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As a canonical and generally covariant gauge theory, loop quantum gravity requires special techniques to derive effective actions or equations. If the proper constructions are taken into account, the theory, in spite of considerable…
We answer to 72 frequently asked questions about theories of multifractional spacetimes. Apart from reviewing and reorganizing what we already know about such theories, we discuss the physical meaning and consequences of the very recent…
We introduce a master constraint operator on the kinematical Hilbert space of loop quantum gravity representing a set of gauge conditions which classically fix the densitized triad to be diagonal. We argue that the master constraint…
A new alternative volume operator is constructed for loop quantum gravity by using the so-called cotriad operators as building blocks. It is shown that the new volume operator shares the same qualitative properties with the standard volume…
In this paper, we give a quantum circuit that calculates symmetrized functions. Our algorithm applies the original Grover's algorithm or a variant thereof such as AFGA (adaptive fixed point Grover's algorithm). Our algorithm uses AFGA in…
A theory of 3-space explains the phenomenon of gravity as arising from the time-dependence and inhomogeneity of the differential flow of this 3-space. The emergent theory of gravity has two gravitational constants: G - Newton's constant,…
Quantifying coherence is an essential endeavor for both quantum mechanical foundations and quantum technologies. We present a bona fide measure of quantum coherence by utilizing the Tsallis relative operator $(\alpha, \beta)$-entropy. We…
We propose the generalized uncertainty principle (GUP) with an additional term of quadratic momentum motivated by string theory and black hole physics as a quantum mechanical framework for the minimal length uncertainty at the Planck scale.…
The implementation of the dynamics in loop quantum gravity (LQG) is still an open problem. Here, we discuss a tentative dynamics for the simplest class of graphs in LQG: Two vertices linked with an arbitrary number of edges. We find an…
Formal proof checkers such as Coq are capable of validating proofs of correction of algorithms for finite field arithmetics but they require extensive training from potential users. The delayed solution of a triangular system over a finite…
The exact renormalization group equation for pure quantum gravity is used to derive the non-perturbative $\Fbeta$-functions for the dimensionless Newton constant and cosmological constant on the theory space spanned by the Einstein-Hilbert…
We present a simple argument which determines the critical value of the anomaly coefficient in four dimensional conformal factor quantum gravity, at which a phase transition between a smooth and elongated phase should occur. The argument is…
In this article, we propose a Lyapunov stability approach to analyze the convergence of the density operator of a quantum system. In analog to the classical probability measure for Markovian processes, we show that the set of invariant…
In perturbative QED, the approximation is improved by summing more Feynman graphs; in non-perturbative QCD, by refining the lattice. Here we observe that in quantum gravity the two procedures may well be the same. We outline the…
Quantum theory is formulated as the only consistent way to manipulate probability amplitudes. The crucial ingredient is a consistency constraint: if there are two different ways to compute an amplitude the two answers must agree. This…
We propose an unified approach to loop quantum gravity and Fedosov quantization of gravity following the geometry of double spacetime fibrations and their quantum deformations. There are considered pseudo-Riemannian manifolds enabled with…
The $\mathcal{O}(\partial^2)$ background independent flow equations for conformally reduced gravity are shown to be equivalent to flow equations naturally adapted to scalar field theory with a wrong sign kinetic term. This sign change is…
Most fluid flow problems that are vital in engineering applications involve at least one of the following features: turbulence, shocks, and/or material interfaces. While seemingly different phenomena, these flows all share continuous…
We investigate 2d gravity quantized in the ADM formulation, where only the loop length $l(z)$ is retained as a dynamical variable of the gravitation, in order to get an intuitive physical insight of the theory. The effective action of…
Attempts to formulate a quantum theory of gravitation are collectively known as {\it quantum gravity}. Various approaches to quantum gravity such as string theory and loop quantum gravity, as well as black hole physics and doubly special…