38 research outputs found
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
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
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
-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 -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
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
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
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
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