Achim Kempf

Non-pointlike particles in harmonic oscillators

Quantum mechanics usually describes particles as being pointlike in the sense that, in principle, the uncertainty, , can be made arbitrarily small. Studies on string theory and quantum gravity motivate correction terms to the uncertainty relations which induce a finite lower bound to spatial localization. This structure is implemented into quantum mechanics through small correction terms to the canonical commutation relations. We calculate the perturbations to the energy levels of a particle which is non-pointlike in this sense in isotropic harmonic oscillators, where we find a characteristic splitting of the usually degenerate energy levels. Possible applications are outlined.

Minimal length uncertainty relation and ultraviolet regularization

Studies in string theory and quantum gravity suggest the existence of a finite lower limit

Mode generating mechanism in inflation with cutoff

\ensuremath{\Delta}{x}_{0}

Maximal localization in the presence of minimal uncertainties in positions and in momenta

to the possible resolution of distances, at the latest on the scale of the Planck length of

On quantum field theory with nonzero minimal uncertainties in positions and momenta

{10}^{\ensuremath{-}35}

Fundamental quantum optics experiments conceivable with satellites : reaching relativistic distances and velocities

m. Within the framework of the Euclidean path integral we explicitly show ultraviolet regularization in field theory through this short distance structure. Both rotation and translation invariance can be preserved. An example is studied in detail.

Black holes, bandwidths and Beethoven

In most inflationary models, space-time inflated to the extent that modes of cosmological size originated as modes of wavelengths at least several orders of magnitude smaller than the Planck length. Recent studies confirmed that, therefore, inflationary predictions for the cosmic microwave background perturbations are generally sensitive to what is assumed about the Planck scale. Here, we propose a framework for field theories on curved backgrounds with a plausible type of ultraviolet cutoff. We find an explicit mechanism by which during cosmic expansion new (comoving) modes are generated continuously. Our results allow the numerical calculation of a prediction for the CMB perturbation spectrum.

Fields over unsharp coordinates.

Small corrections to the uncertainty relations, with effects in the ultraviolet and/or infrared, have been discussed in the context of string theory and quantum gravity. Such corrections lead to small but finite minimal uncertainties in position and/or momentum measurements. It has been shown that these effects could indeed provide natural cutoffs in quantum field theory. The corresponding underlying quantum theoretical framework includes small ‘‘noncommutative geometric’’ corrections to the canonical commutation relations. In order to study the full implications on the concept of locality, it is crucial to find the physical states of then maximal localization. These states and their properties have been calculated for the case with minimal uncertainties in positions only. Here we extend this treatment, though still in one dimension, to the general situation with minimal uncertainties both in positions and in momenta.

Generalized uncertainty principles and localization of a particle in discrete space

We continue studies on quantum field theories on noncommutative geometric spaces, focusing on classes of noncommutative geometries which imply ultraviolet and infrared modifications in the form of nonzero minimal uncertainties in positions and momenta. The case of the ultraviolet modified uncertainty relation which has appeared from string theory and quantum gravity is covered. The example of Euclidean φ4-theory is studied in detail and in this example we can now show ultraviolet and infrared regularization of all graphs.

Spacetime could be simultaneously continuous and discrete, in the same way that information can be

Physical theories are developed to describe phenomena in particular regimes, and generally are valid only within a limited range of scales. For example, general relativity provides an effective description of the Universe at large length scales, and has been tested from the cosmic scale down to distances as small as 10 m (Dimopoulos 2007 Phys. Rev. Lett. 98 111102; 2008 Phys. Rev. D 78 042003). In contrast, quantum theory provides an effective description of physics at small length scales. Direct tests of quantum theory have been performed at the smallest probeable scales at the Large Hadron Collider, ~10−20 m, up to that of hundreds of kilometres (Ursin et al 2007 Nature Phys. 3 481–6). Yet, such tests fall short of the scales required to investigate potentially significant physics that arises at the intersection of quantum and relativistic regimes. We propose to push direct tests of quantum theory to larger and larger length scales, approaching that of the radius of curvature of spacetime, where we begin to probe the interaction between gravity and quantum phenomena. In particular, we review a wide variety of potential tests of fundamental physics that are conceivable with artificial satellites in Earth orbit and elsewhere in the solar system, and attempt to sketch the magnitudes of potentially observable effects. The tests have the potential to determine the applicability of quantum theory at larger length scales, eliminate various alternative physical theories, and place bounds on phenomenological models motivated by ideas about spacetime microstructure from quantum gravity. From a more pragmatic perspective, as quantum communication technologies such as quantum key distribution advance into space towards large distances, some of the fundamental physical effects discussed here may need to be taken into account to make such schemes viable.