Loopkvantgravitation

Loopkvantgravitation, commonly known in English as loop quantum gravity (LQG), is a background-independent approach to quantum gravity that aims to merge general relativity with quantum mechanics without introducing a fixed spacetime geometry.

In LQG, geometry itself is quantized. The theory describes quantum states of space as networks of edges and vertices called spin networks, whose labels correspond to discrete units of area and volume.

The mathematical framework uses Ashtekar variables, recasting general relativity as a gauge theory of SU(2). The kinematical Hilbert space is built from cylindrical functions on graphs, and geometric operators have discrete spectra.

Dynamics are implemented by a Hamiltonian constraint in the canonical formulation, and by a covariant spin foam path integral that sums over labeled foams. Together, these approaches aim to recover classical spacetime in a suitable semiclassical limit.

Predictions include a resolution of certain classical singularities, such as a cosmic bounce in loop quantum cosmology, and an area-entropy relation for black holes that depends on the Immirzi parameter.

The status of loopkvantgravitation is theoretical and mathematical, with no experimental confirmation as of now. Challenges include deriving a complete dynamics, coupling to the Standard Model fields, and demonstrating a clear, testable deviation from general relativity.