Related papers: Quantum geodesics on $\lambda$-Minkowski spacetime
We consider a congruence of null geodesics in the presence of a quantized spacetime metric. The coupling to a quantum metric induces fluctuations in the congruence; we calculate the change in the area of a pencil of geodesics induced by…
Physical spacetime geometry follows from some effective thermodynamics of quantum states of all fields and particles described in frames of General Relativity. In the sense of pure field theoretical Einstein's point of view on gravitation…
We investigate the geodesic deviation equation in the context of quantum improved spacetimes. The improved Raychaudhuri equation is derived, and it is shown that the classical strong energy condition does not necessarily lead to the…
We study the classical analog of the quantum metric tensor and its scalar curvature for two well-known quantum physics models. First, we analyze the geometry of the parameter space for the Dicke model with the aid of the classical and…
Gravity is a phenomenon which arises due to the space-time geometry. The main equations that describe gravity are the Einstein equations. To understand the consequences of these field equations we need to calculate the free particle…
Consider the geodesic flow on a real-analytic closed hypersurface $M$ of $\mathbb{R}^n$, equipped with the standard Euclidean metric. The flow is entirely determined by the manifold and the Riemannian metric. Typically, geodesic flows are…
We derive generalized geodesic equations in curved spacetime that include conservative forces, dissipative effects, and quantum-gravity-motivated minimal-length corrections. Conservative interactions are incorporated through external vector…
We study classical limit for quantum mechanics with two times and temperature, which describes a generalized dynamics of relativistic point mass. In this theory, thermodynamic time means a parameter of evolution, whereas geometric time is…
Finding diffeomorphism-invariant observables to characterize the properties of gravity and spacetime at the Planck scale is essential for making progress in quantum gravity. The holonomy and Wilson loop of the Levi-Civita connection are…
It is possible that relativistic symmetries become deformed in the semiclassical regime of quantum gravity. Mathematically, such deformations lead to the noncommutativity of spacetime geometry and non-vanishing curvature of momentum space.…
We introduce a model of noncommutative geometry that gives rise to the uncertainty relations recently derived from the discussion of a quantum clock. We investigate the dynamics of a free particle in this model from the point of view of…
In General Relativity, gravity around a black hole is universally regarded as an attractive force. However, quantum effects may significantly alter this classical picture and thus affect the dynamics of test particles. In this work, we…
We obtain generally covariant operator-valued geodesic equations on a pseudo-Riemannian manifold $M$ as part of the construction of quantum geodesics on the algebra $D(M)$ of differential operators. Geodesic motion arises here as an…
Following a bi-cylindrical model of geometrical dynamics, in the present study we show that Einstein gravitational equation leads to bi-geodesic description in an extended symmetrical time-space which fit Hubble expansion in a "microscopic"…
Recent and upcoming experimental data as well as the possibility of rich phenomenology have spiked interest in studying the quantum effects in cosmology at low (inflation-era) energy scales. One of the approaches to find covariant quantum…
The geometric quantization of the geodesic flow on a compact Riemannian manifold via the BKS "dragging projection" yields the Laplacian plus a scalar curvature term. To avoid convergence issues, the standard construction involves somewhat…
The task of quantizing gravity is compared with Einstein's relativization of gravity. The philosophical and physical foundations of general relativity are briefly reviewed. The Ehlers-Pirani-Schild scheme of operationally determining the…
We compute second-order quantum corrections, as quantum dispersions and correlations, to a cosmological model coupling a single scalar perturbation mode to a bouncing background within Loop Quantum Cosmology (LQC). Using an effective…
Quantum gravity effects of zeroth order in the Planck constant are investigated in the framework of the low-energy effective theory. A special emphasis is placed on establishing the correspondence between classical and quantum theories, for…
We find a coordinate-independent wave-packet solution of the massive Klein-Gordon equation with the conformal coupling to gravity in the de-Sitter universe. This solution can locally be represented through the superposition of…