Related papers: Comparative Theory of Background Independence
This treatise concerns shapes in the sense of constellations of points with various automorphisms quotiented out: continuous translations, rotations and dilations, and also discrete mirror image identification and labelling…
Bilinear systems emerge in a wide variety of fields as natural models for dynamical systems ranging from robotics to quantum dots. Analyzing controllability of such systems is of fundamental and practical importance, for example, for the…
This paper answers examines the relationship between Diffeomorphism Invariance and Background Independence. First, a review of the relationship between Background Independence, General Relativity (GR) and pre-GR theories are given. Then, a…
Noncommutative gravity, based on a twist-deformation of the differential geometry of spacetime and a first-order formulation of the dynamics, requires additional gravitational degrees of freedom as well as an enlargement of the gauge group…
Kendall-type Shape(-and-Scale) Theory on $\mathbb{R}^d$ involves $N$ point configurations therein quotiented by some geometrically meaningful automorphism group. This occurs in Shape Statistics, the Classical and Quantum $N$-body Problem…
Background independence is often emphasized as an important property of a quantum theory of gravity that takes seriously the geometrical nature of general relativity. In a background-independent formulation, quantum gravity should determine…
We are dealing with boundary conditions for Dirac-type operators, i.e., first order differential operators with matrix-valued coefficients, including in particular physical many-body Dirac operators. We characterize (what we conjecture is)…
The independence gap of a graph was introduced by Ekim et al. (2018) as a measure of how far a graph is from being well-covered. It is defined as the difference between the maximum and minimum size of a maximal independent set. We…
A local resolution of the Problem of Time has recently been given, alongside reformulation as a local theory of Background Independence. The classical part of this can be viewed as requiring just Lie's Mathematics, albeit entrenched in…
Global control offers a promising route to scalable quantum computing. A recent conjecture by Hu et al. (arXiv:2508.19075) proposes that any connected qubit graph equipped with global Ising-type interactions and tunable global transverse…
I argue that background freedom in quantum gravity automatically leads to a dissociation of the quantum state into states having a classical space. That is, interference is not completely well-defined for states with different space…
Interior-boundary conditions (IBCs) have been suggested as a possibility to circumvent the problem of ultraviolet divergences in quantum field theories. In the IBC approach, particle creation and annihilation is described with the help of…
The geometerization of the renormalization group flow triggered by the $T\bar{T}$ deformation of large $c$ conformal field theories in two dimensions is presented. This entails the construction of the off shell Einstein-Hilbert action in…
Kendall's Shape Theory covers shapes formed by $N$ points in $\mathbb{R}^d$ upon quotienting out the similarity transformations. This theory is based on the geometry and topology of the corresponding configuration space: shape space.…
The problems encountered in trying to quantize the various cosmological models, are brought forward by means of a concrete example. The Automorphism groups are revealed as the key element through which G.C.T.'s can be used for a general…
In this note, we use give some algebraic applications of a previous result by the author which compares the deformations parameterized by the Maurer-Cartan elements of a differential graded Lie algebra, and a differential graded Lie…
We show that the partition function of many classical models with continuous degrees of freedom, e.g. abelian lattice gauge theories and statistical mechanical models, can be written as the partition function of an (enlarged)…
In this paper we study the class of bi-arc digraphs, important from two seemingly unrelated perspectives. On the one hand, they are precisely the digraphs that admit certain polymorphisms of interest in the study of constraint satisfaction…
The Standard Model of particle physics is derived from first principles from the free Dirac Lagrangian in 8-dimensional spacetime. Motivated by second quantization arguments, we embed the 4-dimensional Clifford algebra of the Dirac…
Using the Dirac (Clifford) algebra $\gamma^{\mu}$ as initial stage of our discussion, we summarize and extend previous work with respect to the isomorphic 15dimensional Lie algebra su$*$(4) as complex embedding of sl(2,$\mathbb{H}$), the…