Related papers: Reduced phase space: quotienting procedure for gau…
The system of two-dimensional damped harmonic oscillator is revisited in the extended phase space. It is an old problem already addressed by many authors that we present here in some fresh points of view and carry on smoothly a whole…
We discuss a general prototypical constrained Hamiltonian system with a broad application in quantum field theory and similar contexts where dynamics is defined through a functional action obeying a stationarity principle. The prototypical…
We argue that the field-parametrization dependence of Dirac's procedure, for Hamiltonians with first-class constraints not only preserves covariance in covariant theories, but in non-covariant gauge theories it allows one to find the…
Dirac formalism of Hamiltonian constraint systems is studied for the noncommutative Abelian Proca field. It is shown that the system of constraints are of second class in agreement with the fact that the Proca field is not guage invariant.…
These are pedagogical notes on the Hamiltonian formulation of constrained dynamical systems. All the examples are finite dimensional, field theories are not covered, and the notes could be used by students for a preliminary study before the…
We extend a previously successful discussion of the constrained Schr\"{o}dinger system through the Dirac--Bergmann algorithm to the case of the Dirac field. In order to follow the analogy, first we discuss the classical Dirac field as a…
Relevant physical models are described by singular Lagrangians, so that their Hamiltonian description is based on the Dirac theory of constraints. The qualitative aspects of this theory are now understood, in particular the role of the…
Quantum Dirac constraints in generic constrained system are solved by directly calculating in the one-loop approximation the path integral with relativistic gauge fixing procedure. The calculations are based on the reduction algorithms for…
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…
Geometrical interpretation on U(1) gage theory of Dirac monopole, introduced here from the line integral\cite{Brandt} form of vector potentials, shows the gauge representation be multi-valued. In this paper, we construct Euclidean form of…
Recently, there were works claiming that path integral quantisation of gauge theories necessarily requires relaxation of Lagrangian constraints. As has also been noted in the literature, it is of course wrong since there perfectly exist…
We apply newly improved Batalin-Fradkin-Tyutin Hamiltonian method to the chiral Schwinger Model in the case of the regularization ambiguity $a>1$. We show that one can systematically construct the first class constraints by the BFT…
We consider the problem of constrained motion along a conic path under a given external potential function. The model is described as a second-class system capturing the behavior of a certain class of specific quantum field theories. By…
Dirac's quantization of the Maxwell theory on non-commutative spaces has been considered. First class constraints were found which are the same as in classical electrodynamics. The gauge covariant quantization of the non-linear equations of…
We develop a complete Hamiltonian approach to the theory of perturbations around any spatially homogeneous spacetime. We employ the Dirac method for constrained systems which is well-suited to cosmological perturbations. We refine the…
Motivated by certain concepts introduced by the Refined Algebraic Quantization formalism for constrained systems which has been successfully applied within the context of Loop Quantum Gravity, in this paper we propose a phase space…
We examine two singular Lagrangian systems with constraints which apparently reduce the phase space to a 2-dimensional sphere and a 2-dimensional hyperboloid. Rigorous constraint analysis by Dirac's method, however, gives 2-dimensional open…
We use Dirac's method for the quantization of constrained systems in order to quantize a spatially flat Friedmann-Lema\^{i}tre-Robertson-Walker spacetime in the context of $f(Q)$ cosmology. When the coincident gauge is considered, the…
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,…
A standard tenet of canonical quantum gravity is that evolution generated by a Hamiltonian constraint is just a gauge transformation on the phase space and therefore does not change the physical state. The basis for this belief is a theorem…