Related papers: Consistent discretizations as a road to quantum gr…

General Theory of Relativity and Quantum theory gives two different description of the same mother nature in the big and small scale respectively. Mathematical languages of these two theories are entirely different, one is geometric while…

Linearized Einstein gravity (with possibly nonzero cosmological constant) is quantized in the framework of algebraic quantum field theory by analogy with Dimock's treatment of electromagnetism [Rev. Math. Phys. 4 (1992) 223--233]. To…

One of the obstacles to reconciling quantum theory with general relativity, is constructing a theory which is both consistent with observation, and and gives finite answers at high energy, so that the theory holds at arbitrarily short…

The investigation of quantum-classical correspondence may lead to gain a deeper understanding of the classical limit of quantum theory. We develop a quantum formalism on the basis of a linear-invariant theorem, which gives an exact…

The cosmological constant problem is one of the long-standing issues of modern physics. While we can measure the value of the cosmological constant with great accuracy, we are not able to calculate it in a coherent theoretical framework. On…

The paper concerns the fictitious entanglement of the so-called ``singularities'' in problems, pertaining to quantum gravity, due, in point of fact, to the way we try to employ, in that context, differential geometry, the latter being…

A generalization of classical mechanics is obtained from a complex parametrization of the phase space. The formalism supports complex Hamiltonian functions describing non-conservative classical mechanical systems. A quantization scheme that…

Each approach to the quantum-gravity problem originates from expertise in one or another area of theoretical physics. The particle-physics perspective encourages one to attempt to reproduce in quantum gravity as much as possible of the…

We show that a recent proposal for the quantization of gravity based on discrete space-time implies a modification of standard quantum mechanics that naturally leads to a loss of coherence in quantum states of the type discussed by Milburn.…

Precise rules are developed in order to formalize the reasoning processes involved in standard non-relativistic quantum mechanics, with the help of analogies from classical physics. A classical or quantum description of a mechanical system…

The quantization of the Hamiltonian for a scalar field is performed in the framework of Quantum Reduced Loop Gravity. We outline how the regularization can be performed by using the analogous tools adopted in full Loop Quantum Gravity and…

It is well-known that quantum groups are relevant to describe the quantum regime of 3d gravity. They encode a deformation of the gauge symmetries parametrized by the value of the cosmological constant. They appear as a form of…

Here, we present a review about the quantization of spherically-symmetric spacetimes adopting loop quantum gravity techniques. Several models that have been studied so far share similar properties: the resolution of the classical…

A discussion of the meaning of a physical concept cannot be separated from discussion of the conditions for its ideal measurement. We assert that quantization is no more than the invocation of the quantum of action in the explanation of…

Models for deterministic quantum mechanics of Cartan-Randers type are introduced, together with the fundamental notions of the concentration of measure theory. We explain how the application of the concentration of measure to Cartan-Randers…

To obtain a well defined path integral one often employs discretizations. In the case of gravity and reparametrization invariant systems, the latter of which we consider here as a toy example, discretizations generically break…

Quantum computing has traditionally centered around the discrete variable paradigm. A new direction is the inclusion of continuous variable modes and the consideration of a hybrid continuous-discrete approach to quantum computing. In this…

On a family of classical dynamical systems on the 2-torus, we perform a discretization procedure similar to the Anti-Wick quantization. Such a discretization is performed by using a particular class of states, fulfilling an appropriate…

We summarise a recently introduced general canonical formulation of discrete systems which is fully equivalent to the covariant formalism. This framework can handle varying phase space dimensions and is applied to simplicial gravity in…

This is a self-contained introduction to quantum Riemannian geometry based on quantum groups as frame groups, and its proposed role in quantum gravity. Much of the article is about the generalisation of classical Riemannian geometry that…