Related papers: Planck-scale modified dispersion relations and Fin…
Connes' non-commutative geometry (NCG) is a generalization of Riemannian geometry that is particularly apt for expressing the standard model of particle physics coupled to Einstein gravity. In a previous paper, we suggested a reformulation…
We discuss a large class of phenomenological models incorporating quantum gravity motivated corrections to electrodynamics. The framework is that of electrodynamics in a birefringent and dispersive medium with non-local constitutive…
In this work, we make new developments in generic cotangent bundle geometries, depending on all phase-space variables. In particular, we will focus on the so-called generalized Hamilton spaces, discussing how the main ingredients of this…
We review the main features of models where relativistic symmetries are deformed at the Planck scale. We cover the motivations and links to other quantum gravity approaches. We describe in some detail the most studied theoretical…
Motivated by the expectation that relativistic symmetries might acquire quantum features in Quantum Gravity, we take the first steps towards a theory of ''Doubly'' Quantum Mechanics, a modification of Quantum Mechanics in which the…
Vielbeins are necessary when coupling General Relativity (GR) to fermionic matter. This enhances the gauge group of GR to include local Lorentz transformations. In view of a reduced phase space formulation of quantum gravity, in this work…
It has been known for some time now that error correction plays a fundamental role in the determining the emergence of semiclassical geometry in quantum gravity. In this work I connect several different lines of reasoning to argue that this…
Quantum theory is formulated as a probabilistic theory on a flat Minkowski space-time, while general theory of relativity is formulated on a curved manifold as a geometric theory. Bohmian Quantum Gravity approach indicates that one need to…
I give a brief overview of some Quantum-Gravity-Phenomenology research lines, focusing on studies of cosmic rays and gamma-ray bursts that concern the fate of Lorentz symmetry in quantum spacetime. I also stress that the most valuable…
In this paper we propose a geometrization of the non-relativistic quantum mechanics for mixed states. Our geometric approach makes use of the Uhlmann's principal fibre bundle to describe the space of mixed states and as a novelty tool, to…
We investigate several problems in relativity and particle physics where symmetries play a central role; in all cases geometric properties of Lie groups and their quotients are related to physical effects. The first part is concerned with…
This paper discusses the somewhat unintuitive conjecture that many Lorentz-invariant many-particle models can be reinterpreted to satisfy the gtr field equations. It is shown that a careful remapping of coordinates yields a non-trivial…
A brief review of main features of the new approach named ``quantum geometrodynamics in extended phase space'' is given and its possible prospects are discussed. Gauge degrees of freedom are treated as a subsystem of the Universe which…
This paper presents the geometric setting of quantum variational principles and extends it to comprise the interaction between classical and quantum degrees of freedom. Euler-Poincar\'e reduction theory is applied to the Schr\"odinger,…
Finsler geometry is a natural arena to investigate the physics of spacetimes with local Lorentz violating. The directional dependence of the Finsler metric provides a way to encode the Lorentz violating effects into the geometric structure…
States of a quantum mechanical system are represented by rays in a complex Hilbert space. The space of rays has, naturally, the structure of a K\"ahler manifold. This leads to a geometrical formulation of the postulates of quantum mechanics…
We develop a novel approach to gravity that we call `matrix general relativity' (MGR) or `gravitational chromodynamics' (GCD or GQCD for quantum version). Gravity is described in this approach not by one Riemannian metric (i.e. a symmetric…
Recent progress in quantum field theory and quantum gravity relies on mixed boundary conditions involving both normal and tangential derivatives of the quantized field. In particular, the occurrence of tangential derivatives in the boundary…
After a brief review of the first phase of development of Quantum-Gravity Phenomenology, I argue that this research line is now ready to enter a more advanced phase: while at first it was legitimate to resort to heuristic order-of-magnitude…
Emergent modified gravity is a post-Einsteinian gravitational theory where spacetime geometry is not fundamental but rather emerges from the gravitational degrees of freedom in a non-trivial way. The specific relationship between geometry…