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Conformal transformations are frequently used tools in order to study relations between various theories of gravity and the Einstein relativity. In this paper we discuss the rules of these transformations for geometric quantities as well as…
We advance an universal approach to the construction of kinematics in non-inertial and, in particular, rotating reference frames. On its basis a 10-dimensional space including three projections of velocity vector and three turn angles in…
The implications of conformal invariance, as relevant in quantum field theories at a renormalisation group fixed point, are analysed with particular reference to results for correlation functions involving conserved currents and the energy…
The elasticity difference tensor, used in [1] to describe elasticity properties of a continuous medium filling a space-time, is here analysed from the point of view of the space-time connection. Principal directions associated with this…
Theories of physics can be considered viable if the initial value problem and the energy conditions are formulated self-consistently. The former allow a uniquely determined dynamical evolution of the system, and the latter guarantee that…
The present work provides a new conceptual framework for GUT (Grand Unified Theory) based on a picture of fractal universe. Under a hypothesis of multi-scaled matter structure, we find new clues for the conciliation of quantum and…
We compute the curvature tensor of the tangent bundle of a Riemannian manifold endowed with a natural metric and we get some relationships between the geometry of the base manifold and the geometry of the tangent bundle.
We introduce a geometric construction of a gauge field theory of a complex adaptive system. It is based on a suitable simplicial formulation of a discrete geometry that manifests relevant properties valid in the classical differentiable…
Given a measure space ${\mathcal X}$, we can construct a number of induced structures: eg. its $L^2$ space, the space ${\mathcal P}({\mathcal X})$ of probability distributions on ${\mathcal X}$. If, in addition, ${\mathcal X}$ admits a…
This paper is a sequence of the work presented in [1], where, the principles of the general relativity have been used to formulate quantum wave equations taking into account the effect of the electromagnetic and strong interactions in the…
We argue that the natural framework for embedding the ideas of deformed, or doubly, special relativity (DSR) into a curved spacetime is a generalisation of Einstein-Cartan theory, considered by Stelle and West. Instead of interpreting the…
Scalar induced gravitational waves contribute to the cosmological gravitational wave background. They can be related to the primordial density power spectrum produced towards the end of inflation and therefore are a convenient new tool to…
As true as it is that a bricklayer needs a plumb line and a T-square, so it is that a physicist using general relativity needs how to draw geodesics and use fields of congruent vector frames of reference. While the first part of the…
We consider the notion of a connection on a principal bundle $P(M,G)$ from the point of view of the action of the tangential group $TG$. This leads to a new definition of a connection and allows to interpret gauge transformations as effect…
This thesis is situated within the context of quantum gravity, broadly understood as any effort to explore the interplay between gravitation and the quantum realm, without necessarily requiring the quantization of the gravitational field…
Tangent categories offer a categorical context for differential geometry, by categorifying geometric notions like the tangent bundle functor, vector fields, Euclidean spaces, vector bundles, connections, etc. In the last decade, the theory…
This paper explores a new perspective on the universality of the vertical lift in tangent categories by presenting a categorification of the dimension of smooth manifolds. The universality of the vertical lift is a key part of the axioms of…
We develop a description of higher gauge theory with higher groupoids as gauge structure from first principles. This approach captures ordinary gauge theories and gauged sigma models as well as their categorifications on a very general…
In this paper, we expand on previous work describing partial derivatives and metric component estimators to define tangent spaces on causal sets. Partial derivative operators are the basis vectors of the tangent space, and the metric…
We consider generalized energy conditions in modified theories of gravity by taking into account the further degrees of freedom related to scalar fields and curvature invariants. The latter are usually recast as generalized {\it geometrical…