On Kaluza-Klein theory

Assuming the compactification of 4 + K-dimensional space-time implied in Kaluza-Kleintype theories, we consider the case in which the internal manifold is a quotient space, $\text{G}\text{H}$. We develop normal mode expansions on the internal manifold and show that the conventional gravitational plus Yang-Mills theory (realizing local G symmetry) is obtained in the leading approximation. The higher terms in the expansions give rise to field theories of massive particles. In particular, for the original Kaluza-Klein 4 + 1-dimensional theory, the higher excitations describe massive, charged, purely spin-2 particles. These belong to infinite dimensional representations of an O(1,2).     

Kaluza-Klein theory and Machian cosmology

We interpret the 15 equations of Kaluza-Klein gravity as 10 Einstein equations, 1 wave equation and 4 equations of motion. An exact cosmological solution of the apparently empty 5D field equations describes a 4D fluid with an effective density and pressure induced by the curvature associated with the fifth dimension. The rest mass of a particle in the fluid depends on the global solution and changes slowly with time. This approach to Kaluza-Klein theory in general results in Machian cosmologies.     

Cosmological applications in Kaluza-Klein theory

The field equations of Kaluza–Klein (KK) theory have been applied in the domain of cosmology. These equations are solved for a flat universe by taking the gravitational and the cosmological constants as a function of time t. We use Taylor’s expansion of cosmological function, Λ(t), up to the first order of the time t. The cosmological parameters are calculated and some cosmological problems are discussed.     

Soliton supermultiplets and Kaluza-Klein theory

We show that the monopoles of five-dimensional Kaluza-Klein theory, considered as solutions of the N = 8 supergravity theory in five dimensions, fit into the same supermultiplets as the original fields in that theory. We show that there is an electric-magnetic duality between these magnetic monopoles and the electrically charged antigravitating objects anticipated by Scherk. We formulate a Bogomolny inequality for N = 8 supergravity, and we speculate on the wider significance of these monopoles.     

Search for a realistic Kaluza-Klein theory

An attempt is made to construct a realistic model of particle physics based on eleven-dimensional supergravity with seven dimensions compactified. It is possible to obtain an SU(3) × SU(2) × U(1) gauge group, but the proper fermion quantum numbers are difficult to achieve.     

Graviton dominance in quantum Kaluza-Klein theory

We compute, at the one-loop level, the effective potential for pure gravity in a Kaluza-Klein background geometry which is the direct product of four-dimensional Minkowski spacetime M⁴ with the N-sphere S^N, N odd. The computation is performed in the physical Lorentz-signature spacetime, avoiding the difficulties of “euclideanization”. We find that the contribution of each gravitational degree of freedom to the O(?) part of the effective potential is significantly greater than that of a scalar or spinor in the same background geometry. No stable minima of the effective potential exist for 3 ≤ N ≤ 13. Geometries which may be interpreted as “unstable solutions” are found for all N from 3 through 13. These results, obtained in Lorentz-signature spacetimes, differ from those obtained by “euclideanization”; our “euclideanized” results agree with those obtained by Chodos and Myers using a different regularization scheme.     

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.     

The Kaluza-Klein theory and four-dimensional spacetime

The conventional electromagnetism, which includes Maxwell's field equations and the Lorentz force relation, does not provide an explanation of well-known electromagnetic phenomena, such as the Aharonov-Bohm interference effect and the Meissner-Ochsenfeld effect in superconductors. In this paper, it is shown that the Kaluza-Klein five-dimensional theory suggests a simple explanation of these effects on a unified basis.     

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.     

Torsion-induced gauge field doubling in Kaluza-Klein theory

Torsion in Kaluza-Klein theory is considered. It is shown that a part of the components of the torsion tensor can be identified with the components of gauge fields different from the gauge fields of the Kaluza-Klein theory, while the other part can be identified with the field strength tensor of these gauge fields. The gauge fields introduced this way acquire a geometrically induced mass. It is shown that the torsion in the internal space allows to generate any a priori given mass in Kaluza-Klein theory.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 11–15, June, 1988.In conclusion, I want to thank Yu. S. Vladimirov for a discussion of the results of this paper.     

An orifice-string in the standard Kaluza-Klein theory

In the standard Kaluza-Klein theory an orifice solution is proposed which can be spliced into a four-dimensional Reissner-Nordstrom space-time. From the point of view of a four-dimensional observer, the obtained orifice solution can be treated as a string moving in a Wheeler superspace of four geometries.Kyrgyz State University, Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 78–81, June, 1993.     

Phantom scalar fields in five-dimensional Kaluza-Klein theory

The existence of a so-called "phantom" scalar field in some Riemannian spaceV ₄, i.e., a field in which the effective energy momentum tensorT ^(sf) vanishes in the five-dimensional Kaluza-Klein theory, is investigated by means of the integrability conditions for relations of the form _;;=k_,,+bg found in [6]. Phantom fields are found in homogeneous isotropic cosmological models.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 50–56, February, 1996.     

Kaluza-Klein theory from the viewpoint of gauge theory of gravity

We consider Kaluza-Klein theory based on the fiber bundle. We obtain the modified Kaluza-Klein metric as an invariant line element of a bundle. Its reduced action includes a higher derivative action in gravitation as well as a term linear inR.