Related papers: Curved momentum space, locality, and generalized s…
We treat space and time as bona fide quantum degrees of freedom on an equal footing in Hilbert space. Motivated by considerations in quantum gravity, we focus on a paradigm dealing with linear, first-order Hamiltonian and momentum…
We apply Lie algebra deformation theory to the problem of identifying the stable form of the quantum relativistic kinematical algebra. As a warm up, given Galileo's conception of spacetime as input, some modest computer code we wrote zeroes…
We present the first detailed study of the kinematics of free relativistic particles whose symmetries are described by a quantum deformation of the de Sitter algebra, known as $q$-de Sitter Hopf algebra. The quantum deformation parameter is…
The algebras of non-relativistic and of classical mechanics are unstable algebraic structures. Their deformation towards stable structures leads, respectively, to relativity and to quantum mechanics. Likewise, the combined relativistic…
We propose a deepening of the relativity principle according to which the invariant arena for non-quantum physics is a phase space rather than spacetime. Descriptions of particles propagating and interacting in spacetimes are constructed by…
We develop a new description of the much-studied $\kappa$-Minkowski noncommutative spacetime, centered on representing on a single Hilbert space not only the $\kappa$-Minkowski coordinates, but also the associated differential calculus and…
We argue that a (slightly) curved space-time probed with a finite resolution, equivalently a finite minimal length, is effectively described by a flat non-commutative space-time. More precisely, a small cosmological constant (so a constant…
Canonical methods can be used to construct effective actions from deformed covariance algebras, as implied by quantum-geometry corrections of loop quantum gravity. To this end, classical constructions are extended systematically to…
A suitable deformation of the Hopf algebra of the creation and annihilation operators for a complex scalar field, initially quantized in Minkowski space--time, induces the canonical quantization of the same field in a generic gravitational…
The aim of this contribution is twofold. First, we show that when two (or more) different quantum groups share the same noncommutative spacetime, such an 'ambiguity' can be resolved by considering together their corresponding noncommutative…
In relative locality theories the geometric properties of phase space depart from the standard ones given by the fact that spaces of momenta are linear fibers over a spacetime base manifold. In particular here it is assumed that the…
Using the recently proposed covariant framework of general relativistic stochastic mechanics and stochastic thermodynamics, we proved the detailed and integral fluctuation theorems in curved spacetime. The time-reversal transformation is…
Extending the commutator algebra of quantum $\kappa$-Poincar\'e symmetry to the whole of the phase space, and assuming that this algebra is to be covariant under action of deformed Lorentz generators, we derive the transformation properties…
A nonlinear transformation in the momentum space is constructed which converts the deformed action of Lorentz and Weyl generators on momenta into the standard one.
A common approach to metric-affine, local Poincar\'e, special-relativistic and Galilei spacetime geometry is developed. Starting from an affine composite bundle, we introduce local reference frames and their evolution along worldlines and…
Deformations of spacelike hypersurfaces in space-time play an important role in discussions of general covariance and slicing independence in gravitational theories. In a canonical formulation, they provide the geometrical meaning of gauge…
Several arguments suggest that the Planck scale could be the characteristic scale of curvature of momentum space. As other recent studies we assume that the metric of momentum space determines the condition of on-shellness while the…
Recent proposals suggested quantum clock interferometry for tests of the Einstein equivalence principle. However, atom interferometric models often include relativistic effects only in an ad hoc fashion. Here, instead, we start from the…
We investigate the geometry of the energy-momentum space of the Snyder model of noncommmutative geometry and of its generalizations, according to the postulates of relative locality. These relate the geometric structures to the deformed…
General covariant expressions for measurable angles, distances, velocities, and accelerations are provided in terms of fundamental parameters that can be applied in any setup. The relativistic aberration of light relationship is presented…