Related papers: Conserved quantities on multisymplectic manifolds
A geometric framework, called multicontact geometry, has recently been developed to study action-dependent field theories. In this work, we use this framework to analyze symmetries in action-dependent Lagrangian and Hamiltonian field…
We consider general relativity with cosmological constant minimally coupled to the electromagnetic field and assume that the four-dimensional space-time manifold is a warped product of two surfaces with Lorentzian and Euclidean signature…
In this work we show the equivalence between Hamiltonian mechanics and conservation of information entropy. We will show that distributions with coordinate independent values for information entropy require that the manifold on which the…
We study the space of pseudo-holomorphic spheres in compact symplectic manifolds with convex boundary. We show that the theory of Gromov-Witten invariants can be extended to the class of semi-positive manifolds with convex boundary. This…
We identify a conserved quantity in continuous-time optimization dynamics, termed computational inertia. Defined as the sum of kinetic energy (parameter velocity) and potential energy (loss), this scalar remains invariant under idealized,…
In the classical Lagrangian approach to conservation laws of gauge-natural field theories a suitable (vector) density is known to generate the so--called {\em conserved Noether currents}. It turns out that along any section of the relevant…
We provide a variational description of any Liouville (i.e. volume preserving) autonomous vector fields on a smooth manifold. This is obtained via a ``maximal degree'' variational principle; critical sections for this are integral manifolds…
Consider a compact prequantizable symplectic manifold M on which a compact Lie group G acts in a Hamiltonian fashion. The ``quantization commutes with reduction'' theorem asserts that the G-invariant part of the equivariant index of M is…
It is well-known that considerations of symmetry lead to the definition of a host of conserved quantities (energy, linear momentum, center of mass, etc.) for an asymptotically flat initial data set, and a great deal of progress in…
A simple characterization of the action of symmetries on conservation laws of partial differential equations is studied by using the general method of conservation law multipliers. This action is used to define symmetry-invariant and…
We show that the action of spacetime vector fields on the variational bicomplex of general relativity has a homotopy momentum map that extends the map from vector fields to conserved currents given by Noether's first theorem to a morphism…
Given that observations seem to favour a \index{density parameter} $\Omega_0<1$, corresponding to an open universe, we consider gauge\hs invariant perturbations of non\hs flat Robertson\hs Walker universes filled with a general imperfect…
We introduce the process of symplectic reduction along a submanifold as a uniform approach to taking quotients in symplectic geometry. This construction holds in the categories of smooth manifolds, complex analytic spaces, and complex…
In this paper we make use of the concept of conserved geometric phase and of group velocity,in conjunction with the representation theory\cite{Dirac,Dirac-letture}, in order to derive some relevant physical quantities for the description of…
We propose that probability in quantum theory, like energy in general relativity, acquires a fundamentally quasilocal character in curved spacetime. Interpreting Hermiticity as the symmetry associated with inner-product conservation, we…
An explicit determination of all local conservation laws of kinematic type on moving domains and moving surfaces is presented for the Euler equations of inviscid compressible fluid flow on curved Riemannian manifolds in n>1 dimensions. All…
The standard techniques of variational calculus are geometrically stated in the ambient of fiber bundles endowed with a (pre)multisymplectic structure. Then, for the corresponding variational equations, conserved quantities (or, what is…
We present a new approach to the problem of proving global stability, based on symplectic geometry and with a focus on systems with several conserved quantities. We also provide a proof of instability for integrable systems whose momentum…
Let G be an n-dimensional torus and $\tau$ a Hamiltonian action of G on a compact symplectic manifold, M. If M is pre-quantizable one can associate with $\tau$ a representation of G on a virtual vector space, Q(M), by…
General covariance is a crucial notion in the study of field theories in curved spacetime. A field theory defined with respect to a semi-Riemannian metric is generally covariant if two metrics which are related by a diffeomorphism produce…