Regge calculusIn general relativity, Regge calculus is a formalism for producing simplicial approximations of spacetimes that are solutions to the Einstein field equation. The calculus was introduced by the Italian theoretician Tullio Regge in 1961. The starting point for Regge's work is the fact that every four dimensional time orientable Lorentzian manifold admits a triangulation into simplices. Furthermore, the spacetime curvature can be expressed in terms of deficit angles associated with 2-faces where arrangements of 4-simplices meet.
Planck unitsIn particle physics and physical cosmology, Planck units are a set of units of measurement defined exclusively in terms of four universal physical constants, in such a manner that these physical constants take on the numerical value of 1 when expressed in terms of these units. Originally proposed in 1899 by German physicist Max Planck, these units are a system of natural units because their definition is based on properties of nature, more specifically the properties of free space, rather than a choice of prototype object.
Spin foamIn physics, the topological structure of spinfoam or spin foam consists of two-dimensional faces representing a configuration required by functional integration to obtain a Feynman's path integral description of quantum gravity. These structures are employed in loop quantum gravity as a version of quantum foam. Loop quantum gravity The covariant formulation of loop quantum gravity provides the best formulation of the dynamics of the theory of quantum gravity – a quantum field theory where the invariance under diffeomorphisms of general relativity applies.
Causal setsThe causal sets program is an approach to quantum gravity. Its founding principles are that spacetime is fundamentally discrete (a collection of discrete spacetime points, called the elements of the causal set) and that spacetime events are related by a partial order. This partial order has the physical meaning of the causality relations between spacetime events. The program is based on a theorem by David Malament that states that if there is a bijective map between two past and future distinguishing space times that preserves their causal structure then the map is a conformal isomorphism.
Asymptotic safety in quantum gravityAsymptotic safety (sometimes also referred to as nonperturbative renormalizability) is a concept in quantum field theory which aims at finding a consistent and predictive quantum theory of the gravitational field. Its key ingredient is a nontrivial fixed point of the theory's renormalization group flow which controls the behavior of the coupling constants in the ultraviolet (UV) regime and renders physical quantities safe from divergences.
Loop quantum gravityLoop quantum gravity (LQG) is a theory of quantum gravity, which aims to reconcile quantum mechanics and general relativity, incorporating matter of the Standard Model into the framework established for the intrinsic quantum gravity case. It is an attempt to develop a quantum theory of gravity based directly on Einstein's geometric formulation rather than the treatment of gravity as a mysterious mechanism (force). As a theory LQG postulates that the structure of space and time is composed of finite loops woven into an extremely fine fabric or network.
