non-Abelian Kaluza-Klein Theory Research Articles

A black hole solution of higher-dimensional Weyl–Yang–Kaluza–Klein theory

We consider the Weyl–Yang gauge theory of gravitation in a (4 + 3)-dimensional curved space-time within the scenario of the non-Abelian Kaluza–Klein theory for the source and torsion-free limits. The explicit forms of the field equations containing a new spin current term and the energy–momentum tensors in the usual four dimensions are obtained through the well-known dimensional reduction procedure. In this limit, these field equations admit (anti-)dyon and magnetic (anti-)monopole solutions as well as non-Einsteinian solutions in the presence of a generalized Wu–Yang ansatz and some specific warping functions when the extra dimensions associated with the round and squashed three-sphere S 3 are, respectively, included. The (anti-)dyonic solution has similar properties to those of the Reissner–Nordström–de Sitter black holes of the Einstein–Yang–Mills system. However, the cosmological constant naturally appears in this approach, and it associates with the constant warping function as well as the three-sphere radius. It is demonstrated that not only the squashing parameter ℓ behaves as the constant charge but also its sign can determine whether the solution is a dyon/monopole or an antidyon/antimonopole. It is also shown by using the power series method that the existence of nonconstant warping function is essential for finding new exact Schwarzschild-like solutions in the considered model.

Fermion fields in the (non)symmetric Kaluza–Klein theory

The paper is devoted to the unification of fermions within nonsymmetric Kaluza–Klein theories. We obtain a Lagrangian for fermions in non-Abelian Kaluza–Klein theory and non-Abelian Kaluza–Klein theory with spontaneous symmetry breaking and Higgs’ mechanism. A Lagrangian for fermions for geometrized bosonic part of GSW (Glashow–Salam–Weinberg) model in our approach has been derived. Yukawa-type terms and mass terms coming from higher dimensions have been obtained. In the paper, 1/2-spin fields and 3/2-spin fields are considered.

Generalized Dirac monopoles in non-Abelian Kaluza–Klein theories

A method is proposed for constructing the geometries of the non-Abelian Kaluza–Klein theories of generalized monopoles in arbitrary dimensions. These represent a natural generalization of the Euclidean Taub-NUT space, regarded as the appropriate background of the Dirac magnetic monopole. A recent theory of induced representations governing the isometries of the Euclidean Taub-NUT space is combined with usual geometrical methods obtaining a conjecture in which the potentials of the generalized monopoles can be written down without to solve explicitly the Yang–Mills equations. Moreover, in this way one finds that apart from the monopole models, which are of a space-like type, there exists a new type of time-like models that cannot be interpreted as monopoles. The space-like models are studied pointing out that their monopole fields strength are particular solutions of the Yang–Mills equations with central symmetry, producing the standard flux of 4 π through the two-dimensional spheres surrounding the monopole. Examples are given of manifolds with Einstein metrics carrying SU ( 2 ) monopoles.

Teleparallel equivalent of non-Abelian Kaluza-Klein theory

Based on the equivalence between a gauge theory for the translation group and general relativity, a teleparallel version of the non-Abelian Kaluza-Klein theory is constructed. In this theory, only the fiber-space turns out to be higher dimensional, spacetime being kept always four dimensional. The resulting model is a gauge theory that unifies, in the Kaluza-Klein sense, gravitational and gauge fields. In contrast with the ordinary Kaluza-Klein models, this theory defines a natural length scale for the compact submanifold of the fiber space, which is shown to be of the order of the Planck length.

A study of cosmological solutions on non-Abelian Kaluza-Klein theory with variable internal size

The authors investigate the time dependence of the space radius and the internal space radius in a seven-dimensional Kaluza-Klein theory where both the spacelike sections and sections of internal space are 3-spheres. For an action consisting of a single, dimensionally continued, four-dimensional Euler form, the cosmological constant in spacetime vanishes. It is shown that for equations of state describing a radiation filled spacetime and an empty internal space, the classical field equations have a solution such that the internal space radius remains constant for most of the evolution of the universe. The numerical solution suggests that the internal space radius starts evolving from zero at non-zero, but small, value of the space radius and quickly reaches a constant value. They analytically show that such behaviour is consistent with the equations of motion.

The Schwarzschild solution in non-Abelian Kaluza-Klein theory

A non-Abelian Kaluza-Klein theory, based on a Lagrangian consisting of a 2N-dimensional Euler form, leads to an effective four-dimensional theory with vanishing cosmological constant in 2N+2 or 2N+3 dimensions. The authors investigate the existence of the Schwarzschild solution for such theories in six and seven dimensions where the internal space is a 2-sphere and a 3-sphere respectively. The authors show that the vacuum field equations do not have any static solutions which are spherically symmetric in spacetime. However, in odd dimensions, for any homogeneous internal manifold, the Schwarzschild solution exists provided the Lagrangian is complemented with a 2N+2-dimensional Euler form.

Euler-form actions and the vanishing of the cosmological constant.

We investigate the conditions of the vanishing cosmological constant and the presence of gravity and vector gauge fields in a $D$-dimensional non-Abelian Kaluza-Klein theory based on a dimensionally continued $2N$-dimensional Euler-form action. It is shown that these conditions can be satisfied only for $D=2N+3$.

Quantum interference effects in Einstein-Maxwell, supergravity and non-abelian Kaluza-Klein theories

Quantum interference effects in Einstein-Maxwell, supergravity and non-abelian Kaluza-Klein theories have been calculated following the idea of Parthasarathy, Rajasekharan and Vasedevan.

Equivalence of the degrees of freedom in a unified gravitational theory

A discussion of the nouniqueness of physical laws and their invariance groups is illustrated by the construction of a physical theory (presented earlier) in which the law of motion of structureless and spinning particles is unified in the geometry of the manifold of the de Sitter groupSO(3,2). The theory has the structure of a non-Abelian Kaluza-Klein theory with very special properties resulting from the topology and noncompactness of the groups. The physical interpretation of the field equation is discussed. The physical requirement of equivalence of the interaction of spinning and orbiting systems, generally unconsidered in related theories, is here taken into account by the structure of the theory. The possibility of deviations from predictions of general relativity exists. Generalizations of the theoretical structure to higher dimensional groups are outlined and open the possibility for observations.

Testing the surrogate zeta-function method

Use of the surrogate zeta-function method was crucial in calculating the Casimir energy in non-Abelian Kaluza–Klein theories. We establish the validity of this method for the case where the background metric is (Euclidean space) × (N sphere). Our techniques do not apply to the case where the background is (Minkowski space) × (N sphere).

Magnetic monopoles in nonabelian Kaluza-Klein theories

We consider the possibility of constructing magnetic monopole and dyon solutions to the classical field equations in nonabelian Kaluza-Klein theories. We take as model theories a six-dimensional theory compactified to M 4 × S 2 and a seven-dimensional theory compactified to M 4 × S 3. We then select ansatze and try to solve the equations of motion. For the six-dimensional theory we are unable to find a suitable ansatz; however, we are able to find a good ansatz for the seven-dimensional theory. We then present an asymptotic solution to the field equations for the seven-dimensional theory, the equations of motion being much too difficult to solve exactly.

Gravitational Casimir energy in non-Abelian Kaluza-Klein theories.

The Casimir energy of the gravitational field in certain Kaluza-Klein theories is computed. Specifically, the one-loop quantum effective potential of the gravitational field on the background manifold (Minkowski space)\ifmmode\times\else\texttimes\fi{}(N-sphere) is evaluated as a function of the radius of the N-sphere. (N is restricted to be odd for technical reasons.) Minima of the (real part of the) potential for which the observed cosmological constant is zero are found numerically for N=13, 15, 17, 19, and 21. The potential has an imaginary part which is attributed to ``tachyonic'' terms in the mode sum, although it is argued that the Faddeev-Popov ghost modes do not contribute to this imaginary part.

Induced gravitational and gauge field actions from quantized matter fields in non-abelian Kaluza-Klein theory

We study the problem of quantized matter fields on a non-abelian Kaluza-Klein background. It is shown how the Einstein-Hilbert-Yang-Mills action may be induced from quantum effects. A new method of calculating the low curvature limit of the effective action is presented and used to derive general formulae for the terms in the induced action arising from scalar and spinor fields in the case where the extra dimensions form a coset space. Explicit results for the induced cosmological, gravitational, and gauge-coupling constant are found when the extra dimensions are odd-dimensional spheres.

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.

Geometry of multidimensional universes

LetG be a compact group of transformation (global symmetry group) of a manifoldE (multidimensional universe) with all orbits of the same type (one stratum). We studyG invariant metrics onE and show that there is one-to-one correspondence between those metrics and triples (g μv,A äμ ,h αβ), whereg μv is a (pseudo-) Riemannian metric on the space of orbits (space-time),A äμ is a Yang-Mills field for the gauge groupN|H, whereN is the normalizer of the isotropy groupH inG, andh αβ are certain scalar fields characterizing geometry of the orbits (internal spaces). The scalar curvature ofE is expressed in terms of the component fields onM. Examples and model building recipes are also given. The results generalize those of non-abelian Kaluza-Klein theories to the case where internal spaces are not necessarily group manifolds.

Group covariance and spin motion in gravitational theory

The kinematics of a metric theory is developed which exhibits all the degrees of freedom of a semisimple local invariance group. The theory is a modification of multidimensional non-Abelian Kaluza-Klein theories with the Cartan-Killing metric of the group manifold as a source-free solution. The De Sitter group SO(3, 2) gives rise to additional degrees of freedom which may be interpreted as classical spin motion and spin-spin interaction. More extended invariance groups are considered.

Equivalence principle and multidimensional unified gauge theories

Equations of motion for point-like test masses subjected to Yang-Mills-Lorentz and gravitational forces are derived from geodesic motion in the multidimensional space of a non-Abelian Kaluza-Klein theory with vanishing cosmological constant.

Spontaneous compactification, gauge symmetry and the vanishing of the cosmological constant

We show that standard nonabelian Kaluza-Klein (K-K) theories violate gauge invariance. Gauge-symmetric K-K theories are outlined; for any compact gauge group, they lead to spontaneously compactified solutions which imply the vanishing of the cosmological constant.