Kaluza-Klein Description Research Articles

Quantum holonomy based in a Kaluza–Klein description for defects in C60 fullerenes

In this paper, we discuss a new way to get a quantum holonomy around topological defects in [Formula: see text] fullerenes. For this, we use a Kaluza–Klein extra dimension approach. Furthermore, we discuss how an extra dimension could promote the formation of new freedom degrees which would open a discussion about a possible qubits computation.

Modification of the laws of gravity in the DGP model by the presence of a second DGP brane

We investigate how the laws of gravity change in the DGP model, if we add a second, parallel 3-brane, endowed with a localized gravitational curvature term. We calculate the gravitational potential energy between two static point sources localized on different branes. We discover a new length scale, which is equal to the geometric mean of the DGP cross-over scale and the separation of the two branes in the extra dimension. For distances, which are larger than this new length scale, we recover the original DGP result, but for smaller distances the gravitational potential is weaker. Furthermore, a region emerges, where a 4-dimensional observer measures a distance independent force. We discuss a possible application of the present scenario for deriving rotation curves of low surface brightness galaxies. Using the Kaluza-Klein description, we observe a curious pattern, in which even and odd KK-modes contribute to the attractive and repulsive parts of the gravitational potential, respectively. Finally, since this setup allows for the existence of a sector of particle species that are interacting arbitrarily weakly with “our” sector, we discuss the implications of this phenomenon for black holes and the bound on the number of species. We find that the behavior is qualitatively different from theories with a normalizable zero-mode graviton.

A Kaluza–Klein description of geometric phases in graphene

In this paper, we use the Kaluza–Klein approach to describe topological defects in a graphene layer. Using this approach, we propose a geometric model allowing us to discuss the quantum flux in K-spin subspace. Within this model, the graphene layer with a topological defect is described using a four-dimensional metric, where the deformation produced by the topological defect is introduced via the three-dimensional part of a metric tensor, while an Abelian gauge field is introduced via an extra dimension. We use this new geometric model to discuss the arising of topological quantum phases in a graphene layer with a topological defect.

Establishing analogies between the physics of extra dimensions and carbon nanotubes

We point out a conceptual analogy between the physics of extra spatial dimensions and the physics of carbon nanotubes which arises for principle reasons, although the corresponding energy scales are at least ten orders of magnitude apart. For low energies, one can apply the Kaluza–Klein description to both types of systems, leading to two completely different but consistent interpretations of the underlying physics. In particular, we discuss in detail the Kaluza–Klein description of armchair and zig-zag carbon nanotubes. Furthermore, we describe how certain experimental results for carbon nanotubes could be re-interpreted in terms of the Kaluza–Klein description. Finally, we present ideas for new measurements that could allow to probe concepts of models with extra spatial dimensions in table-top experiments, providing further links between condensed matter and particle physics.

Geometric models of matter

Inspired by soliton models, we propose a description of static particles in terms of Riemannian 4-manifolds with self-dual Weyl tensor. For electrically charged particles, the 4-manifolds are non-compact and asymptotically fibred by circles over physical 3-space. This is akin to the Kaluza–Klein description of electromagnetism, except that we exchange the roles of magnetic and electric fields, and only assume the bundle structure asymptotically, away from the core of the particle in question. We identify the Chern class of the circle bundle at infinity with minus the electric charge and, at least provisionally, the signature of the 4-manifold with the baryon number. Electrically neutral particles are described by compact 4-manifolds. We illustrate our approach by studying the Taub–Newman, Unti, Tamburino (Taub–NUT) manifold as a model for the electron, the Atiyah–Hitchin manifold as a model for the proton, with the Fubini–Study metric as a model for the neutron and S 4 with its standard metric as a model for the neutrino.

Nonlocal braneworld action: An alternative to the Kaluza-Klein description

We construct the nonlocal braneworld action in the two-brane Randall-Sundrum model in a holographic setup alternative to Kaluza-Klein description: the action is written as a functional of the two metric and radion fields on the branes. This action effectively describes the dynamics of the gravitational field both on the branes and in the bulk in terms of the brane geometries directly accessible for observations. Its nonlocal form factors incorporate the cumulative effect of the bulk Kaluza-Klein modes. We also consider the reduced version of this action obtained by integrating out the fields on the negative-tension brane invisible from the viewpoint of the Planckian brane observer. This effective action features a nontrivial transition (AdS flow) between the local and nonlocal phases of the theory associated with the limits of small and large interbrane separation. Our results confirm a recently proposed braneworld scenario with diverging (repulsive) branes and suggest possible new implications of this phase transition in brane cosmology.

Kaluza-klein description of the electrical field due to an infinitely long, straight line charge

It is shown that according to the Kaluza-Klein theory the electromagnetic scalar potential is equal to the angular velocity of the rotational inertial dragging effect in five-dimensional space-time. The gravitational vacuum field equations for a five-dimensional space-time outside a rotating cylindrical shell are solved. The angular velocity of the inertial dragging field outside the shell is determined in terms of the angular momentum of the shell by means of Israel's geometric description of surface layers in general relativity. Projecting the solution into four-dimensional space-time, the inertial dragging field due to the rotation of the shell is interpreted as an electrical field. We conjecture that according to the Kaluza-Klein theory all electromagnetic phenomena are four-dimensional manifestations of the five-dimensional inertial dragging effect.

Charge quantization without superheavy masses in a Kaluza–Klein description of electromagnetism

A scalar matter field coupled to general relativity and electromagnetism in a five-dimensional Kaluza–Klein model is considered. The five-dimensional space is assumed to be a fiber bundle as in the usual description of a gauge theory and not a more general manifold. Properly taking this into account allows one to use a Lagrangian density for the scalar field which includes charge quantization but not the unphysical superheavy masses found by other authors. A natural, satisfactory explanation of why charge is quantized results.