Related papers: An Alternate Path Integral for Quantum Gravity
We summarize our work on spherically symmetric midi-superspaces in loop quantum gravity. Our approach is based on using inhomogeneous slicings that may penetrate the horizon in case there is one and on a redefinition of the constraints so…
A question is studied whether an observer can discover quantum gravity being in the semi-classical regime. It is shown that it is indeed possible to probe a certain quantum gravity effect by employing an appropriately designed detector. The…
We study the fractional gravity for spacetimes with non-integer dimensions. Our constructions are based on a geometric formalism with the fractional Caputo derivative and integral calculus adapted to nonolonomic distributions. This allows…
The theme of doing quantum mechanics on all abelian groups goes back to Schwinger and Weyl. If the group is a vector space of finite dimension over a non-archimedean locally compact division ring, it is of interest to examine the structure…
We show that that four dimensional conformal gravity plus a simple Neumann boundary condition can be used to get the semiclassical (or tree level) wavefunction of the universe of four dimensional asymptotically de-Sitter or Euclidean…
The method of the factorization of the path integral measure, based on a nonlinear filtering equation, is extended to the case of a nonfree isometric action of the compact semisimple unimodular Lie group on a smooth compact Riemannian…
The path integral approach to a quantum theory of gravity is widely regarded as an indispensable strategy. However, determining what additional elements, beyond black hole or AdS spacetime, should be incorporated into the path integral…
Adapting ideas of Daubechies and Klauder [J. Math. Phys. {\bf 26} (1985) 2239] we derive a rigorous continuum path-integral formula for the semigroup generated by a spin Hamiltonian. More precisely, we use spin-coherent vectors parametrized…
The essence of the path integral method in quantum physics can be expressed in terms of two relations between unitary propagators, describing perturbations of the underlying system. They inherit the causal structure of the theory and its…
An earlier proposed theory with linear-gonihedhic action for quantum gravity is reviewed. One can consider this theory as a "square root" of classical gravity with a new fundamental constant of dimension one. We demonstrate also, that the…
In this work, we employ the Hamiltonian approach to analyze the Lorentzian path integral in 2+1 AdS gravity, with an aim to sum over all possible geometries, including naked singularities and BTZ black holes, between fixed initial and final…
Consistency of Einstein's gravitational field equation $G_{\mu\nu} \propto T_{\mu\nu}$ imposes a "conservation condition" on the $T$-tensor that is satisfied by (i) matter stress tensors, as a consequence of the matter equations of motion,…
A proper understanding of boundary-value problems is essential in the attempt of developing a quantum theory of gravity and of the birth of the universe. The present paper reviews these topics in light of recent developments in spectral…
An approach to approximate evaluation of the continuum Feynman path integrals is developed for the study of quantum fluctuations of particles and fields in Euclidean time-space. The paths are described by sum of Gauss functions and are…
Recently the so-called mimetic gravity approach has been used to obtain corrections to Friedmann equation of General Relativity similar to the ones present in loop quantum cosmology. In this paper, we propose an alternative way to derive…
We continue recent work and formulate the gravitational vacuum Einstein equations over a locally finite spacetime by using the basic axiomatics, techniques, ideas and working philosophy of Abstract Differential Geometry. The whole…
The new emerging quantum physics - quantum computing conceptual bridge, mandates a ``grand unification'' of space-time-matter and quantum information (all quantized), with deep implications for science in general. The major physics…
By parametrizing the action integral for the standard Schrodinger equation we present a derivation of the recently proposed method for quantizing a parametrized theory. The reformulation suggests a natural extension from conventional to…
We develop a generally applicable method for constructing functions, $C$, which have properties similar to Zamolodchikov's $C$-function, and are geometrically natural objects related to the theory space explored by non-perturbative…
The quantum potential approach makes it possible to construct a complementary picture of quantum mechanical evolution which reminds classical equation of motion. The only difference as compared to equations of motion for the underlying…