Related papers: Canonical Gravity, Diffeomorphisms and Objective H…
We discuss the Hamiltonian hybrid coupling between a classical and a quantum subsystem. If applicable to classical gravity coupled to quantized matter, this hybrid theory might realize a captivating `postquantum' alternative to full…
We argue that the standard canonical treatment of GR breaks manifest spacetime covariance. We present new variables which carry a reducible representation of gauge transformations and spacetime diffeomorphisms. A proposal is presented for…
It has long been recognized that lattice gauge theory formulations, when applied to general relativity, conflict with the invariance of the theory under diffeomorphisms. Additionally, the traditional lattice field theory approach consists…
The basic features of the complex canonical formulation of general relativity and the recent developments in the quantum gravity program based on it are reviewed. The exposition is intended to be complementary to the review articles…
The framework of a theory of gravity from the quantum to the classical regime is presented. The paradigm shift from full spacetime covariance to spatial diffeomorphism invariance, together with clean decomposition of the canonical…
We investigate the fate of diffeomorphisms when the radial gauge is imposed in canonical general relativity. As shown elsewhere, the radial gauge is closely related to the observer's observables. These observables are invariant under a…
For various theories, in particular gauge field theories, the algebraic form of the Hamiltonian simplifies considerably if one writes it in terms of certain complex variables. Also general relativity when written in the new canonical…
The covariant phase space method of Iyer, Lee, Wald, and Zoupas gives an elegant way to understand the Hamiltonian dynamics of Lagrangian field theories without breaking covariance. The original literature however does not systematically…
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 discuss a covariant setting for Hamiltonian formalism in a relativistic field theory and we use this to obtain again the properties of Hamilton principal functional in Newtonian mechanics, relativistic mechanics, Klein-Gordon,…
We propose a first-order geometric Lagrangian for four-dimensional conformal gravity within the Cartan formulation, which yields, dynamically, the standard constraints on the fields, expected for conformal gravity. Upon imposing the…
To guarantee the stability of the cosmological constant sector against radiative corrections coming from quantum matter fields, one of the most natural ingredients to invoke is the symmetry under scale transformations of the gravitational…
This paper deals with several technical issues of non-perturbative four-dimensional Lorentzian canonical quantum gravity in the continuum that arose in connection with the recently constructed Wheeler-DeWitt quantum constraint operator. 1)…
We apply the ``consistent discretization'' approach to general relativity leaving the spatial slices continuous. The resulting theory is free of the diffeomorphism and Hamiltonian constraints, but one can impose the diffeomorphism…
The two-dimensional effective Polyakov action is often realized as the anomalous contributions of string theories and fermions coupled to gravity in two-dimensions. However, as a result of the reparameterization invariance, one finds that…
We show that representations of the group of spacetime diffeomorphism and the Dirac algebra both arise in a phase-space histories version of canonical general relativity. This is the general-relativistic analogue of the novel time structure…
We study covariant models for vacuum spherical gravity within a canonical setting. Starting from a general ansatz, we derive the most general family of Hamiltonian constraints that are quadratic in first-order and linear in second-order…
We show that the algebra of discretized spatial diffeomorphism constraints in Hamiltonian lattice quantum gravity closes without anomalies in the limit of small lattice spacing. The result holds for arbitrary factor-ordering and for a…
We give an overview of some conceptual difficulties, sometimes called paradoxes, that have puzzled for years the physical interpetation of classical canonical gravity and, by extension, the canonical formulation of generally covariant…
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…