Related papers: Quantization of singular systems with second order…
The canonical method of constrained system is discussed. The equations of motion for a free relativistic spinning particle are obtained without using gauge fixing conditions. The quantization of this model is discussed.
The path integral formulation of quantum mechanics, i.e., the idea that the evolution of a quantum system is determined as a sum over all the possible trajectories that would take the system from the initial to its final state of its…
In this article the methods of canonical analysis and quantization that were reviewed in the first part of the series are applied to the case of the Dirac field in the presence of electromagnetic interaction. It is shown that the…
We continue the study of symmetries in the Lagrangian formalism of arbitrary order with the help of the so-called Anderson-Duchamp-Krupka equations. For the case of second-order equations and arbitrary vector fields we are able to establish…
The purpose of this paper is describe Lagrangian Mechanics for constrained systems on Lie algebroids, a natural framework which covers a wide range of situations (systems on Lie groups, quotients by the action of a Lie group, standard…
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…
A comparative analysis of two different versions of the Legendre transformation is presented. We provide an almost complete although somewhat superficial review of the geometric background for analytical mechanics. Complete coordinate…
The existence of a Lagrangian description for the second-order Riccati equation is analyzed and the results are applied to the study of two different nonlinear systems both related with the generalized Riccati equation. The Lagrangians are…
A path integral (Lagrangian formalism) is used to derive the effective equations of motion of the anomalous Hall effect with Berry's phase on the basis of the adiabatic condition $|E_{n\pm1}-E_{n}|\gg 2\pi\hbar/T$, where $T$ is the typical…
Anti-selfdual Lagrangians on a state space lift to path space provided one adds a suitable selfdual boundary Lagrangian. This process can be iterated by considering the path space as a new state space for the newly obtained anti-selfdual…
The massive non-Abelian gauge fields are quantized Lorentz-covariantly in the Hamiltonian path-integral formalism. In the quantization, the Lorentz condition, as a necessary constraint, is introduced initially and incorporated into the…
Path integrals are a ubiquitous tool in theoretical physics. However, their use is sometimes hindered by the lack of control on various manipulations -- such as performing a change of the integration path -- one would like to carry out in…
We present a new path integral method to analyze stochastically perturbed ordinary differential equations with multiple time scales. The objective of this method is to derive from the original system a new stochastic differential equation…
We show that the ``effective Lagrangian'' constructed in [1] is inconsistent with the exact result for the complete Lagrangian presented in [2]. We trace the origin of the inconsistence to the peculiar way in which the path integral methods…
The Maslov index of a periodic orbit is an important piece in the semiclassical quantization of non-integrable systems, while almost all existing techniques that lead to a rigorous calculation of this index are elaborate and mathematically…
We survey a new approach to the duality-invariant systems of nonlinear electrodynamics, based on introducing auxiliary bi-spinor fields. In this approach, the entire information about the given self-dual system is encoded in the U(1)…
A practical method is developed to deal with the second quantization of the many-body system containing the composite particles. In our treatment, the modes associated with composite particles are regarded approximately as independent ones…
A path-integral approach for the computation of quantum-mechanical propagators and energy Green's functions is presented. Its effectiveness is demonstrated through its application to singular interactions, with particular emphasis on the…
We investigate particle trajectories in equatorial flows with geophysical corrections caused by the earth's rotation. Particle trajectories in the flows are constructed using pairs of analytic functions defined over the labelling space used…
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.