相关论文: From areas to lengths in quantum Regge calculus
The existence of a fundamental scale, a lower bound to any output of a position measurement, seems to be a model-independent feature of quantum gravity. In fact, different approaches to this theory lead to this result. The key ingredients…
Quantum field theory unifies concepts from quantum theory and from special relativity. Its mathematically rigorous description is quite intricate and is only partially understood; this is particularly true for the construction of operators…
The continuous limit of one dimensional discrete-time quantum walks with time- and space-dependent coefficients is investigated. A given quantum walk does not generally admit a continuous limit but some families (1-jets) of quantum walks…
We consider spinfoam quantum gravity for general triangulations in the regime $l_P^2\ll a\ll a/\gamma$, namely in the combined classical limit of large areas $a$ and flipped limit of small Barbero-Immirzi parameter $\gamma$, where $l_P$ is…
A Kantowski-Sachs model with a modified quantization prescription is considered. Such quantization rules, inspired by the so-called Generalized Uncertainty Principle (GUP), correspond to a modified commutation relation between…
In this paper we suggest gauge invariant discretization of Poincare quantum gravity. We generalize Regge calculus to the case of Riemann-Cartan space. The basic element of the constructed discretization is piecewize linear Riemann-Cartan…
We propose in this paper an alternative method for the quantisation of systems with first-class constraints. This method is a combination of the coherent-state-path-integral quantisation developed by Klauder, with the ideas of reduced state…
We study a system of two pointlike particles coupled to three dimensional Einstein gravity. The reduced phase space can be considered as a deformed version of the phase space of two special-relativistic point particles in the centre of mass…
In the present discussion Background Independent framework of Quantum Mechanics and its possible implications in the studies of gravity and Physics at short distance are addressed. The expression of the metric of quantum state space…
We study finite-dimensional integrals in a way that elucidates the mathematical meaning behind the formal manipulations of path integrals occurring in quantum field theory. This involves a proper understanding of how Wick's theorem allows…
We introduce a quantum geometric tensor in a curved space with a parameter-dependent metric, which contains the quantum metric tensor as the symmetric part and the Berry curvature corresponding to the antisymmetric part. This…
The metric known to be relevant for standard quantization procedures receives a natural interpretation and its explicit use simultaneously gives both physical and mathematical meaning to a (coherent-state) phase-space path integral, and at…
Relativity and quantum mechanics are generalized by considering a finite limit for the smallest measurable distance. The value a of this quantum of length is unknown, but it is a universal constant, like c and h. It depends on the total…
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…
The problem of constructing a quantum theory of gravity is considered from a novel viewpoint. It is argued that any consistent theory of gravity should incorporate a relational character between the matter constituents of the theory. In…
This article provides a cartoon of the quantization of General Relativity using the ideas of effective field theory. These ideas underpin the use of General Relativity as a theory from which precise predictions are possible, since they show…
A model for quantum gravity in one (time) dimension is discussed, based on Regge's discrete formulation of gravity. The nature of exact continuous lattice diffeomorphisms and the implications for a regularized gravitational measure are…
The number of classical paths of a given length, connecting any two events in a (pseudo) Riemannian spacetime is, of course, infinite. It is, however, possible to define a useful, finite, measure $N(x_2,x_1;\sigma)$ for the effective number…
We define a simplified version of Regge quantum gravity where the link lengths can take on only two possible values, both always compatible with the triangle inequalities. This is therefore equivalent to a model of Ising spins living on the…
Different approaches are compared to formulation of quantum mechanics of a particle on the curved spaces. At first, the canonical, quasi-classical and path integration formalisms are considered for quantization of geodesic motion on the…