Related papers: The Lagrangian and Hamiltonian formalisms for the …
We present an approach to the canonical quantization of systems with equations of motion that are historically called non-Lagrangian equations. Our viewpoint of this problem is the following: despite the fact that a set of differential…
The constrained Hamiltonian systems admitting no gauge conditions are considered. The methods to deal with such systems are discussed and developed. As a concrete application, the relationship between the Dirac and reduced phase space…
Collective center-of-mass variables are introduced in the Lagrangian formalism of the relativistic classical mechanics of directly interacting particles. It is shown that the transition to the Hamiltonian formalism leads to the…
In this work, we have studied classical and quantum systems in interaction by means of geometric reduction procedure. The main target is the description in these terms of fundamental interactions. We have shown that, to describe in a…
The hypothesis is suggested that the equation for the Dirac free wave field is, in fact, a group-theoretical relation describing propagation of specific microscopic deviations of space geometry from the euclidean one (closed topological…
The problem of ultraviolet divergences is analysed in the quantum field theory. It was found that it has common roots with the problem of cosmological singularity. In the context of fibre bundles the second quantization method is…
The usual canonical Hamiltonian or Lagrangian formalism of classical mechanics applied to macroscopic systems describes energy conserving adiabatic motion. If irreversible diabatic processes are to be included, then the law of increasing…
We present the Dirac Hamiltonian formalism for a pair of $1$-form fields with a topological-like potential coupled to first-order gravity in three-dimensional spacetime. By considering the complete phase space, we derive the full structure…
Connecting ideas of geometric formulation of quantum mechanics with new results in symplectic geometry a new approach to geometrical quantization procedure is proposed. As a first result we verify that the correspondence between "classical"…
Classical physics is reformulated as a constrained Hamiltonian system in the history phase space. Dynamics, i.e. the Euler-Lagrange equations, play the role of first-class constraints. This allows us to apply standard methods from the…
Contact Hamiltonian dynamics is a subject that has still a short history, but with relevant applications in many areas: thermodynamics, cosmology, control theory, and neurogeometry, among others. In recent years there has been a great…
This paper uses elementary techniques drawn from renormalization theory to derive the Lorentz-Dirac equation for the relativistic classical electron from the Maxwell-Lorentz equations for a classical charged particle coupled to the…
In this work we will develop the canonical structure of Podolsky's generalized electrodynamics on the null-plane. This theory has second-order derivatives in the Lagrangian function and requires a closer study for the definition of the…
The application of the Legendre transformation to a hyperregular Lagrangian system results in a Hamiltonian vector field generated by a Hamiltonian defined on the phase space of the mechanical system. The Legendre transformation in its…
The semiclassical approximation for the Hamiltonian of Dirac particles interacting with an arbitrary gravitational field is investigated. The time dependence of the metrics leads to new contributions to the in-band energy operator in…
A "minimal" generalization of Quantum Mechanics is proposed, where the Lagrangian or the action functional is a mapping from the (classical) states of a system to the Lie algebra of a general compact Lie group, and the wave function takes…
We discuss a version of Hamiltonian (2+1)-dimensional dynamics, in which one allows nonvanishing Poisson brackets also between the coordinates, and between the momenta. The resulting equations of motion are not any more derivable from a…
Classical electrodynamics including classical electromagnetic zero-point radiation leads to a ground state and resonant excited states for a charged particle in a Coulomb potential. These resonant states correspond to integer values of the…
The Hamiltonian formulation for the mechanical systems with reparametrization-invariant Lagrangians, depending on the worldline external curvatures is given, which is based on the use of moving frame. A complete sets of constraints are…
A starting point for the present work was the statement recently discussed in the literature that two Hamiltonian formulations for the theory of gravity, the one proposed by Dirac and the other by Arnowitt - Deser - Misner, may not be…