Related papers: Canonical Gauges in the Path Integral for Parametr…
Ambiguities arising in different approaches (canonical, quasiclassical, path integration) to quantization are discussed by an example of the mechanics of a point-like particle in the Riemannian space (the geodesic dynamics). A way to select…
We study the approach in which independent variables describing gravity are functions of the space-time embedding into a flat space of higher dimension. We formulate a canonical formalism for such a theory in a form, which requires imposing…
This paper presents the general theory of canonical transformations of coordinates in quantum mechanics. First, the theory is developed in the formalism of phase space quantum mechanics. It is shown that by transforming a star-product, when…
Quantum canonical transformations are defined in analogy to classical canonical transformations as changes of the phase space variables which preserve the Dirac bracket structure. In themselves, they are neither unitary nor non-unitary. A…
Although the Hamiltonian formalism is so far favored for quantum computation of lattice gauge theory, the path integral formalism would never be useless. The advantages of the path integral formalism are the knowledge and experience…
While there does not at this time exist a complete canonical theory of full 3+1 quantum gravity, there does appear to be a satisfactory canonical quantization of minisuperspace models. The method requires no `choice of time variable' and…
Systems with singular higher order- Lagrangians are investigated by using the extended form of the canonical method. Besides, the canonical path integral formulation is generalized using the Hamilton- jacobi formulation to investigate…
Following Dirac, the rules of canonical quantization include classical and quantum contact transformations of classical and quantum phase space variables. While arbitrary classical canonical coordinate transformations exist that is not the…
Canonical quantization entails using Cartesian coordinates, and Cartesian coordinates exist only in flat spaces. This situation can either be questioned or accepted. In this paper we offer a brief and introductory overview of how a flat…
The Hamiltonian description of classical gauge theories is a very well studied subject. The two best known approaches, namely the covariant and canonical Hamiltonian formalisms have received a lot of attention in the literature. However, a…
Reparametrization invariance being treated as a gauge symmetry shows some specific peculiarities. We study these peculiarities both from a general point of view and on concrete examples. We consider the canonical treatment of…
Starting from the canonical formalism of relativistic (timeless) quantum mechanics, the formulation of timeless path integral is rigorously derived. The transition amplitude is reformulated as the sum, or functional integral, over all…
The Covariant Canonical Gauge theory of Gravity is generalized by including at the Lagrangian level all possible quadratic curvature invariants. In this approach, the covariant Hamiltonian principle and the canonical transformation…
The path integral on a homogeneous space $ G/H $ is constructed, based on the guiding principle `first lift to $ G $ and then project to $ G/H $'. It is then shown that this principle admits inequivalent quantizations inducing a gauge field…
The path integral formulation of quantum mechanics constructs the propagator by evaluating the action S for all classical paths in coordinate space. A corresponding momentum path integral may also be defined through Fourier transforms in…
In this work we address the problem of the quantization of a simple harmonic oscillator that is perturbed by a time dependent force. The approach consists of removing the perturbation by a canonical change of coordinates. Since the…
We investigate the canonical quantization of gravity coupled to pointlike matter in 2+1 dimensions. Starting from the usual point particle action in the first order formalism, we introduce auxiliary variables which make the action locally…
The semiclassical solution of quantum Dirac constraints in generic constrained system is obtained by directly calculating in the one-loop approximation the gauge field path integral with relativistic gauge fixing procedure. The gauge…
The simple physics of a free particle reveals important features of the path-integral formulation of relativistic quantum theories. The exact quantum-mechanical propagator is calculated here for a particle described by the simple…
We address an apparent conflict between the traditional canonical quantization framework of quantum theory and the spatially restricted quantum dynamics, when the translation invariance of the otherwise free quantum system is broken by…