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

Cosmological consequences of the NonCommutative Geometry Spectral Action

Cosmological consequences of the noncommutative geometry spectral action are presented. Neglecting the nonminimal coupling of the Higgs field to the curvature, background cosmology remains unchanged, and only the inhomogeneous perturbations will evolve differently from the equivalent classical system. However, considering the nonminimal coupling, corrections will be obtained even at the level of the background cosmologies. Finally, the Higgs field may act as an inflaton field, due to its nonminimal coupling with geometry.Comment: 7 pages, LaTeX. Invited talk at the XXV Max Bonn Symposium "Physics at the Planck Scale", in Wroclaw (Poland), 29th June-3rd July 2009. To appear in the Conference Proceeding

AdS--Maxwell superalgebra and supergravity

In this paper we derive the Anti de Sitter counterpart of the super-Maxwell algebra presented recently by Bonanos et.\ al. Then we gauge this algebra and derive the corresponding supergravity theory, which turns out to be described by the standard N=1 supergravity lagrangian, up to topological terms.Comment: 8 pages, in v2 reference adde

Quantum geometry and quantum dynamics at the Planck scale

Canonical quantum gravity provides insights into the quantum dynamics as well as quantum geometry of space-time by its implications for constraints. Loop quantum gravity in particular requires specific corrections due to its quantization procedure, which also results in a discrete picture of space. The corresponding changes compared to the classical behavior can most easily be analyzed in isotropic models, but perturbations around them are more involved. For one type of corrections, consistent equations have been found which shed light on the underlying space-time structure at the Planck scale: not just quantum dynamics but also the concept of space-time manifolds changes in quantum gravity. Effective line elements provide indications for possible relationships to other frameworks, such as non-commutative geometry.Comment: 10 pages, 2 figures, Proceedings of "The Planck Scale" (XXV Max Born Symposium, Wroclaw

Semiclassical Analysis of Constrained Quantum Systems

Exact procedures that follow Dirac's constraint quantization of gauge theories are usually technically involved and often difficult to implement in practice. We overview an "effective" scheme for obtaining the leading order semiclassical corrections to the dynamics of constrained quantum systems developed elsewhere. Motivated by the geometrical view of quantum mechanics, our method mimics the classical Dirac-Bergmann algorithm and avoids direct reference to a particular representation of the physical Hilbert space. We illustrate the procedure through the example of a relativistic particle in Minkowski spacetime.Comment: 8 pages, Proceedings of "The Planck Scale" (XXV Max Born Symposium, Wroclaw

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

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

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

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