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The well-known geometric approach to field theory is based on description of classical fields as sections of fibred manifolds, e.g. bundles with a structure group in gauge theory. In this approach, Lagrangian and Hamiltonian formalisms…
Diffeomorphism invariance is a feature that gets sometimes highlighted as something with profound implications in the physics of spacetime. Moreover, it is often wrongly associated exclusively with General Relativity. The fact that…
The classical procedures which define the relativistic notion of space-time can be implemented in the framework of Quantum Field Theory. Only relying on the conformal symmetries of field propagation, time-frequency transfer and localization…
Change and local spatial variation are missing in canonical General Relativity's observables as usually defined, part of the problem of time. Definitions can be tested using equivalent formulations, non-gauge and gauge, because they must…
A cosmological time variable is emerged from the hamiltonian formulation of unimodular theory of gravity to measure the evolution of dynamical observables in the theory. A set of constants of motion has been identified for the theory on the…
I describe an approach which relates classical gravity to the quantum microstructure of spacetime. In this approach, the field equations arise from maximizing the density of states of the matter plus geometry. The former is identified using…
We work on a 4-manifold equipped with Lorentzian metric $g$ and consider a volume-preserving diffeomorphism which is the unknown quantity of our mathematical model. The diffeomorphism defines a second Lorentzian metric $h$, the pullback of…
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…
Consistent nontrivial interactions within a special class of covariant mixed-symmetry type tensor gauge fields of degree three are constructed from the deformation of the solution to the master equation combined with specific cohomological…
The detection of gravitational waves in 2015 ushered in a new era of gravitational wave astronomy capable of probing into the strong field dynamics of black holes and neutron stars. It has opened up an exciting new window for laboratory and…
We study a deformation of infinitesimal diffeomorphisms of a smooth manifold. The deformation is based on a general twist. This leads to a differential geometry on a noncommutative algebra of functions whose product is a star-product. The…
The identification of physical subsystems in quantum mechanics as compared to classical mechanics poses significant conceptual challenges, especially in the context of quantum gravity. Traditional approaches associate quantum systems with…
A four dimensional generally covariant field theory is presented which describes non-dynamical three geometries coupled to scalar fields. The theory has an infinite number of physical observables (or constants of the motion) which are…
The relativistic conception of space and time is challenged by the quantum nature of physical observables. It has been known for a long time that Poincar\'e symmetry of field theory can be extended to the larger conformal symmetry. We use…
We review the construction of Lagrangians for higher spin fields of mixed symmetry in the framework of graded geometry. The main advantage of the graded formalism in this context is that it provides universal expressions, in the sense that…
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…
The gravity is classically formulated as the geometric curvature of the space-time in general relativity which is completely different from the other well-known physical forces. Since seeking a quantum framework for the gravity is a great…
The curvature invariants have been subject of interest due to the debate concerning the notions of intrinsic/extrinsic frame-dragging, the use of the electromagnetic analogy in such classification, and the question of whether there is a…
We discuss the possibility that spacetime geometry may be an emergent phenomenon. This idea has been motivated by the Analogue Gravity programme. These are systems where the kinematics of small perturbations are dominated by an effective…
Quantum gravity is expected to be necessary in order to understand situations where classical general relativity breaks down. In particular in cosmology one has to deal with initial singularities, i.e. the fact that the backward evolution…