Imitation of matter by a scalar field in five-dimensional Kaluza-Klein theory

The interpretation of the scalar field ={ie96-1} in the five-dimensional variant of Kaluza-Klein theory is considered. It is proposed that the scalar field be considered as the generalized potential of four material velocities. It can be shown that with additional limitations on the scalar field the right side of the split five-dimensional Einstein equations transform to a hydrodynamic energy-momentum tensor for an ideal liquid with a limited set of equations of state. Concrete five-dimensional metrics, which are obligatorily nonstationary, are analyzed from this viewpoint.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 111–117, January, 1995.     

Quantum effects in five-dimensional Kaluza-Klein theory

The role of quantum effects in five-dimensional Kaluza-Klein theory is discussed. We concentrate in particular on the evaluation of terms in the one-loop effective action which look like the Maxwell action. A detailed discussion of the reduction of the five-dimensional gravitational action to an equivalent four-dimensional form is given. Self-consistent solutions of the form R⁴ x S¹ are examined. We consider how the inclusion of quantized matter fields into the five-dimensional theory can change results based only on quantum gravitational effects. The importance of including the induced Maxwell term is stressed. It is also noted how a finite renormalization of the one-loop effective action is important.     

Temperature effects in five-dimensional Kaluza-Klein theory

We examine the combined effectsof thermal and quantum-mechanical fluctuations in a Kaluza-Klein universe with a single compact spatial dimension of length ${\overline{L}}_5$. From the one-loop effective potential for ${\overline{L}}_5$ two types of instability are evident. If initially ${\overline{L}}_5$ is less than a temperature-dependent critical length, ${\overline{L}}_5$ will shrink at least down to a length comparable to the Planck length. This instability has been noted by Appelquist and Chodos in the zero-temperature limit. If, on the other hand, ${\overline{L}}_5$ starts out larger than the critical length, it will tend to increase. This result suggests that temperature effects may play an important role in Kaluza-Klein cosmological models.     

Black holes coupled to scalar fields in higher-dimensional Kaluza-Klein theory

We derive in this paper an exact spherically symmetric solution coupled to scalar fields inn-dimensional Kaluza-Klein theory. A seven-dimensional solution is shown as a special case of the general solution. The solution has two even horizons. The inner horizon corresponds to the Schwarzschild black hole and the outer horizon is due to the scalar fields.     

Derivation of a Bogomol'ny inequality in five-dimensional Kaluza-Klein theory

We prove an inequality bounding the mass from below by the electromagnetic charge in five-dimensional Kaluza-Klein theory without assuming the existence of globalU(1) symmetry.Supported in part by NSF-Grant No. PHY-8318350     

The geodesic equation in five-dimensional relativity theory of Kaluza-Klein

In five-dimensional relativity theory of Kaluza-Klein the projection of the 5-geodesic equation is discussed in detail. The scalar occurring within this framework is first assumed to be variable. A simple classification of 5-geodesics is found and pictured with the help of a deformed 5-cone. On the assumption that the scalar is constant the 5-geodesic equation yields the Lorentz equation of motion for a charged particle. Intrinsic mass and intrinsic charge are introduced as new particle parameters. Mass and charge formulas are proposed.     

Spectral asymmetry of Dirac Hamiltonian in a five-dimensional Kaluza-Klein theory

It is shown that the fermion number in a five-dimensional Kaluza-Klein theory (M⁴×S¹) in which the fermion is interacting with a monopole field, is quantized in units of (ϕR)² where the scalar ϕ is asymptotically constant andR is the radius of S¹.     

Solution of the five-dimensional vacuum Einstein equations in Kaluza-Klein theory

In a recent paper Ross obtained the five-dimensional vacuum Einstein equations in Kaluza-Klein theory with energy-momentum tensor equal to zero and solved the equations for a particular case. Here we obtain the complete set of solutions of these equations.     

Path integrals and quantum interference effects in a five-dimensional Kaluza-Klein theory

The Aharonov-Bohm (AB) effect, the gravitational analogue to the AB effect, and the topological shifts in an AB set-up are derived by evaluating the propagator for a particle in a five-dimensional Kaluza-Klein spacetime via path integrals.     

Cosmology and the large-mass problem of the five-dimensional Kaluza-Klein theory

It is shown that in five-dimensional Kaluza-Klein theories the large-mass problem leads to circulus vitiosus: the huge recent e²/G value produces the large mass problem, which restricts the ratio e²/Gm² to the order of unity, in contradiction with the present 10⁴⁰ value for elementary particles.     

A study of the Higgs effect in the five-dimensional Kaluza-Klein theory

The complete expression of the five-dimensional Einstein-Hilbert action as an expansion in fields in the Appelquist-Chodos parametrization of the Kaluza-Klein metric has been given in this paper. It is explicitly shown that a unitary gauge can be fixed in which in each of the charge sectors the vector and the scalar fields are absorbed as Goldstone modes leaving behind the Pauli-Fierz Lagrangian for massive charged spin-2 field.     

Plane-wave solutions in five-dimensional Kaluza-Klein theories

Exact solutions representing mixed plane-electromagnetic and planegravitational waves in five-dimensional Kaluza-Klein theories are obtained. Two extreme cases, corresponding to the plane waves of the four-dimensional Einstein-Maxwell theory and the dilation waves, respectively, are discussed. In addition, it is found that the five-dimensional harmonic condition is reduced to the usual four-dimensional harmonic condition plus the Lorentz condition.     

Fundamental constants in singularity-free five-dimensional Kaluza-Klein cosmological model

Expressions for the time dependence of the fundamental constants are derived through dimensional reduction and one-loop quantum corrections to scalar fields. Moreover, singularity-free solutions of Einstein's field equations are obtained. Using these solutions, we discuss the time dependence of fundamental constants. It is interesting to see that the fine structure constant asymptotically approaches to 1/137,G _eff (effective four-dimensional constant) approachesG _N (Newtonian gravitational constant), and _eff vanishes. Graphical representations of these results are also given for a special case.     

Trapping the Kaluza-Klein scalar

The Kaluza-Klein unified theory predicts the existence of a Brans-Dicke type scalar field with = 0. Solar system experiments do, however, imply that gravitational scalar fields must be suppressed either by a very weak coupling to matter ( > 500) or a self-interaction. Here the consequences of a self-interaction potential of the Kaluza-Klein scalar are investigated. By suppressing the scalar field in this way, the one-body metric reduces to the Schwarzschild solution. The cosmologies of the scalar-tensor model are, however, very different from cosmologies of Einstein's theory, since here the time evolution of the cosmic scale-factor is determined only by the initial conditions. These may be chosen so that the theory is compatible with the hypothesis of primordial nucleosynthesis.     

Spinor fields in the nonsymmetric,non-Abelian Kaluza-Klein theory

Spinor fields are considered in the framework of the nonsymmetric Kaluza-Klein theory and the nonsymmetric Jordan-Thiry theory (in non-Abelian case). Dipole moments for fermions of value 10^–31 and pseudomass-like terms are found.     

Perturbation theory and non-renormalizable scalar fields

We study how to set up systematic summation rules that could permit us to interpret the divergent expressions arising in the perturbation theory of :P(): _d when one does not allow any renormalization besides the usual coupling constants, mass and wave function renormalizations.Supported in part by NSF grant PHY-8342570. Address after March 1985: Theoretische Physik, ETH-Hönggerberg, CH-8093 Zürich, SwitzerlandSupported in part by NSF grant MCS-8108814 (A03)     

Periodic fields in five-dimensional relativity

The concept of periodic fields in the framework of five-dimensional relativity is introduced in a 5-covariant manner. An analysis is given of periodic scalar, vector and bivector fields. The resulting 4-dimensional theories are examined, and it is found that some of them correspond to familiar physical theories in space-time, whereas others require further investigation.