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Under certain assumptions (such as weak exacteness or monotonicity) we show that splitting Lagrangians through cobordism has an energy cost and, from this cost being smaller than certain explicit bounds, we deduce some strong forms of…

An additive fast Fourier transform over a finite field of characteristic two efficiently evaluates polynomials at every element of an $\mathbb{F}_2$-linear subspace of the field. We view these transforms as performing a change of basis from…

The theory of gauge fields in Theoretical Physics poses several mathematical problems of interest in Differential Geometry and in Field Theory. Below we tackle one of these problems: The existence of a finite system of generators of…

We consider a self-interacting scalar field theory in a slowly varying gravitational background field. Using zeta-function regularization and heat-kernel techniques, we derive the one-loop effective Lagrangian up to second order in the…

We discuss continuous duality transformations and the properties of classical theories with invariant interactions between electromagnetic fields and matter. The case of scalar fields is treated in some detail. Special discrete elements of…

Examples of the construction of Hamiltonian structures for dynamical systems in field theory (including one reputedly non-Hamiltonian problem) without using Lagrangians, are presented. The recently developed method used requires the…

The task of finding a consistent relationship between a quantum Hamiltonian and a classical Lagrangian is of utmost importance for basic, but ubiquitous techniques like canonical quantization and path integrals. Nonconvex kinetic energies…

The variational formalism for classical field theories is extended to the setting of Lie algebroids. Given a Lagrangian function we study the problem of finding critical points of the action functional when we restrict the fields to be…

There exists in nature many examples of systems presenting self-limiting behaviour: population dynamics, structure engineering, Townsend's electron breakdown, nuclear decay in radioactive equilibrium, histeresis process, meteorological…

In this paper, to fit the multi-scale perturbations, the single-parameter Lie transform perturbation theory given in [Ann Phys, 151 1 (1983)] is generalized to a multi-parameter case, which provides a formal solution of the new Lagrangian…

An alternative class of the Lagrangian called the multiplicative form is suc- cessfully derived for a system with one degree of freedom for both non-relativistic and relativistic cases. This new Lagrangian can be considered as a…

We present a foliation-focused critical review of the boundary conditions and dynamics of 4D gravitational theories. A general coordinate transformation introduces a new foliation and changes the hypersurface on which a natural boundary…

Hierarchies of Lagrangians of degree two, each only partly determined by the choice of leading terms and with some coefficients remaining free, are considered. The free coefficients they contain satisfy the most general differential…

Using effective-lagrangian techniques we perform a systematic survey of the lowest-dimension effective interactions through which heavy physics might manifest itself in present experiments. We do not restrict ourselves to special classes of…

Using Lie symmetry methods for differential equations we have investigated the symmetries of a Lagrangian for a plane symmetric static spacetime. Perturbing this Lagrangian we explore its approximate symmetries. It has a non-trivial…

We consider a simple modification of standard phase-space path integrals and show that it leads in configuration space to Lagrangians depending also on accelerations.

The study of mechanical systems on Lie algebroids permits an understanding of the dynamics described by a Lagrangian or Hamiltonian function for a wide range of mechanical systems in a unified framework. Systems defined in tangent bundles,…

Searching for a Lagrangian may seem either a trivial endeavour or an impossible task. In this paper we show that the Jacobi last multiplier associated with the Lie symmetries admitted by simple models of classical mechanics produces (too?)…

We give a Lagrangian description of an electric charge in a field sourced by a continuous magnetic monopole distribution. The description is made possible thanks to a doubling of the configuration space. The Legendre transform of the…

Here we consider scale invariant dynamical systems within a classical particle description of Lagrangian mechanics. We begin by showing the condition under which a spatial and temporal scale transformation of such a system can lead to a…