Related papers: Gauge Symmetries and Noether Currents in Optimal C…
We formulate gauge invariance for the equilibrium statistical mechanics of classical multi-component systems. Species-resolved phase space shifting constitutes a gauge transformation which we analyze using Noether's theorem and shifting…
For nonsmooth Euler-Lagrange extremals, Noether's conservation laws cease to be valid. We show that Emmy Noether's theorem of the calculus of variations is still valid in the wider class of Lipschitz functions, as long as one restrict the…
We consider Noether symmetries of the equations defined by the sections of characteristic line bundles of nondegenerate 1-forms and of the associated perturbed systems. It appears that this framework can be used for time-dependent systems…
An optimal control problem with a time-parameter is considered. The functional to be optimized includes the maximum over time-horizon reached by a function of the state variable, and so an $L^\infty$-term. In addition to the classical…
This paper develops numerical methods for optimal control of mechanical systems in the Lagrangian setting. It extends the theory of discrete mechanics to enable the solutions of optimal control problems through the discretization of…
Recently, a number of new Ward identities for large gauge transformations and large diffeomorphisms have been discovered. Some of the identities are reinterpretations of previously known statements, while some appear to be genuinely new. We…
Why is gauge symmetry so important in modern physics, given that one must eliminate it when interpreting what the theory represents? In this paper we discuss the sense in which gauge symmetry can be fruitfully applied to constrain the space…
We begin an investigation of supersymmetric theories based on exceptional groups. The flat directions are most easily parameterized using their correspondence with gauge invariant polynomials. Symmetries and holomorphy tightly constrain the…
Noether's 2nd theorem applied to a total system states that a global symmetry which is a part of local symmetries does not provide a physically meaningful conserved charge but it instead leads to off-shell constraints as a form of conserved…
A geometric setup for control theory is presented. The argument is developed through the study of the extremals of action functionals defined on piecewise differentiable curves, in the presence of differentiable non-holonomic constraints.…
We consider a family of optimal control problems where the control variable is given by a boundary condition of Neumann type. This family is governed by parabolic variational inequalities of the second kind. We prove the strong convergence…
We embark on a systematic study of continuous non-invertible symmetries, focusing on 1+1d CFTs. We describe a generalized version of Noether's theorem, where continuous non-invertible symmetries are associated to $\textit{non-local}$…
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…
In this work, we study an optimal control problem for a multi-agent system modeled by an undirected formation graph with nodes describing the kinematics of each agent, given by a left-invariant control system on a Lie group. The agents…
It is broadly known that Lie point symmetries and their subcase, Noether symmetries, can be used as a geometric criterion to select alternative theories of gravity. Here, we use Noether symmetries as a selection criterion to distinguish…
The paper discusses the mathematical consequences of the application of derived variables in gauge fields. Physics is aware of several phenomena, which depend first of all on velocities (like e.g., the force caused by charges moving in a…
The first and second Noether theorems are formulated in a general case of reducible degenerate Grassmann-graded Lagrangian theory of even and odd variables on graded bundles. Such Lagrangian theory is characterized by a hierarchy of…
Using a generalised Noether prescription we are able to extract all the currents and their conservation laws in space dependent shift symmetric theories. Various identities among the currents in the matter sector are found that form the…
A coordinate-free proof of the Maximum Principle is provided in the specific case of an optimal control problem with fixed time. Our treatment heavily relies on a special notion of variation of curves that consist of a concatenation of…
We exhibit two symmetries of one-dimensional Newtonian mechanics whereby a solution is built from the history of another solution via a generally nonlinear and complex potential-dependent transformation of the time. One symmetry intertwines…