Related papers: On-shell symmetries
The present paper develops a variational theory of discrete fields defined on abstract cellular complexes. The discrete formulation is derived solely from a variational principle associated to a discrete Lagrangian density on a discrete…
For difference variational problems on lattice, this paper presents a relation between divergence variational symmetries and conservation laws for the associated Euler-Lagrange system provided by Noether's theorem. This hence inspires us to…
We provide new insights into the contact Hamiltonian and Lagrangian formulations of dissipative mechanical systems. In particular, we state a new form of the contact dynamical equations, and we review two recently presented Lagrangian…
The fundamental role of on-shell diagrams in quantum field theory has been recently recognized. On-shell diagrams, or equivalently bipartite graphs, provide a natural bridge connecting gauge theory to powerful mathematical structures such…
Lie symmetries of systems of second-order linear ordinary differential equations with constant coefficients are exhaustively described over both the complex and real fields. The exact lower and upper bounds for the dimensions of the maximal…
The new linear theory of elastic shells is presented in this paper. This theory is free from various logical imperfections, that may be found in the approaches of earlier researchers. On the base of this theory the equations of shells of…
Complex textured surfaces occur in nature and industry, from fingerprints to lithography-based micropatterns. Wrinkling by confinement to an incompatible substrate is an attractive way of generating reconfigurable patterned topographies,…
The Lagrange problem is established in the discrete field theory subject to constraints with values in a Lie group. For the admissible sections that satisfy a certain regularity condition, we prove that the critical sections of such…
This paper is a summary of the theory of discrete embeddings introduced in [5]. A discrete embedding is an algebraic procedure associating a numerical scheme to a given ordinary differential equation. Lagrangian systems possess a…
We discuss the characterization of relative equilibria of Lagrangian systems with symmetry.
We analyze the constraint structure of a spin-3/2 particle interacting with a pseudoscalar. Requiring the self consistency of the considered effective field theory imposes restrictions on the possible interaction terms. In the present case…
Some key features of the symmetries of the Schr\"odinger equation that are common to a much broader class of dynamical systems (some under construction) are illustrated. I discuss the algebra/superalgebra duality involving first and…
A variational structure for the potential AKP system is established using the novel formalism of a Lagrangian multiforms. The structure comprises not only the fully discrete equation on the 3D lattice, but also its semi-discrete variants…
We study the structure and dynamics of the infinite sequence of extensions of the Poincar{\'e} algebra whose method of construction was described in a previous paper [1]. We give explicitly the Maurer-Cartan (MC) 1-forms of the extended Lie…
We study the theory of a (global) texture with DBI-like Lagrangian, the higher-dimensional generalization of the previously known chiral Born-Infeld theory. This model evades Derrick's theorem and enables the existence of solitonic…
Pluri-Lagrangian systems are variational systems with the multi-dimensional consistency property. This notion has its roots in the theory of pluriharmonic functions, in the Z-invariant models of statistical mechanics, in the theory of…
We present examples of Lax-integrable multi-dimensional systems of partial differential equations with higher local symmetries. We also consider Lagrangian deformations of these equations and construct variational bivectors on them.
We elucidate consistency of the so-called corner equations which are elementary building blocks of Euler-Lagrange equations for two-dimensional pluri-Lagrangian problems. We show that their consistency can be derived from the existence of…
In the framework of polysymplectic Hamiltonian formalism, degenerate Lagrangian field systems are described as multi-Hamiltonian systems with Lagrangian constraints. The physically relevant case of degenerate quadratic Lagrangians is…
These are intended to be review notes on emergent symmetries, i.e., symmetries which manifest themselves in specific sectors of energy in many systems. The emphasis is on the physical aspects rather than computation methods. We include some…