Resonant algebras and gravity

The $S$-expansion framework is analyzed in the context of a freedom in closing the multiplication tables for the abelian semigroups. Including the possibility of the zero element in the resonant decomposition and associating the Lorentz generator with the semigroup identity element leads to the wide class of the expanded Lie algebras introducing interesting modifications to the gauge gravity theories. Among the results, we find all the Maxwell algebras of type $\mathfrak{B}_m$, $\mathfrak{C}_m$, and recently introduced $\mathfrak{D}_m$. The additional new examples complete resulting generalization of the bosonic enlargements to an arbitrary number of the Lorentz-like and translational-like generators. Some further prospects concerning enlarging the algebras are discussed, along with providing all the necessary constituents for constructing the gravity actions based on the obtained results.Comment: 17 pages, v3 (improved version prepared for publication in JPhysA

Fun from none: deformed symmetries and Fock space

We give a pedagogical introduction to the basics of deformations of relativistic symmetries and the Hilbert spaces of free quantum fields built as their representations. We focus in particular on the example of a $\kappa$-deformed scalar quantum field for which the generators of spatial translations that label the field modes act according to a deformed Leibnitz rule. We explore the richer structure of the $\kappa$-Fock space and point out possible physical consequences of the deformation.Comment: 7 pages, no figures. Invited talk at XXV Max Born Symposium, The Planck scale, Wroclaw (Poland), June 29 - July 3, 2009. To appear in the Proceeding

Twisted Covariance and Weyl Quantisation

In this letter we wish to clarify in which sense the tensor nature of the commutation relations [x^mu,x^nu]=i theta ^{mu nu} underlying Minkowski spacetime quantisation cannot be suppressed even in the twisted approach to Lorentz covariance. We then address the vexata quaestio "why theta"?Comment: 6 pages, pdf has active hyperlinks Slight change in title. Appendix added on more general coordinates for symbols. References added. To appear in the Proceedings of the XXV Max Born Symposium, Wroclaw, June 29-July 3, 200

M2-branes, Einstein manifolds and triple systems

This is the written version of a talk given on 1 July 2009 at the XXV Max Born Symposium: the Planck Scale, held in Wroclaw, Poland. I review the possible transverse geometries to supersymmetric M2-brane configurations and discuss the representation-theoretic description of their conjectured dual superconformal Chern-Simons theories.Comment: 12 pages; V2: reference(s) adde

Breaking and restoring of diffeomorphism symmetry in discrete gravity

We discuss the fate of diffeomorphism symmetry in discrete gravity. Diffeomorphism symmetry is typically broken by the discretization. This has repercussions for the observable content and the canonical formulation of the theory. It might however be possible to construct discrete actions, so--called perfect actions, with exact symmetries and we will review first steps towards this end.Comment: to appear in the Proceedings of the XXV Max Born Symposium "The Planck Scale", Wroclaw, 29 June - 3 July, 200

Field theories with homogenous momentum space

We discuss the construction of a scalar field theory with momentum space given by a coset. By introducing a generalized Fourier transform, we show how the dual scalar field theory actually lives in Snyder's space-time. As a side-product we identify a star product realization of Snyder's non-commutative space, but also the deformation of the Poincare symmetries necessary to have these symmetries realized in Snyder's space-time. A key feature of the construction is that the star product is non-associative.Comment: 9 pages, To appear in the Proceedings of the XXV Max Born Symposium, "The Planck Scale", Wroclaw, Poland, July 200

In, Through and Beyond the Planck Scale

In this paper we have recalled the semiclassical metric obtained from a classical analysis of the loop quantum black hole (LQBH). We show that the regular Reissner-Nordstr\"om-like metric is self-dual in the sense of T-duality: the form of the metric is invariant under the exchange r -> a0/r where a0 is proportional to the minimum area in LQG. Of particular interest, the symmetry imposes that if an observer at infinity sees a black hole of mass m an observer in the other asymptotic infinity beyond the horizon (near r=0) sees a dual mass proportional to m_P^2/m. We then show that small LQBHs are stable and could be a component of dark matter. Ultra-light LQBHs created shortly after the Big Bang would now have a mass of approximately 10^(-5) m_P and emit radiation with a typical energy of about 10^(13) - 10^(14) eV but they would also emit cosmic rays of much higher energies, albeit few of them. If these small LQBHs form a majority of the dark matter of the Milky Way's Halo, the production rate of ultra-high-energy-cosmic-rays (UHECR) by these ultra light black holes would be compatible with the observed rate of the Auger detector.Comment: 10 pages, 8 figures; to appear in the Proceedings of the XXV Max Born Symposium "The Planck Scale", Wroclaw, 29 June - 3 July, 200

Geometrizing the Quantum - A Toy Model

It is shown that the equations of relativistic Bohmian mechanics for multiple bosonic particles have a dual description in terms of a classical theory of conformally "curved" space-time. This shows that it is possible to formulate quantum mechanics as a purely classical geometrical theory. The results are further generalized to interactions with an external electromagnetic field.Comment: Talk given the XXV Max Born Symposium, 6 pages, no figur

Deformed Maxwell Algebras and their Realizations

We study all possible deformations of the Maxwell algebra. In D=d+1\neq 3 dimensions there is only one-parameter deformation. The deformed algebra is isomorphic to so(d+1,1)\oplus so(d,1) or to so(d,2)\oplus so(d,1) depending on the signs of the deformation parameter. We construct in the dS (AdS) space a model of massive particle interacting with Abelian vector field via non-local Lorentz force. In D=2+1 the deformations depend on two parameters b and k. We construct a phase diagram, with two parts of the (b,k) plane with so(3,1)\oplus so(2,1) and so(2,2)\oplus so(2,1) algebras separated by a critical curve along which the algebra is isomorphic to Iso(2,1)\oplus so(2,1). We introduce in D=2+1 the Volkov-Akulov type model for a Abelian Goldstone-Nambu vector field described by a non-linear action containing as its bilinear term the free Chern-Simons Lagrangean.Comment: 10 pages, Talk based on [1] in the XXV-th Max Born Symposium "Planck Scale", held in Wroclaw 29.06-3.07.200