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This paper is a summary of the theory of discrete embeddings introduced in [5]. A discrete embedding is an algebraic procedure associating a numerical scheme to a given ordinary differential equation. Lagrangian systems possess a…
A Lagrangian formulation is constructed for particle interpretations of quantum mechanics, a well-known example of such an interpretation being the Bohm model. The advantages of such a description are that the equations for particle motion,…
I review the use of effective lagrangians in describing the physics beyond the standard model, several theoretical and practical aspects are discussed. It is argued that the only situations where new physics can be observed corresponds to…
This paper concerns the Routh reduction procedure for Lagrangians systems with symmetry. It differs from the existing results on geometric Routh reduction in the fact that no regularity conditions on either the Lagrangian $L$ or the…
A gauge independent method of obtaining the reduced space of constrained dynamical systems is discussed in a purely lagrangian formalism. Implications of gauge fixing are also considered.
Classical mechanical systems with internal constraints will be examined using the extended symplectic formalism of Faddeev-Jackiw. We will derive the generalized brackets of the theory and the corresponding equations of motion. The…
The link between the tratment of singular Lagrangians as field systems and the canonical Hamiltonian approach is studied. It is shown that the singular Lagrangians as field systems are always in exact agreement with the canonical approach…
Effective Lagrangians represent an important, model independent tool for studying physics beyond the Standard Model, via its impact on electroweak scale observables. In particular, two different effective descriptions may be appropriate,…
The aim of the present text is twofold: to provide a compendium of Lagrangian and Hamiltonian geometries and to introduce and investigate new analytical Mechanics: Finslerian, Lagrangian and Hamiltonian. The fundamental equations (or…
This document is an addendum to "One-point remapping of Lagrangian perturbation theory in the mildly non-linear regime of cosmic structure formation" (arXiv:1305.4642).
We discuss that the thermodynamical Legendre transform structure can be retained not only for the arbitrary entropic form but also for the arbitrary form of the energy constraints by following the discussion of Plastino and Plastino. The…
The standard relation between the field momentum and the force is generalized for the system with a field singularity: in addition to the regular force, there appear the singular one. This approach is applied to the description of the…
In this paper, Lagrangian formalisms of Classical Mechanics was deduced on Kaehlerian manifold being geometric model of a generalized Lagrange space.Then, it was given two applications of complex Euler-Lagrange equations on mechanics…
Under conventional Legendre transformation, systems with a non-convex Lagrangian will result in a multi-valued Hamiltonian as a function of conjugate momentum. This causes problems such as non-unitary time evolution of quantum state and…
We discuss the characterization of relative equilibria of Lagrangian systems with symmetry.
A natural geometric framework is proposed, based on ideas of W. M. Tulczyjew, for constructions of dynamics on general algebroids. One obtains formalisms similar to the Lagrangian and the Hamiltonian ones. In contrast with recently studied…
We study the connection between Lagrangian and Hamiltonian descriptions of closed/open dynamics, for a collection of particles with quadratic interaction (closed system) and a sub-collection of particles with linear damping (open system).…
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…
Effective Lagrangians, including those that are spontaneously broken, contain redundant terms. It is shown that the classical equations of motion may be used to simplify the effective Lagrangian, even when quantum loops are to be…
In this paper we show how to compute algorithmically the full set of algebraically independent constraints for singular mechanical and field-theoretical models with polynomial Lagrangians. If a model under consideration is not singular as a…