I am editing a Special Issue for the journal Symmetry, together with Angel Ballesteros and Francisco Herranz. We are accepting submissions until 15th of March 2020. Below is the Special Issue description. Please feel free to contact me if you have any question.
Quantum groups appeared during the eighties as the underlying algebraic symmetries of several two-dimensional integrable models. They are noncommutative generalizations of Lie groups endowed with a Hopf algebra structure, and the possibility of defining noncommutative spaces that are covariant under quantum group (co)actions soon provided a fruitful link with noncommutative geometry. At the same time, when quantum group analogues of the Lie groups of spacetime symmetries (Galilei, Poincare’ and (anti-) de Sitter) were constructed, they attracted the attention of quantum gravity researchers. In fact, they provided a possible mathematical framework to model the “quantum” geometry of space–time and the quantum deformations of its kinematical symmetries at the Planck scale, where nontrivial features are expected to arise because of the interplay between gravity and quantum theory.
This Special Issue is open to contributions dealing with any of the many facets of quantum group symmetry and their generalizations. On the more formal side, possible topics include the theory of Poisson–Lie groups and Poisson homogeneous spaces as the associated semiclassical objects; Hopf algebras; the classification of quantum groups and spaces, their representation theory and its connections with q-special functions; the construction of noncommutative differential calculi; and the theory of quantum bundles. On application side, possible topics are: classical and quantum integrable models with quantum group invariance; the applications of quantum groups in different (2+1) quantum gravity contexts (like combinatorial quantisation, state sum models or spin foams); and quantum kinematical groups and their noncommutative spacetimes in connection with deformed special relativity and quantum gravity phenomenology.
Prof. Angel Ballesteros Dr. Giulia Gubitosi Prof. Francisco J. Herranz Guest Editors
We follow the life of a generic primordial perturbation mode (scalar or tensor) subject to modified dispersion relations (MDR), as its proper wavelength is stretched by expansion. A necessary condition ensuring that travelling waves can be converted into standing waves is that the mode starts its life deep inside the horizon and in the trans-Planckian regime, then leaves the horizon as the speed of light corresponding to its growing wavelength drops, to eventually become cis-Planckian whilst still outside the horizon, and finally re-enter the horizon at late times. We find that scalar modes in the observable range satisfy this condition, thus ensuring the viability of MDR models in this respect. For tensor modes we find a regime in which this does not occur, but in practice it can only be realised for wavelengths in the range probed by future gravity wave experiments if the quantum gravity scale experienced by gravity waves goes down to the PeV range. In this case travelling—rather than standing—primordial gravity waves could be the tell-tale signature of MDR scenarios.
Action Chair: Jose Manuel Carmona (University of Zaragoza) Action Vice-Chair: Giovanni Amelino-Camelia (University of Naples)
The exploration of the Universe has recently entered a new era thanks to the multi-messenger paradigm. The detection of cosmic particles (photons, neutrinos, cosmic rays), now joined by the birth of gravitational wave astronomy, gives us information about the different sources in the Universe and the properties of the intergalactic medium. In particular, the most energetic events allow us to test our physical theories at energy regimes which are not directly accessible in accelerators. This is in fact the target of quantum gravity phenomenology, a quite recent field of physics that tries to set phenomenological models that may incorporate some of the effects of the Planck scale, thus providing a bottom-up approach to the largely studied quantum gravity problem.
The main objective of the proposed COST Action is to gather theoretical and experimental working groups from the relevant communities (with proper geographical, age and gender balance) to work in the prediction and possibility of detection of physical phenomena characteristic from quantum gravity theories. This cooperation is necessary to address this challenge properly, which may result in extraordinary advancements in fundamental physics. A second objective will be the formation of a generation of scientists that will be competent in the interdisciplinary expertise that is needed in the effective search of quantum gravity footprints in the production, propagation and detection of these cosmic messengers. Whatever the outcomes of this search may be, it will certainly have an important impact on science through a better understanding of the Universe and its fundamental laws.
We investigate the relativistic properties under boost transformations of the κ-Poincaré model with multiple causally connected interactions, both at the level of its formulation in momentum space only and when it is endowed with a full phase space construction, provided by the relative locality framework. Previous studies focusing on the momentum space picture showed that in the presence of just one interaction vertex the model is relativistic, provided that the boost parameter acting on each given particle receives a “backreaction” from the momenta of the other particles that participate in the interaction. Here we show that in the presence of multiple causally connected vertices the model is relativistic if the boost parameter acting on each given particle receives a backreaction from the total momentum of all the particles that are causally connected, even those that do not directly enter the vertex. The relative locality framework constructs spacetime by defining a set of dual coordinates to the momentum of each particle and interaction coordinates as Lagrange multipliers that enforce momentum conservation at interaction events. We show that the picture is Lorentz invariant if one uses an appropriate “total boost” to act on the particles’ worldlines and on the interaction coordinates. The picture we develop also allows for a reinterpretation of the backreaction as the manifestation of the total boost action. Our findings provide the basis to consistently define distant relatively boosted observers in the relative locality framework.