Related papers: Modified Hamiltonian formalism for higher-derivati…
We analyze a singular theory with first class constraints of an arbitrary stage. Relation among the formulations of the constrained system in terms of complete and extended Hamiltonians is clarified. We replace the extended Hamiltonian…
We study the Hamiltonian formalism for second order and fourth order nonlinear Schr\"{o}dinger equations. In the case of second order equation, we consider cubic and logarithmic nonlinearities. Since the Lagrangians generating these…
We consider all degenerate scalar-tensor theories that depend quadratically on second order derivatives of a scalar field, which we have identified in a previous work. These theories, whose degeneracy in general ensures the absence of…
Newtons second law, Schrodingers equation and Maxwells equations are all theories composed of at most second-time derivatives. Indeed, it is not often we need to take the time derivative of the acceleration. So why are we not seeing more…
Lagrangians for massive, unconstrained, higher-spin bosons and fermions are proposed. The idea is to modify the geometric, gauge invariant Lagrangians describing the corresponding massless theories by the addition of suitable quadratic…
The main goal of these lectures is to introduce and review the Hamiltonian formalism for classical constrained systems and in particular gauge theories. Emphasis is put on the relation between local symmetries and constraints and on the…
A discussion of Lagrangian and Hamiltonian dynamics is presented at a level which should be suitable for advanced high school students. This is intended for those who wish to explore a version of mechanics beyond the usual Newtonian…
The purpose of this article is to initiate a study of a class of Lorentz invariant, yet tractable, Lagrangian Field Theories which may be viewed as an extension of the Klein-Gordon Lagrangian to many scalar fields in a novel manner. These…
Recently the Hamilton-Jacobi formulation for first order constrained systems has been developed. In such formalism the equations of motion are written as total differential equations in many variables. We generalize the Hamilton-Jacobi…
This work is devoted to giving a geometric framework for describing higher-order non-autonomous mechanical systems. The starting point is to extend the Lagrangian-Hamiltonian unified formalism of Skinner and Rusk for these kinds of systems,…
The fractional Hamiltonian analysis of 1+1 dimensional field theory is investigated and the fractional Ostrogradski's formulation is obtained. The fractional path integral of both simple harmonic oscillator with an acceleration-squares part…
The multiplicative Lagrangian and Hamiltonian introduce an additional parameter that, despite its variation, results in identical equations of motion as those derived from the standard Lagrangian. This intriguing property becomes even more…
In some previous papers, a Legendre duality between Lagrangian and Hamiltonian Mechanics has been developed. The (\rho,\eta)-tangent application of the Legendre bundle morphism associated to a Lagrangian L or Hamiltonian H is presented.…
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…
In previous papers, a geometric framework has been developed to describe non-conservative field theories as a kind of modified Lagrangian and Hamiltonian field theories. This approach is that of $k$-contact Hamiltonian systems, which is…
In the jet bundle description of Field Theories (multisymplectic models, in particular), there are several choices for the multimomentum bundle where the covariant Hamiltonian formalism takes place. As a consequence, several proposals for…
A general formalism for obtaining the Lagrangian and Hamiltonian for a one dimensional dissipative system is developed. The formalism is illustrated by applying it to the case of a relativistic particle with linear dissipation. The…
Lepage's improvement scheme is a recent major progress in lattice $QCD$, allowing to obtain continuum physics on very coarse lattices. Here we discuss improvement in the Hamiltonian formulation, and we derive an improved Hamiltonian from a…
The Hamilton theories for higher orders classical Lagrange functions result on a well known Ostrogradski's instabilities. In this work, we propose a different definition for the second order canonical momentum and obtain a new set of second…
We present both the Lagrangian and Hamiltonian procedures for treating higher-order equations of motion for mechanical models by adopting the Riemann-Liouville Fractional integral to describe their action. We point out and discuss its…