Related papers: Classical Gravity on Fuzzy Space-Time
The vacuum correlations of the gravitational field are highly non-trivial to be defined and computed, as soon as their arguments and indices do not belong to a background but become dynamical quantities. Their knowledge is essential however…
We offer a perspective on some recent results obtained in the context of the group field theory approach to quantum gravity, on top of reviewing them briefly. These concern a natural mechanism for the emergence of non-commutative field…
We propose an action for gravity on a fuzzy sphere, based on a matrix model. We find striking similarities with an analogous model of two dimensional gravity on a noncommutative plane, i.e. the solution space of both models is spanned by…
This paper is a sequel to one in which we examined the affine symmetry algebras of arbitrary classical principal chiral models and symmetric space models in two dimensions. It examines the extension of those results in the presence of…
We describe a theory of gravitation on canonical noncommutative spacetimes. The construction is based on theta-twisted General Coordinate Transformations and Local Lorentz Invariance.
We construct functions and tensors on noncommutative spacetime by systematically twisting the corresponding commutative structures. The study of the deformed diffeomorphisms (and Poincare) Lie algebra allows to construct a noncomutative…
Based on the construction of the 4-dim noncommutative gravity model described in our previous work, first, a more extended description of the covariant noncommutative space (fuzzy 4-dim de Sitter space), which accommodates the gravity…
The theory of noncommutative geometry provides an interesting mathematical background for developing new physical models. In particular, it allows one to describe the classical Standard Model coupled to Euclidean gravity. However,…
Two questions are investigated by looking successively at classical mechanics, special relativity, and relativistic gravity: first, how is space related with spacetime? The proposed answer is that each given reference fluid, that is a…
We derive the interaction of fermions with a dynamical space-time based on the postulate that the description of physics should be independent of the reference frame, which means to require the form-invariance of the fermion action under…
We give formulations of noncommutative two dimensional gravities in terms of noncommutative gauge theories. We survey their classical solutions and show that solutions of the corresponding commutative theories continue to be solutions in…
We provide a brief overview into recent tests of gravity, focusing on its foundational spacetime symmetries. In particular, we work with an agnostic, effective field-theory framework, named the Standard-Model Extension, that allows for…
We study gauge and gravitational field theories in which the gauge fixing conditions are imposed as constraints on classical fields. Quantization of fluctuations can be performed in a BRST invariant manner, while the main novelty is that…
Several versions of fuzzy four-dimensional de Sitter space are constructed using the noncommutative frame formalism. Although all noncommutative spacetimes which are found have commutative de Sitter metric as a classical limit, the algebras…
We discuss gauge theories for commutative but non-associative algebras related to the $ SO(2k+1)$ covariant finite dimensional fuzzy $2k$-sphere algebras. A consequence of non-associativity is that gauge fields and gauge parameters have to…
I consider a hybrid cosmological model with a classical gravitational field and a quantized massive scalar field in spherically symmetric gravity. The interaction between classical and quantum fields is described using the formalism of…
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…
We review some recent progress in quantum field theory in non-commutative space, focusing onto the fuzzy sphere as a non-perturbative regularisation scheme. We first introduce the basic formalism, and discuss the limits corresponding to…
In recent years Quantum Superstrings and Quantum Gravity approaches have come to rely on non differenciable spacetime manifolds. These throw up a noncommutative spacetime geometry and we consider the origin of mass and a related…
We briefly discuss some possible cosmological implications of noncommutative geometry. While the noncommutativity we consider does not affect gravity, it can play an important role in the dynamics of other fields that are present in the…