Related papers: Canonical Gauges in the Path Integral for Parametr…
An integrable anharmonic oscillator is presumably simulable by a classical computer and therefore by a quantum computer. An integrable anharmonic oscillator whose Hamiltonian is of normal type and quartic in the canonical coordinates is not…
We derive the first order canonical formulation of cosmological perturbation theory in a Universe filled by a few scalar fields. This theory is quantized via well-defined Hamiltonian path integral. The propagator which describes the…
A careful reexamination of the quantization of systems with first- and second-class constraints from the point of view of coherent-state phase-space path integration reveals several significant distinctions from more conventional…
The path integral approach to quantum mechanics provides a method of quantization of dynamical systems directly from the Lagrange formalism. In field theory the method presents some advantages over Hamiltonian quantization. The Lagrange…
In this paper I raise a worry about the most extended resolutions of the problem of time of canonical quantizations of general relativity. The reason for this is that these resolutions are based on analogies with deparametrizable models for…
This is a review of the aspirations and disappointments of the canonical quantization of geometry. I compare the two chief ways of looking at canonical gravity, geometrodynamics and connection dynamics. I capture as much of the classical…
Any particular classical system and its quantum version are normally viewed as separate formulations that are strictly distinct. Our goal is to overcome the two separate languages and create a smooth and common procedure that provides a…
We present a parameter-free gauge formulation of general relativity in terms of a new set of real spin connection variables. The theory is constructed by extending the phase space of the recently formulated conformal geometrodynamics for…
This article serves as a continuation for the discussion in arXiv:0911.3433, we analyze the invariance properties of the gravity path-integral measure derived from canonical framework, and discuss which path-integral formula may be employed…
We use a canonical parametrization of twisted geometries describing the classical phase space of loop quantum gravity on a fixed graph, and establish its explicit correspondence with the associated frame bases and spinorial descriptions.…
We discuss the canonical structure of a spacetime version of the radial gauge, i.e. Gau{\ss}ian normal spacetime coordinates. While it was found for the spatial version of the radial gauge that a "local" algebra of observables can be…
A method is presented which restricts the space of paths entering the path integral of quantum mechanics to subspaces of $C^\alpha$, by only allowing paths which possess at least $\alpha$ derivatives. The method introduces two external…
We describe how to overcome some problems that usually prevent from obtaining an efficient algorithm to fix a generic covariant gauge on the lattice. This gauge is the lattice equivalent of the generic gauge usually adopted in perturbative…
It has long been recognized that lattice gauge theory formulations, when applied to general relativity, conflict with the invariance of the theory under diffeomorphisms. Additionally, the traditional lattice field theory approach consists…
We show that the generators of canonical transformations in the triplectic manifold must satisfy constraints that have no parallel in the usual field antifield quantization. A general form for these transformations is presented. Then we…
Representations of propagators by means of path integrals over velocities are discussed both in nonrelativistic and relativistic quantum mechanics. It is shown that all the propagators can only be expressed through bosonic path integrals…
For classical gravitational systems the lapse function and the shift vector are usually determined by imposing appropriate gauge fixing conditions and then demanding their preservation with respect to the dynamics generated by a canonical…
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…
We show how to implement the background field method by means of canonical transformations and comment on the applications of the method to non-perturbative techniques in non-Abelian gauge theories. We discuss the case of the lattice in…
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.