar field in elliptic coordinates, a new dynamical variable is found for the free electromagnetic field. The conservation law associated to this variable cannot be obtained by direct…
A description of how the principle of stationary action reproduces itself in terms of the intrinsic geometry of variational equations is proposed. A notion of stationary points of an internal Lagrangian is introduced. A connection between…
Local symmetry transformations play an important role for establishing the existence and form of a conserved (Noether) current in systems with a global continuous symmetry. We explain how this fact leads to the existence of linear relations…
Consistency relations involving the soft limit of the (n + 1)-correlator functions of dark matter and galaxy overdensities can be obtained, both in real and redshift space, thanks to the symmetries enjoyed by the Newtonian equations of…
We derive the equations of nonlinear electroelastostatics using three different variational formulations involving the deformation function and an independent field variable representing the electric character - considering either one of…
Evolution equations which describe the changes in a velocity field over time have been classically studied within the Eulerian or Lagrangian frame of reference. Classically, these frameworks are equivalent descriptions of the same problem,…
Well known biological approximations are universal, i.e. invariant to transformations from one species to another. With no other experimental data, such invariance yields exact conservation (with respect to biological diversity and…
We sketch the main features of the Noether Symmetry Approach, a method to reduce and solve dynamics of physical systems by selecting Noether symmetries, which correspond to conserved quantities. Specifically, we take into account the…
The direct method based on the definition of conserved currents of a system of differential equations is applied to compute the space of conservation laws of the (1+1)-dimensional wave equation in the light-cone coordinates. Then Noether's…
The one-dimensional shallow water equations in Eulerian and Lagrangian coordinates are considered. It is shown the relationship between symmetries and conservation laws in Lagrangian (potential) coordinates and symmetries and conservation…
Scale invariance is a central organizing principle in physics, underlying phenomena that range from critical behaviour in statistical mechanics to transport and chaos in nonlinear dynamical systems. Here we present a unified and physically…
By considering the closure property of a Lagrangian multiform as a conservation law, we use Noether's theorem to show that every variational symmetry of a Lagrangian leads to a Lagrangian multiform. In doing so, we provide a systematic…
The interplay between off-shell and on-shell unfolded systems is analysed. The formulation of invariant constraints that put an off-shell system on shell is developed by adding new variables and derivation in the target space, that extends…
Recently, an extension of the standard four-dimensional scalar conformal action, yielding a second-order field equation that remains conformally invariant, was proposed. In spite of this, the corresponding action is not invariant under…