Related papers: About Boundary Terms in Higher Order Theories

The causality and stability of a relativistic hydrodynamic theory is shown to require a consensus between, either (i) newer degrees of freedom apart from the fundamental fluid fields, or (ii) a general hydrodynamic frame other than the…

It is proved that for any finite dimensional representation of a prime order group over the field of rational numbers, polynomial invariants of degree at most $3$ separate the orbits. A result providing an upper degree bound for separating…

Classical results of second order parabolic quasi-linear equations always require that the nonlinear terms are controlled by a power of the unknown functions and their first derivatives. We improve the previous results. More precisely, in…

The study of stochastic variational principles involves the problem of constructing fixed-endpoint and adapted variations of semimartingales. We provide a detailed construction of variations of semimartingales that are not only fixed at…

The covariant phase space method of Iyer, Lee, Wald, and Zoupas gives an elegant way to understand the Hamiltonian dynamics of Lagrangian field theories without breaking covariance. The original literature however does not systematically…

After reviewing the Lagrangian-Hamiltonian unified formalism (i.e, the Skinner-Rusk formalism) for higher-order (non-autonomous) dynamical systems, we state a unified geometrical version of the Variational Principles which allows us to…

Is field space infinite? If not, it either loops back on itself or ends altogether. Periodic boundary conditions are of course familiar, but field space endpoints--which appear in real-world systems--are far less explored. In this paper we…

Currently available models for spatial extremes suffer either from inflexibility in the dependence structures that they can capture, lack of scalability to high dimensions, or in most cases, both of these. We present an approach to spatial…

The Weiss variational principle in mechanics and classical field theory is a variational principle which allows displacements of the boundary. We review the Weiss variation in mechanics and classical field theory, and present a novel…

We consider some possible approaches to the fractional-order generalization of definition of variation (functional) derivative. Some problems of formulation of a fractional-order variational derivative are discussed. To give a consistent…

We extend the lattice gauge theory-type derivation of the Barrett-Crane spin foam model for quantum gravity to other choices of boundary conditions, resulting in different boundary terms, and re-analyze the gluing of 4-simplices in this…

Cobordism invariance shows that the index, in K-theory, of a family of pseudodifferential operators on the boundary of a fibration vanishes if the symbol family extends to be elliptic across the whole fibration. For Dirac operators with…

Motivated by recent developments in Hamiltonian variational principles, Hamiltonian variational integrators, and their applications such as to optimization and control, we present a new Type II variational approach for Hamiltonian systems,…

In General Relativity and gauge field theory, one often encounters a claim, which may be called the boundary problem, according to which "boundaries break diffeomorphism and gauge symmetries". We argue that this statement has the same…

Higher-order quantum theory is an extension of quantum theory where one introduces transformations whose input and output are transformations, thus generalizing the notion of channels and quantum operations. The generalization then goes…

A variational method is discussed, extending the Gaussian effective potential to higher orders. The single variational parameter is replaced by trial unknown two-point functions, with infinite variational parameters to be optimized by the…

The fact that quantum theory is non-differentiable, while general relativity is built on the assumption of differentiability sources an incompatibility between quantum theory and gravity. Higher order geometry addresses this issue directly…

Existential rules are a positive fragment of first-order logic that generalizes function-free Horn rules by allowing existentially quantified variables in rule heads. This family of languages has recently attracted significant interest in…

We discuss boundary conditions for conformal field theories that preserve the boundary Poincare invariance. As in the bulk field theories, a question arises whether boundary scale invariance leads to boundary conformal invariance. With…

We study Hadamard variations with respect to general domain perturbations, particularly for the Neumann boundary condition. They are derived from new Liouville's formulae concerning the transformation of volume and area integrals. Then,…