Related papers: Canonical Lie-transform method in Hamiltonian gyro…
We present a new variational principle for the gyrokinetic system, similar to the Maxwell-Vlasov action presented in Ref. 1. The variational principle is in the Eulerian frame and based on constrained variations of the phase space fluid…
It is most common to construct the Hamiltonian function and Hamilton's canonical equations through a Legendre transformation of the Lagrangean function or through the central equation. These common perspectives, however, seem abstract and…
A covariant Hamiltonian description was introduced in the dynamics of charges and electromagnetic interaction. By a canonical transformation this Hamiltonian formalism was transformed to obtain the Dirac generators for any form of…
We present a new approach for numerical solutions of ab initio quantum chemistry systems. The main idea of the approach, which we call canonical diagonalization, is to diagonalize directly the second quantized Hamiltonian by a sequence of…
We present a general formalism for the Hamiltonian description of perturbation theory around any spatially homogeneous spacetime. We employ and refine the Dirac method for constrained systems, which is very well-suited to cosmological…
We review in simple terms the covariant approaches to the canonical formulation of classical relativistic field theories (in particular gauge field theories and general relativity) and we discuss the relationships between these approaches…
In purely non-dissipative systems, Lagrangian and Hamiltonian reduction have proven to be powerful tools for deriving physical models with exact conservation laws. We have discovered a hint that an analogous reduction method exists also for…
This work is a continuation of our previous works concerning linear canonical transformations and phase space representation of quantum theory. It is mainly focused on the description of an approach which allows to establish spinorial…
We construct explicitly the canonical transformation that controls the full dependence (local and non-local) of the vertex functional of a Yang-Mills theory on a background field. After showing that the canonical transformation found is…
The work is devoted to studying some new classical electrodynamics models of interacting charged point particles and the aspects of the quantization via the Dirac procedure related to them. Based on the vacuum field theory no-geometry…
We consider a model of classical noncommutative particle in an external electromagnetic field. For this model, we prove the existence of generalized gauge transformations. Classical dynamics in Hamiltonian and Lagrangian form is discussed,…
A redefinition of the Lagrangian of a multi-particle system in fields reformulates the single-particle, kinetic, and fluid equations governing fluid and plasma dynamics as a single set of generalized Maxwell's equations and Ohm's law for…
We consider classical and quantum mechanics for an extended Heisenberg algebra with additional canonical commutation relations for position and momentum coordinates. In our approach this additional noncommutativity is removed from the…
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…
It has long been recognized that lattice gauge theory formulations, when applied to general relativity, conflict with the invariance of the theory under diffeomorphisms. Additionally, the traditional lattice field theory approach consists…
This work builds on an existing model of discrete canonical evolution and applies it to the general case of a linear dynamical system, i.e., a finite-dimensional system with configuration space isomorphic to $ \mathbb{R}^{q} $ and linear…
We discuss the one-dimensional, general quadratic Hamiltonian and the bi-dimensional charged particle in time-dependent electromagnetic fields through the Lie algebraic approach. Such method consists in finding a set of generators that form…
By means of an analogy with Classical Mechanics and Geometrical Optics, we are able to reduce Lagrangians to a kinetic term only. This form enables us to examine the extended solution set of field theories by finding the geodesics of this…
This work is devoted to review the modern geometric description of the Lagrangian and Hamiltonian formalisms of the Hamilton--Jacobi theory. The relation with the "classical" Hamiltonian approach using canonical transformations is also…
We emphasize the usefulness of the Lie brackets in the context of classical and quantum mechanics. By way of examples we show that many dynamical systems, especially the ones with (gauge) constraints, can equally be treated in their time…