Related papers: Canonical path integral quantization of Einstein's…
The nontrivial transformation of the phase space path integral measure under certain discretized analogues of canonical transformations is computed. This Jacobian is used to derive a quantum analogue of the Hamilton-Jacobi equation for the…
The path integral formulation of constrained systems leads to obtain the equations of motion as total differential equations in many variables. If these equations are integrable then one can constuct a valid and a canonical phase space…
The Hamilton-Jacobi method of constrained systems is discussed. The equations of motion of a singular system with time dependent constraints are obtained as total differential equations in many variables. The integrability conditions for…
Path integration is a respected form of quantization that all theoretical quantum physicists should welcome. This elaboration begins with simple examples of three different versions of path integration. After an important clarification of…
This paper is a generalization of previous work on the use of classical canonical transformations to evaluate Hamiltonian path integrals for quantum mechanical systems. Relevant aspects of the Hamiltonian path integral and its measure are…
We propose a new way to perform path integrals in quantum mechanics by using a quantum version of Hamilton-Jacobi theory. In classical mechanics, Hamilton-Jacobi theory is a powerful formalism, however, its utility is not explored in…
A review of the path integral approach to quantum cosmology and its relation to canonical quantisation. The initial derivation of the Hartle-Hawking and Vilenkin wavefunctions from the Euclidean Einstein-Hilbert action, and later, from the…
We consider the form of the path integral that follows from canonical quantization and apply it to the first order form of the Einstein-Hilbert action in $d > 2$ dimensions. We show that this is inequivalent to what is obtained from…
The "Newtonian" or non-relativistic decomposition of Einstein's gravitational field is useful in the post-Newtonian approximation. We obtain the full non-quadratic Einstein-Hilbert action in terms of these fields as well as the harmonic…
An important aspect in defining a path integral quantum theory is the determination of the correct measure. For interacting theories and theories with constraints, this is non-trivial, and is normally not the heuristic "Lebesgue measure"…
We discuss the Hamilton-Jacobi approach for a constrained system. We obtain the equation of motion for a singular system as total differential equations in many variables. We investigate the integrability conditions without using any gauge…
The canonical functional action in the path integral in phase space is discretized by linking each pair of consecutive vertebral points --${\bf q}_k$ and ${\bf p}_{k+1}$ or ${\bf p}_k$ and ${\bf q}_{k+1}$-- through the invariant complete…
We show the exact equality of the path integral of the general renormalizable fourth order gravitational action to the path integral of the Einstein action coupled to a massive spin-0 field and a massive spin-2 ghost-like field with…
Simple cosmological models are used to show that gravitation can be quantized as an ordinary gauge system if the Hamilton-Jacobi equation for the model under consideration is separable. In this situation, a canonical transformation can be…
In this contribution we deal with several issues one encounters when trying to couple quantum matter to classical gravitational fields. We start with a general background discussion and then move on to two more technical sections. In the…
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…
The path integral quantization method is applied to a relativistically covariant version of the Hopfield model, which represents a very interesting mesoscopic framework for the description of the interaction between quantum light and…
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…
We apply the topological quantization method to some gravitational fields which can be represented as generalized harmonic maps. This representation extends the well-known concept of harmonic maps and allows us to describe some solutions to…
Path integral formulation based on the canonical method is discussed. Path integral for Yang-Mills theory is obtained by this procedure. It is shown that gauge fixing which is essential procedure to quantize singular systems by Faddeev's…