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There is solid consensus among physicists and philosophers that, in gauge field theory, for a quantity to be physically meaningful or real, it must be gauge-invariant. Yet, every "elementary" field in the Standard Model of particle physics…
This is an introduction to an algebraic construction of a gravity theory on noncommutative spaces which is based on a deformed algebra of (infinitesimal) diffeomorphisms. We start with some fundamental ideas and concepts of noncommutative…
The relativistic theory of structure formation in cosmology is based mainly on linear perturbations about a homogeneous background. But we are now driven to understand the theory of higher-order perturbations in full detail, both from…
Perturbative algebraic quantum field theory (pAQFT) is a mathematically rigorous framework that allows to construct models of quantum field theories on a general class of Lorentzian manifolds. Recently this idea has been applied also to…
Gravity, and the puzzle regarding its energy, can be understood from a gauge theory perspective. Gravity, i.e., dynamical spacetime geometry, can be considered as a local gauge theory of the symmetry group of Minkowski spacetime: the…
Gravitational effective field theories with nondynamical backgrounds explicitly break diffeomorphism and local Lorentz invariance. At the same time, to maintain observer independence the action describing these theories is required to be…
We consider two concepts often discussed as significant features of general relativity (particularly when contrasted with the other forces of the Standard Model): background independence and diffeomorphism invariance. We remind the reader…
We present a manifestly Lorentz- and SO(2)-Duality-invariant local Quantum Field Theory of electric charges, Dirac magnetic monopoles and dyons. The manifest invariances are achieved by means of the PST-mechanism. The dynamics for classical…
The issue of local gauge invariance in the simplicial lattice formulation of gravity is examined. We exhibit explicitly, both in the weak field expansion about flat space, and subsequently for arbitrarily triangulated background manifolds,…
A covariant reformulation of General Relativity is briefly considered from three points of view: geometrodynamics, Lagrange-Euler field theory, and gauge field theory. From a geometrodynamics perspective, a definition of the reference frame…
The framework of locally covariant quantum field theory is discussed, motivated in part using "ignorance principles". It is shown how theories can be represented by suitable functors, so that physical equivalence of theories may be…
We propose an operator constraint equation for the wavefunction of the Universe that admits genuine evolution. While the corresponding classical theory is equivalent to the canonical decomposition of General Relativity, the quantum theory…
A review of some errors made by the author and others in their search for quantum models of gravity in cosmological space-times that asymptote to de Sitter (dS) space in the future. The "static de Sitter Hamiltonian", which measures the…
We study cosmological correlators in de Sitter quantum gravity in the limit where $G_N \to 0$. This limit is distinct from a nongravitational QFT because the gravitational constraints still force states and observables to be de Sitter…
The evolution of a generally covariant theory is under-determined. One hundred years ago such dynamics had never before been considered; its ramifications were perplexing, its future important role for all the fundamental interactions under…
The standard formulation of quantum theory relies on a fixed space-time metric determining the localisation and causal order of events. In general relativity, the metric is influenced by matter, and is expected to become indefinite when…
It is generally believed that a full-fledged theory of quantum gravity should exhibit background independence and diffeomorphism invariance. In its most general form, the latter comprises field redefinitions, which are diffeomorphisms in…
We derive for generally covariant theories the generic dependency of observables on the original fields, corresponding to coordinate-dependent gauge fixings. This gauge choice is equivalent to a choice of intrinsically defined coordinates…
The matrix models are non-perturbative formulations of string theory, from which many believe that spacetime arises. The matrix fluctuations around the spacetime thus created should represent both matter and gravitational fields. In this…
Quantum General Relativity (QGR), sometimes called Loop Quantum Gravity, has matured over the past fifteen years to a mathematically rigorous candidate quantum field theory of the gravitational field. The features that distinguish it from…