Related papers: Remarks on gravity and quantum mechanics
An approach to quantization of fields and gravity based on the De Donder-Weyl covariant Hamiltonian formalism is outlined. It leads to a hypercomplex extension of quantum mechanics in which the algebra of complex numbers is replaced by the…
We briefly review the remarkable connections between light-front QCD, gravity in AdS space, and conformal quantum mechanics. We discuss, in particular, the group theoretical and geometrical aspects of the underlying one-dimensional quantum…
This lecture reviews aspects of and prospects for progress towards a theory of quantum gravity from a particle physics perspective, also paying attention to recent findings of the LHC experiments at CERN.
We discuss the nature and a general formulation of the relativity principle and we show that it can be justified starting from a strictly operational point of view. We give some remark on the connection with the spacetime symmetry groups.…
In this note we wish to complement some recent work in the cosmological literature concerning the Weyl conformal curvature tensor and its parts. In particular, we shall give a clear-cut definition of the Newtonian limits of electric and…
This paper surveys some selected topics in the theory of conformal metrics and their connections to complex analysis, partial differential equations and conformal differential geometry.
A seminar given about 30 years ago by Ruben Aldrovandi motivates this text where some reflexions about constructing theories that modify General Relativity are made. Two particular cases, the Brans-Dicke and Unimodular Gravity ones, are…
We will consider the torsional completion of gravity for a background filled with Dirac matter fields, studying the weak-gravitational non-relativistic approximation, in view of an assessment about their effective phenomenology: we discuss…
It is shown that the Evans-Vigier modified electrodynamics is compatible with the Relativity Theory.
Three of the four forces of Nature are described by quantum Yang-Mills theories with remarkable precision. The fourth force, gravity, is described classically by the Einstein-Hilbert theory. There appears to be an inherent incompatibility…
I give a brief introduction to the relation between loop quantum gravity and twistor theory, and comment on some perspectives on the problem of time.
This is an informal review of the formulation of canonical general relativity and of its implications for quantum gravity; the various versions are compared, both in the continuum and in a discretized approximation suggested by Regge…
The conformal anomaly (also known as the stress-energy trace anomaly) of an interacting quantum theory, associated with violation of Weyl (conformal) symmetry by quantum effects, can be amended if one endows the theory with a dilatation…
We investigate the behavior of generic, matter-coupled, 2D dilaton gravity theories under dilaton-dependent Weyl rescalings of the metric. We show that physical observables associated with 2D black holes, such as the mass, the temperature…
We discuss the $q$ deformation of Weyl-Heisenberg algebra in connection with the von Neumann theorem in Quantum Mechanics. We show that the $q$-deformation parameter labels the Weyl systems in Quantum Mechanics and the unitarily…
In this conceptual paper we construct a local version of Shape Dynamics that is equivalent to General Relativity in the sense that the algebras of Dirac observables weakly coincide. This allows us to identify Shape Dynamics observables with…
Recent work by physicists on gravity in two dimensions has a natural generalization to four dimensions, formulated in terms of an analogue of Segal's category [defined for the study of conformal field theory].
In a recent comment [arXiv:2112.05658], Grudka and W\'ojcik object to some of our earlier claims concerning a link between fundamental postulates of quantum theory and special relativity extended to superluminal frames of reference. In this…
The Weyl double copy is a relationship between classical solutions in gauge and gravity theories, and has previously been applied to vacuum solutions in both General Relativity and its generalisations. There have also been suggestions that…
The equations of the conformal field theory of gravitation with the Dirac's scalar field in Weyl-Cartan spacetime have been received. Exact solutions for Dirac's scalar field for an early Universe have been derived. Intensive decrease of…