The nonsymmetric Kaluza-Klein (Jordan-Thiry) theory in the electromagnetic case

We present the nonsymmetric Kaluza-Klein and Jordan-Thiry theories as interesting propositions of physics in higher dimensions. We consider the five-dimensional (electromagnetic) case. The work is devoted to a five-dimensional unification of the NGT (nonsymmetric theory of gravitation), electromagnetism, and scalar forces in a Jordan-Thiry manner. We find interference effects between gravitational and electromagnetic fields which appear to be due to the skew-symmetric part of the metric. Our unification, called the nonsymmetric Jordan-Thiry theory, becomes the classical Jordan-Thiry theory if the skew-symmetric part of the metric is zero. It becomes the classical Kaluza-Klein theory if the scalar field=1 (Kaluza's Ansatz). We also deal with material sources in the nonsymmetric Kaluza-Klein theory for the electromagnetic case. We consider phenomenological sources with a nonzero fermion current, a nonzero electric current, and a nonzero spin density tensor. From the Palatini variational principle we find equations for the gravitational and electromagnetic fields. We also consider the geodetic equations in the theory and the equation of motion for charged test particles. We consider some numerical predictions of the nonsymmetric Kaluza-Klein theory with nonzero (and with zero) material sources. We prove that they do not contradict any experimental data for the solar system and on the surface of a neutron star. We deal also with spin sources in the nonsymmetric Kaluza-Klein theory. We find an exact, static, spherically symmetric solution in the nonsymmetric Kaluza-Klein theory in the electromagnetic case. This solution has the remarkable property of describing mass without mass and charge without charge. We examine its properties and a physical interpretation. We consider a linear version of the theory, finding the electromagnetic Lagrangian up to the second order of approximation with respect toh _v =g _v –n _v . We prove that in the zeroth and first orders of approximation there is no skewonoton interaction. We deal also with the Lagrangian for the scalar field (connected to the gravitational constant). We prove that in the zeroth and first orders of approximation the Lagrangian vanishes.     

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.     

Spontaneous Symmetry Breaking and Higgs' Mechanism in the Nonsymmetric Jordan-Thiry Theory

In the paper we construct the nonsymmetric Jordan-Thiry theory unifying Moffat's theory of gravitation, the Yang-Mills' field, the Higgs' fields and scalar forces in a geometric manner. We discuss spontaneous symmetry breaking, the Higgs' mechanism and mass generation in the theory. The scalar field Ψ (as in classical Jordan-Thiry theory) is connected to the effective gravitational constant. This field is massive and has Yukawa-type behavior. We discuss the relation between R₊ invariance and U(1)_F from G. U. T. within Einstein λ-transformation, and fermion number conservation. In this way we connect W _μ-field from nonsymmetric theory of gravitation with a gauge field A from G. U. T. We derive the equation of motion for a test particle from conservation laws in the hydrodynamic limit.     

Conformal flatness, non-Abelian Kaluza-Klein reduction and quaternions

The non-Abelian Kaluza-Klein reduction of conformally flat spaces is considered for arbitrary dimensions and signatures. The corresponding equations are particularly elegant when the internal space supports a global Killing parallelization. Assuming this imposes the generalized ‘spacetime’ to be maximally symmetric with holonomy in the unitary quaternionic group Sp(d/4). Recalling an analogous result for the complex case, we conclude that all special manifolds with constant properly ‘holonomy-related’ sectional curvature, are in natural correspondence with conformally flat, possibly non-Abelian, Kaluza-Klein spaces.     

Vanishing of the cosmological constant in non-Abelian Kaluza-Klein theories

We present a new approach to the unification of gravity and non-Abelian gauge fields in the framework of Kaluza-Klein theory. It consists in introducing a new connection on the (n + 4)-dimensional manifoldP (metrized principal fiber bundle). This connection is metrical, but with nonvanishing torsion. An enormous cosmological term in the Einstein equations vanishes due to this connection. The new connection simultaneously cancels Planck's mass term in the Dirac equation for the five-dimensional case. The usual interpretation of geodesic equations is still valid.     

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).     

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.     

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.     

Isotropization times in non-Abelian gauge theory

We consider non-perturbative estimates of isotropization times for gauge theory on a lattice, relevant for the discussion of thermalization in collisions of heavy nuclei.     

The energy-momentum tensor in a non-Abelian quark gluon theory

A finite energy-momentum tensor is constructed in an asymptotically free non-Abelian gauge theory with massive fermions (quarks). An explicit formula is found for the trace when inserted into a gauge-invariant Green function, and its properties at short distances are discussed.     

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.     

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