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The minimal Hamiltonian for a family of relativistic rotators is constructed by a direct application of the Dirac procedure for constrained systems. The Hamiltonian equations can be easily solved. It is found that the resulting motion is…
We present a novel framework for quantizing constrained quantum systems in which the processes of quantization and constraint enforcement are performed simultaneously. The approach is based on an extension of the stationary action…
The Dirac-Bergmann algorithm is a recipe for converting a theory with a singular Lagrangian into a constrained Hamiltonian system. Constrained Hamiltonian systems include gauge theories -- general relativity, electromagnetism, Yang Mills,…
We analyze the canonical treatment of classical constrained mechanical systems formulated with a discrete time. We prove that under very general conditions, it is possible to introduce nonsingular canonical transformations that preserve the…
We constructed a symplectic realization of the dynamic structure of two interacting spin-two fields in three dimensions. A significant simplification refers to the treatment of constraints: instead of performing a Hamiltonian analysis…
Lie-Poisson gauge formalism provides a semiclassical description of noncommutative $U(1)$ gauge theory with Lie algebra type noncommutativity. Using the Dirac approach to constrained Hamiltonian systems, we focus on a class of Lie-Poisson…
The Hamilton-Jacobi formalism of constrained systems is used to study superstring. That obtained the equations of motion for a singular system as total differential equations in many variables. These equations of motion are in exact…
Open quantum systems are traditionally described by decomposing the total Hilbert space into a system and an external environment, linked by an explicit interaction Hamiltonian. We propose an alternative framework in which the environment…
We propose a systematic procedure that solves the Dirac bracket commutators. The method is based on the Gauge Unfixing formalism, a procedure that converts second class systems into first class ones without the enlargement of the original…
Hamiltonian systems with functionally dependent constraints (irregular systems), for which the standard Dirac procedure is not directly applicable, are discussed. They are classified according to their behavior in the vicinity of the…
A new framework for deriving equations of motion for constrained quantum systems is introduced, and a procedure for its implementation is outlined. In special cases the framework reduces to a quantum analogue of the Dirac theory of…
We present a pseudoclassical mechanics model which exhibits gauge symmetry and time-reparametrization invariance. As such, first- and second-class constraints restrict the phase space, and the Hamiltonian weakly vanishes. We show that the…
New features of a previously introduced Group Approach to Quantization are presented. We show that the construction of the symmetry group associated with the system to be quantized (the "quantizing group") does not require, in general, the…
An elementary presentation of the methods for the canonical quantization of constraint systems with Fermi variables is given. The emphasis is on the subtleties of the construction of an appropriate classical bracket that could be…
The Dirac method of quantizing Hamiltonian systems with constraints is applied to the massless Thirring model. We solve the quantum Hamiltonian equation for the energy-momentum tensor and obtain a violation of the classical conservation…
Systems under holonomic constraints are classified within the generalized Hamiltonian framework as second-class constraints systems. We show that each system of point particles with holonomic constraints has a hidden gauge symmetry which…
The Yukawa Model is revisited in one space - one time dimensions in an approach completely different to those available in the literature. We show that at the classical level it is a constrained system. We apply the Dirac method of…
A quantum phase space version of the continuity equation for systems with internal degrees of freedom is derived. The $1$ -- D Dirac equation is introduced and its phase space counterpart is found. The phase space representation of free…
This is a collection of lectures given at the University of Heidelberg, especially but not exclusively for people who want to learn something about the canonical approach to quantum gravity, which is however not included in these lectures.…
We outline the principal results of a recent examination of the quantization of systems with first- and second-class constraints from the point of view of coherent-state phase-space path integration. Two examples serve to illustrate the…