Related papers: Lagrange-Poincare field equations
A general variational principle of classical fields with a Lagrangian containing the field quantity and its derivatives of up to the N-th order is presented. Noether's theorem is derived. The generalized Hamilton-Jacobi's equation for the…
Classical point-particle relativistic lagrangians are constructed that generate the momentum-velocity and dispersion relations for quantum wave packets in Lorentz-violating effective field theory.
The analytic continuation to an imaginary velocity of the canonical partition function of a thermal system expressed in a moving frame has a natural implementation in the Euclidean path-integral formulation in terms of shifted boundary…
The Universal Field Equations, recently constructed as examples of higher dimensional dynamical systems which admit an infinity of inequivalent Lagrangians are shown to be linearised by a Legendre transformation. This establishes the…
An invertible field transformation is such that the old field variables correspond one-to-one to the new variables. As such, one may think that two systems that are related by an invertible transformation are physically equivalent. However,…
Classical field theory is considered as a theory of unparametrized surfaces embedded in a configuration space, which accommodates, in a symmetric way, spacetime positions and field values. Dynamics is defined via the (Hamiltonian)…
We present an old and regretfully forgotten method by Jacobi which allows one to find many Lagrangians of simple classical models and also of nonconservative systems. We underline that the knowledge of Lie symmetries generates Jacobi last…
In this note, we develop a theory of Euler-Poincare reduction for discrete Lagrangian field theories. We introduce the concept of Euler-Poincare equations for discrete field theories, as well as a natural extension of the Moser-Veselov…
A mechanical covariant equation is introduced which retains all the effectingness of the Lagrange equation while being able to describe in a unified way other phenomena including friction, non-holonomic constraints and energy radiation…
We develop a reduction theory for $G$-invariant Lagrangian field theories defined on the higher-order jet bundle of a principal $G$-bundle, thus obtaining the higher-order Euler-Poincar\'e field equations. To that end, we transfer the…
Essential properties of semiclassical approximation for quantum mechanics are viewed as axioms of an abstract semiclassical mechanics. Its symmetry properties are discussed. Semiclassical systems being invariant under Lie groups are…
Using supervector fields and graded forms along a morphism, we study the geometry of ordinary differential superequations, extend the formalism of higher order Lagrangian mechanics to the graded context and prove a generalization of…
A theoretical scheme, based on a probabilistic generalization of the Hamilton's principle, is elaborated to obtain an unified description of more general dynamical behaviors determined both from a lagrangian function and by mechanisms not…
A discrete version of Lagrangian reduction is developed in the context of discrete time Lagrangian systems on $G\times G$, where $G$ is a Lie group. We consider the case when the Lagrange function is invariant with respect to the action of…
Relativistic field theory for a vector field on a curved space-time is considered assuming that the Lagrangian field density is quadratic and contains field derivatives of first order at most. By applying standard variational calculus, the…
We define a new algebraic extension of the Poincar\'e symmetry; this algebra is used to implement a field theoretical model. Free Lagrangians are explicitly constructed; several discussions regarding degrees of freedom, compatibility with…
A class of generalized Galileon cosmological models, which can be described by a point-like Lagrangian, is considered in order to utilize Noether's Theorem to determine conservation laws for the field equations. In the…
The symmetry properties of a proposal to go beyond relativistic quantum field theory based on a modification of the commutation relations of fields are identified. Poincar\'e invariance in an auxiliary spacetime is found in the Lagrangian…
The Noether theorem connecting symmetries and conservation laws can be applied directly in a Hamiltonian framework without using any intermediate Lagrangian formulation. This requires a careful discussion about the invariance of the…
In this paper we use Lagrange-Poincare reduction to understand the coupling between a fluid and a set of Lagrangian particles that are supposed to simulate it. In particular, we reinterpret the work of Cendra et al. by substituting velocity…