Related papers: Lattice diffeomorphism invariance
The application of the notion of `observable' from gauge theory to diffeomorphism-invariant theories -- most relevantly to general relativity -- has led to numerous conceptual and technical issues when interpreting classical theories with…
In this paper we work out in detail a new proposal to define rigorously a sector of loop quantum gravity at the diffeomorphism invariant level corresponding to homogeneous and isotropic cosmologies, and propose how to compare in detail the…
Relativity and classical dynamics, as defined so far, form distinct parts of classical physics and are formulated based on independent principles. We propose that the formalism of classical dynamics can be considered as the theoretical…
We study deterministic and quantum dynamics from a constructive "finite" point of view, since the introduction of a continuum, or other actual infinities in physics poses serious conceptual and technical difficulties, without any need for…
This manuscript is the first in a series of instalments that investigate spherically symmetric solutions within the effective dynamics program of Loop Quantum Gravity. The choice of lattice is adapted such that it remains invariant under a…
To date, all proposed quantum algorithms for simulating quantum field theory (QFT) simulate (continuous-time) Hamiltonian lattice QFT as a stepping stone. Two overlooked issues are how large we can take the timestep in these simulations…
We present a stochastic framework for emergent quantum gravity coupled to matter. The Hamiltonian constraint in diffeomorphism-invariant theories demands the identification of a clock relative to which dynamics may be defined, and other…
On a lattice, we construct an overlap Dirac operator which describes the propagation of a Dirac fermion in external gravity. The local Lorentz symmetry is manifestly realized as a lattice gauge symmetry, while the general coordinate…
We use perturbation theory to construct perfect lattice actions for fermions and gauge fields by blocking directly from the continuum. When one uses a renormalization group transformation that preserves chiral symmetry the resulting lattice…
This note is to bring to the reader's attention the fact that general relativity and quantum mechanics differ from each other in one main aspect. General relativity is based on the diffeomorphism covariant formulation of the laws of physics…
We consider a diffeomorphism invariant theory of a gauge field valued in a Lie algebra that breaks spontaneously to the direct sum of the spacetime Lorentz algebra, a Yang-Mills algebra, and their complement. Beginning with a fully gauge…
First-order general relativity in $n$ dimensions ($n \geq 3$) has an internal gauge symmetry that is the higher-dimensional generalization of three-dimensional local translations. We report the extension of this symmetry for $n$-dimensional…
There is a precise sense in which the requirement of background independence suffices to uniquely select the kinematics of loop quantum gravity (LQG). Specifically, the fundamental kinematic algebra of LQG admits a unique diffeomorphism…
(Abridged Abstract) This paper deals with a number of technical achievements that are instrumental for a dis-solution of the so-called {\it Hole Argument} in general relativity. The work is carried through in metric gravity for the class of…
A consistent theory of quantum gravity will require a fully quantum formulation of the classical equivalence principle. Such a formulation has been recently proposed in terms of the equality of the rest, inertial and gravitational mass…
Shape dynamics is a completely background-independent universal framework of dynamical theories from which all absolute elements have been eliminated. For particles, only the variables that describe the shapes of the instantaneous particle…
Given an area-preserving diffeomorphism of the closed unit disk which is a rotation near the boundary, one can naturally define an "action" function on the disk which agrees with the rotation number on the boundary. The Calabi invariant of…
Symmetries play an important role in fundamental physics. In gravity and field theories, particular attention has been paid to Weyl (or conformal) symmetry. However, once the theory contains a scalar field, conformal transformations of the…
An algorithmic approach towards the formulation of non-relativistic diffeomorphism invariance has been developed which involves both matter and gauge fields. A step by step procedure has been provided which can accommodate all types of…
We present a separable version of Loop Quantum Gravity (LQG) based on an inductive system of cubic lattices. We construct semi-classical states for which the LQG operators -- the flux, the area and the volume operators -- have the right…