Related papers: Path Integral Quantisation of Finite Noncommutativ…
We study general relativity in the framework of non-commutative differential geometry. In particular, we introduce a gravity action for a space-time which is the product of a four dimensional manifold by a two-point space. In the simplest…
We develop a mathematically well-defined path integral formalism for general symplectic manifolds. We argue that in order to make a path integral quantization covariant under general coordinate transformations on the phase space and involve…
Path integral quantization of generic two-dimensional dilaton gravity non-minimally coupled to a Dirac fermion is performed. After integrating out geometry exactly, perturbation theory is employed in the matter sector to derive the lowest…
Local path integral quantization of generic 2D dilaton gravity is considered. Locality means that we assume asymptotic fall off conditions for all fields. We demonstrate that in the absence of `matter' fields to all orders of perturbation…
We consider a model of 2D gravity with the action quadratic in curvature and represent path integrals as integrals over the SL(2, R) invariant Gaussian functional measure. We reduce these path integrals to the products of Wiener path…
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…
We present an extension to arbitrary dimensions of a worldline path integral approach to one-loop quantum gravity, which was previously formulated in four spacetime dimensions. By utilizing this method, we recalculate gauge invariant…
One of several possibilities to construct a quantum theory of gravity is employing the Feynman path integral. This approach is plagued by some problems: the integration measure is not uniquely defined, the Einstein-Hilbert action unbounded,…
We define a (semi-classical) path integral for gravity with Neumann boundary conditions in $D$ dimensions, and show how to relate this new partition function to the usual picture of Euclidean quantum gravity. We also write down the action…
We study a quantum system in a Riemannian manifold M on which a Lie group G acts isometrically. The path integral on M is decomposed into a family of path integrals on a quotient space Q=M/G and the reduced path integrals are completely…
We formulate path integrals on any Riemannian manifold which admits the action of a compact Lie group by isometric transformations. We consider a path integral on a Riemannian manifold M on which a Lie group G acts isometrically. Then we…
A new method for nonperturbative investigations of quantum gravity is presented in which the simplicial path integral is approximated by the partition function of a spin system. This facilitates analytical and numerical computations…
We describe how to construct and compute unambiguously path integrals for particles moving in a curved space, and how these path integrals can be used to calculate Feynman graphs and effective actions for various quantum field theories with…
We propose a method for demonstrating equivalences beyond the saddlepoint approximation between quantities in quantum gravity that are defined by the Euclidean path integral, without assumptions about holographic duality. The method…
Path integral quantization of quantum gauge general relativity is discussed in this paper. First, we deduce the generating functional of green function with external fields. Based on this generating functional, the propagators of…
A method based on the path integral approach is engaged to consider the gravitational emission from a quantum mechanical bound system in a locally inertial frame. In such a frame, interaction between the electromagnetic (bound potential)…
Geometric quantization is an attempt at using the differential-geometric ingredients of classical phase spaces regarded as symplectic manifolds in order to define a corresponding quantum theory. Generally, the process of geometric…
A new path integral approach of quantum gravity based on relational variables and quantum test objects is presented. We take as a basic variables the squared invariant distance. This invariant quantity is technically simpler to work with…
We investigate quantum gravity in the path integral formulation using the Regge calculus. Restricting the quadratic link lengths of the originally triangular lattice the path integral can be transformed to the partition function of a spin…
We revisit the gravity path integral formalism of JT gravity. We explain how to gauge fix the path integral in the presence of asymptotic boundaries and conical defects, and resolve an ambiguity regarding the dilaton gravity operator that…