Related papers: Quantum Gravity Boundary Terms from Spectral Actio…
In this article the geometry of quantum gravity is quantized in the sense of being noncommutative (first quantization) but it is also quantized in the sense of being emergent (second quantization). A new mechanism for quantum geometry is…
The possibility of testing spatial noncommutativity by current experiments on normal quantum scales is investigated. For the case of both position-position and momentum-momentum noncommuting spectra of ions in crossed electric and magnetic…
These are expanded lecture notes of a mini-course whose objectives were to introduce the basic concepts, constructions and techniques of noncommutative geometry, as well as their uses as a framework for modelling quantum spacetime. Key…
Local supersymmetry leads to boundary conditions for fermionic fields in one-loop quantum cosmology involving the Euclidean normal to the boundary and a pair of independent spinor fields. This paper studies the corresponding classical…
In analogy with conventional quantum mechanics, non-commutative quantum mechanics is formulated as a quantum system on the Hilbert space of Hilbert-Schmidt operators acting on non-commutative configuration space. It is argued that the…
Using the recently found first order formulation of two-dimensional dilaton gravity with boundary, we perform a Hamiltonian analysis and subsequent path integral quantization. The importance of the boundary terms to obtain the correct…
The principles of noncommutative geometry impose severe restrictions on the structure of (almost) commutative field theories. The Standard Model fits surprisingly well into the noncommutative framework. Here we overview some universal…
The gravitational measure on an arbitrary topological three-manifold is constructed. The nontrivial dependence of the measure on the conformal factor is discussed. We show that only in the case of a compact manifold with boundary the…
Invariance principles determine many key properties in quantum field theory, including, in particular, the appropriate form of the boundary conditions. A crucial consistency check is the proof that the resulting boundary-value problem is…
The trace anomaly induced dynamics of the conformal factor is investigated in four-dimensional quantum gravity with torsion. The constraints for the coupling constants of torsion matter interaction are obtained in the infrared stable fixed…
The covariant Hamiltonian formulation for general relativity is studied in terms of self-dual variables on a manifold with an internal and lightlike boundary. At this inner boundary, new canonical variables appear: a spinor and a…
A finite action principle for three-dimensional gravity with negative cosmological constant, based on a boundary condition for the asymptotic extrinsic curvature, is considered. The bulk action appears naturally supplemented by a boundary…
For a physical interpretation of a theory of quantum gravity, it is necessary to recover classical spacetime, at least approximately. However, quantum gravity may eventually provide classical spacetimes by giving spectral data similar to…
Motivated by quantum gravity on spacetimes with multi-scale geometry, we analyze quantum field theories with a self-adjoint fractional power $(\Box^2)^{\gamma/2}$ of the d'Alem\-bert\-ian in the kinetic term, for any real $\gamma>0$.…
The Hamiltonian for dynamic geometry generates the evolution of a spatial region along a vector field. It includes a boundary term which determines both the value of the Hamiltonian and the boundary conditions. The value gives the…
In this paper, we aim to explore the interplay between neutrinos and quantum gravity, illustrating some proposals about the use of these particles as probes for the supposed quantized structure of spacetime. The residual signatures of a…
We investigate Lorentzian quantum gravity coupled to a template matter sector with gauge fields, scalars and fermions. In the absence of quantised gravity, the matter sector by itself is renormalisable, but UV-incomplete. Provided quantum…
Exactly soluble models can serve as excellent tools to explore conceptual issues in non-perturbative quantum gravity. In perturbative approaches, it is only the two radiative modes of the linearized gravitational field that are quantized.…
The central principle of affine quantum gravity is securing and maintaining the strict positivity of the matrix $\{\hg_{ab}(x)\}$ composed of the spatial components of the local metric operator. On spectral grounds, canonical commutation…
We consider a discrete model of euclidean quantum gravity in four dimensions based on a summation over random simplicial manifolds. The action used is the Einstein-Hilbert action plus an $R^2$-term. The phase diagram as a function of the…