Related papers: Practical Introduction to Action-Dependent Field T…

We describe geometrically contact Lagrangian systems under impulsive forces and constraints, as well as instantaneous nonholonomic constraints which are not uniform along the configuration space. In both situations, the vector field…

In this short note we show that any action for $N$ interacting particles can be made invariant under gauged Galilean transformations. While resulting Lagrangian is generally very complicated its Hamiltonian has simple form with first class…

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…

Massive integrable field theories in $1+1$ dimensions are defined at the Lagrangian level, whose classical equations of motion are related to the ``non-abelian'' Toda field equations. They can be thought of as generalizations of the…

The Lagrangian of self-dual gauge theory in various formulations are reviewed. From these results we see a simple rule and use it to present some new non-covariant Lagrangian based on the decomposition of spacetime into $D=D_1+D_2+D_3$. Our…

Many applications in Lattice field theory require to determine the Taylor series of observables with respect to action parameters. A primary example is the determination of electromagnetic corrections to hadronic processes. We show two…

This paper studies nonlinear deformations of the linear gauge theory of any number of spin-2 and spin-3/2 fields with general formal multiplication rules in place of standard Grassmann rules for manipulating the fields, in four spacetime…

It is widely accepted that the fundamental geometrical law of nature should follow from an action principle. The particular subset of transformations of a system's dynamical variables that maintain the form of the action principle comprises…

We generalize the known equivalence between higher order gravity theories and scalar tensor theories to a new class of theories. Specifically, in the context of a first order or Palatini variational principle where the metric and connection…

In this article, we analyze the Pontryagin model adopting different geometric-covariant approaches. In particular, we focus on the manner in which boundary conditions must be imposed on the background manifold in order to reproduce an…

In this article one introduces a formalism of classical mechanics where complex Lagrangian functions are admitted. The results include complex versions of the Lagrangian function, of the Euler-Lagrange equation, of the Hamilton principle, a…

We perform a Hamiltonian analysis of a large class of scalar-tensor Lagrangians which depend quadratically on the second derivatives of a scalar field. By resorting to a convenient choice of dynamical variables, we show that the Hamiltonian…

We shall here consider extended theories of gravitation in the metric-affine formalism with matter coupled directly to the connection. A sufficiently general procedure will be exhibited to solve the resulting field equation associated to…

In this work we analyze systems described by Lagrangians with higher order derivatives in the context of the Hamilton-Jacobi formalism for first order actions. Two different approaches are studied here: the first one is analogous to the…

Field theories for complex systems traditionally focus on collective behaviors emerging from simple, reciprocal pairwise interaction rules. However, many natural and artificial systems exhibit behaviors driven by microscopic decision-making…

We present a direct approach to the construction of Lagrangians for a large class of one-dimensional dynamical systems with a simple dependence (monomial or polynomial) on the velocity. We rederive and generalize some recent results and…

For classical field theories with probabilistic initial conditions the classical field observables are an idealization. Their arbitrarily precise values poorly reflect the characteristic uncertainty in the presence of substantial…

We present some generic arguments demonstrating that an effective Lagrangian $L_{eff}$ which, by definition, contains operators $O^n$ of arbitrary dimensionality in general is not convergent, but rather an asymptotic series. It means that…

An axiomatic quantum field theory applied to the self-interacting boson field is realised in terms of generalised operators that allows us to form products and take derivatives of the fields in simple and mathematically rigorous ways.…

A formulation of singular classical theories (determined by degenerate Lagrangians) without constraints is presented. A partial Hamiltonian formalism in the phase space having an initially arbitrary number of momenta (which can be smaller…