Related papers: Diffeomorphism invariance and general covariance: …
Diffeomorphism invariance is often considered to be a hallmark of the theory of general relativity (GR). But closer analysis reveals that this cannot be what makes GR distinctive. The concept of diffeomorphism invariance can be defined in…
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…
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…
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 show that diffeomorphism invariance of the Maxwell and the Dirac-Hestenes equations implies the equivalence among different universe models such that if one has a linear connection with non-null torsion and/or curvature the others have…
We study the extent to which diffeomorphism invariance restricts the properties of the primordial perturbations in single scalar field models. We derive a set of identities that constrain the connected correlators of the cosmological…
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…
Deformations of spacelike hypersurfaces in space-time play an important role in discussions of general covariance and slicing independence in gravitational theories. In a canonical formulation, they provide the geometrical meaning of gauge…
Conceptual difficulties in semiclassical and quantum gravity arise from diffeomorphism invariance of classical general relativity. With a motivation to shed some light on these difficulties, we study a class of toy models for which…
It is shown that when the Einstein-Hilbert Lagrangian is considered without any non-covariant modifications or change of variables, its Hamiltonian formulation leads to results consistent with principles of General Relativity. The…
Diffeomorphism-induced symmetry transformations and time evolution are distinct operations in generally covariant theories formulated in phase space. Time is not frozen. Diffeomorphism invariants are consequently not necessarily constants…
If general relativity is an emergent phenomenon, there may be small violations of diffeomorphism invariance. We propose a phenomenology of perturbatively small violations of general relativity by the inclusion of terms which break general…
General covariance is a crucial notion in the study of field theories in curved spacetime. A field theory defined with respect to a semi-Riemannian metric is generally covariant if two metrics which are related by a diffeomorphism produce…
Diffeomorphism invariance is sometimes taken to be a criterion of background independence. This claim is commonly accompanied by a second, that the genuine physical magnitudes (the "observables") of background-independent theories and those…
Since the appearance of General Relativity, its intrinsec general covariance has been very often misinterpreted as implying that physically meaningful quantitities (and conclusions extracted from the theory) have to be absolutely…
Attempts to quantize general relativity encounter an odd problem. The Hamiltonian that normally generates time evolution vanishes in the case of general relativity as a result of diffeomorphism invariance. The theory seems to be saying that…
This paper discusses the implementation of diffeomorphism invariance in purely Hamiltonian formulations of General Relativity. We observe that, if a constrained Hamiltonian formulation derives from a manifestly covariant Lagrangian, the…
Diffeomorphism invariance breaking has been investigated in the literature in several contexts, including emergent General Relativity (GR). If GR emerges from an underlying theory without diffeomorphism invariance, there may be small…
We study certain aspects of the recently proposed notion of nonrelativistic diffeomorphism invariance. In particular, we consider specific examples of invariant actions, extended gauge symmetry as well as an application to the theory of…
Gravitational theories with fixed background fields break diffeomorphism invariance. This breaking can be spontaneous or explicit. A brief summary of the main consequences of these types of breaking is presented.