A geometrical theory of spin motion

A discussion of the fundamental interrelation of geometry and physical laws with Lie groups leads to a reformulation and heuristic modification of the principle of inertia and the principle of equivalence, which is based on the simple de Sitter group instead of the Poincaré group. The resulting law of motion allows a unified formulation for structureless and spinning test particles. A metrical theory of gravitation is constructed with the modified principle, which is structured after the geometry of the manifold of the de Sitter group. The theory is equivalent to a particular Kaluza-Klein theory in ten dimensions with the Lorentz group as gauge group. A restricted version of this theory excludes torsion. It is shown by a reformulation of the energy momentum complex that this version is equivalent to general relativity with a cosmologic term quadratic in the curvature tensor and in which the existence of spinning particle fields is inherent from first principles. The equations of the general theory with torsion are presented and it is shown in a special case how the boundary conditions for the torsion degree of freedom have to be chosen such as to treat orbital and spin angular momenta on an equal footing. The possibility of verification of the resulting anomalous spin-spin interaction is mentioned and a model imposed by the group topology ofSO(3,2) is outlined in which the unexplained discrepancy between the magnitude of the discrete valued coupling constants and the gravitational constant in Kaluza-Klein theories is resolved by the identification of identical fermions as one orbit. The mathematical structure can be adapted to larger groups to include other degrees of freedom.     

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.     

Gravitation in the light cone gauge

The formulation of gravitation theory in the light cone gauge is studied. After a brief discussion of Yang- Mills theory for purposes of illustration, tensor and scalartensor gravitation are investigated. We show that if the gauge conditions are properly chosen the constrained components of the metric tensor can be explicitly solved for by quadrature, so that the field theory can be reformulated entirely in terms of the physical transverse fields. It is also shown that the light cone gauge is useful for finding wave solutions of classical field equations. Occasional reference is made to dual models, primarily to explain our motivation, but familiarity with them is not required for an understanding of this paper.     

Harmonic expansions and quasi-riemannian geometry in Kaluza-Klein theories

Since Kaluza-Klein supergravity does not contain the observed particles as elementary fields, alternative approaches in Kaluza-Klein theories without external gauge fields may be considered. We take up Weinberg's suggestion of changing the tangent space group and we find that some or all of the gauge field strengths associated with isometry group vanish unless there is torsion.     

Spaces with flat symmetry in poincaré gauge theory of gravity

A Taub space is considered in the Poincare gauge theory of gravity. It is shown that the torsion tensor has four nonvanishing components, which can be split into two independent pairs S₀₁ ⁰, S₀₁ ¹, and S₂₃ ⁰, S₂₃ ¹. The analysis of the gravitational field equations leads to the conclusion that in this case only a flat space-time with torsion is possible, and that its metric coefficients and the components of the torsion tensor are described by a wave equation.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 92–98, April, 1990.     

Finsler and Kaluza-Klein gauge theories

A comparison of Kaluza-Klein and Finsler-type gauge theories is sketched. It is shown that the two can be related by a mapping between fiber spaces which is equivalent to a transformation from one representation of the gauge group to another. The Finsler theory lends itself to an interpretation of the mapping operators as being geometrically similar to Yang-Mills potentials. The equations of motion in this theory contain fields which are comparable to connections instead of curvatures. This gives a new geometrical framework for unified field theories.     

Quadratic torsion-metric model consistent with then-dimensional gravitational theories of einstein and weyl

We examine a gauge model with a Lagrangian, quadratic in the Riemann-Cardan curvature, without a separate Hilbert Lagrangian. It is argued that torsions must be massive particles, the torsion field does not act on world fields, and the orthogonal components of the contorsion tensor must not vary with variations of the metric. It is shown that a new torsion-metric interaction arises in this case, which generates the gravitational theories of Einstein and Weyl. Kazan State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 21–25, June, 1998.     

Vacuum Stability in Kaluza-Klein Geometric Sigma Models

In Kaluza-Klein geometric sigma models, the scalar fields coupled to higher-dimensional gravity are pure gauge. The gauge fixed theory contains no matter fields, and can consistently be reduced to 4 dimensions, provided the internal space is chosen in the form of a group manifold. The effective 4-dimensional theory includes standard Einstein and Yang-Mills sectors, and is free of the classical cosmological constant problem. In this paper, the stability of the internal excitations is analyzed. It is shown that the initial Lagrangian can be modified to lead to a classically stable effective 4-dimensional theory, independently of the particular group used, and retaining all the basic features of the unmodified theory.     

High energy field theory in truncated anti-de Sitter space

In this Letter we show that in five-dimensional anti-de Sitter (AdS) space truncated by boundary branes, effective field theory techniques are reliable at high energy (much higher than the scale suggested by the Kaluza-Klein mass gap), provided one computes suitable observables. We argue that in the model of Randall and Sundrum for generating the weak scale from the AdS warp factor, the high energy behavior of gauge fields can be calculated in a cutoff independent manner, provided one restricts Green's functions to external points on the Planck brane. Using the AdS/CFT (conformal field theory) correspondence, we calculate the one-loop correction to the Planck brane gauge propagator due to charged bulk fields. These effects give rise to nonuniversal logarithmic energy dependence for a range of scales above the Kaluza-Klein gap.     

Geometric Origin of Physical Constants in a Kaluza-Klein Tetrad Model

An important feature of Kaluza-Klein theories is their ability to relate fundamental physical constants to the radii of higher dimensions. In previous Kaluza-Klein theory, which unifies the electromagnetic field with gravity as dimensionless components of a Kaluza-Klein metric, i) all fields have the same physical dimensions, ii) the Lagrangian has no explicit dependence on any physical constants except mass, and hence iii) all physical constants in the field equations except for mass originate from geometry. While it seems natural in Kaluza-Klein theory to add fermion fields by defining higher-dimensional bispinor fields on the Kaluza-Klein manifold, these Kaluza-Klein theories do not satisfy conditions (i), (ii), and (iii). In this paper, we show how conditions (i), (ii), and (iii) can be satisfied by including bispinor fields in a tetrad formulation of the Kaluza-Klein model, as well as in an equivalent teleparallel model. This demonstrates an unexpected feature of Dirac's bispinor equation, since conditions (i), (ii), (iii) imply a special relation among the terms in the Kaluza-Klein or teleparallel Lagrangian that would not be satisfied in general.     

Skew-symmetric tensor gauge field theory dynamically realized in the QCD U(1) channel

It is shown that, in order for the U(1) Goldstone boson to decouple from the physical sector, a third rank skew-symmetric tensor gauge field theory has to be realized dynamically by asymptotic fields of bound states in QCD. The abelian-like gauge invariance of this tensor gauge theory is just a realization of the original QCD gauge (BRS) invariance which hence assures the decoupling of all the bound-state modes by the “quarlet mechanism”. A general procedure for fixing gauges in such types of skew-symmetric tensor gauge theories is also presented.     

The double duals and gauges of the Lanczos tensor

It is shown that: i) the Weyl tensor can be expressed in terms of the sum of a tensor and its double dual, where the tensor is constructed from the covariant derivatives of the Lanczos tensor, ii) a similar expression does not exist for the Riemann tensor in electromagnetic theory, iii) the electromagnetic field cannot be identified with the differential gauge freedom of the Lanczos tensor, iv) the symmetries of Einstein Maxwell theory and the Lanczos tensor do not prohibit the identification of the electromagnetic field with the algebraic gauge freedom of the Lanczos tensor, these symmetries require a differential equation relating the electromagnetic field tensor to the algebraic gauge vector and this is given.     

Kaluza-Klein unification in the poincaré gauge theory of gravitation

We show that we can unify the gravitational and internal gauge interactions in a high dimensional Riemann-Cartan spacetime in the spirit of Kaluza-Klein, if we identify some of the connection coefficients as Yang-Mills potentials and if the dynamics of the spacetime is governed by the Poincaré gauge theory of gravitation whose lagrangian contains curvature and torsion squared.     

Kaluza-Klein reduction and consistency of the massive spin-3/2 theory with external interaction

A gauge-invariant Rarita-Schwinger theory of a massive spin-3/2 particle interacting with external electromagnetic, gravitational and dilaton fields is obtained by Kaluza-Klein reduction of a massless Rarita-Schwinger theory with graviational interaction. Fermionic gauge invariance serves to determine the background equations of motion. The couplings with external fields obtained by the Kaluza-Klein reduction are shown to lead to the absence of the classical Velo-Zwanziger problem and on quantizing using Dirac's procedure, the field anticommutators are found to be positive definite.     

An alternative method of reduction to four-dimensional space in Kaluza-Klein theory

A method for constructing gauge field theories with spontaneous symmetry breaking is suggested, and applied to the theory of Kaluza-Klein type. It is shown that the method naturally leads to the appearance of fields and a lagrangian, providing spontaneous breaking of the gauge invariance. The method also allows one to interpret in a novel way the nature of the extra dimensions of space.     

Hamiltonian Map to Conformal Modification of Spacetime Metric: Kaluza-Klein and TeVeS

It has been shown that the orbits of motion for a wide class of non-relativistic Hamiltonian systems can be described as geodesic flows on a manifold and an associated dual by means of a conformal map. This method can be applied to a four dimensional manifold of orbits in spacetime associated with a relativistic system. We show that a relativistic Hamiltonian which generates Einstein geodesics, with the addition of a world scalar field, can be put into correspondence in this way with another Hamiltonian with conformally modified metric. Such a construction could account for part of the requirements of Bekenstein for achieving the MOND theory of Milgrom in the post-Newtonian limit. The constraints on the MOND theory imposed by the galactic rotation curves, through this correspondence, would then imply constraints on the structure of the world scalar field. We then use the fact that a Hamiltonian with vector gauge fields results, through such a conformal map, in a Kaluza-Klein type theory, and indicate how the TeVeS structure of Bekenstein and Saunders can be put into this framework. We exhibit a class of infinitesimal gauge transformations on the gauge fields U_m(x){\mathcal{U}}_{\mu}(x) which preserve the Bekenstein-Sanders condition U_mU^m=-1{\mathcal{U}}_{\mu}{\mathcal{U}}^{\mu}=-1. The underlying quantum structure giving rise to these gauge fields is a Hilbert bundle, and the gauge transformations induce a non-commutative behavior to the fields, i.e. they become of Yang-Mills type. Working in the infinitesimal gauge neighborhood of the initial Abelian theory we show that in the Abelian limit the Yang-Mills field equations provide residual nonlinear terms which may avoid the caustic singularity found by Contaldi et al.     

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.     

Theory of a gauged gravitational field with localization of the Einstein group

A theory of a gauged gravitational field with localization of the group of motions of a homogeneous static Einstein universe (Einstein group R x SO(4)) is formulated. Starting from the tetradic components of Einstein's universe, a relationship is established between the Riemannian metric and the gauge fields of Einstein's group. The metric connection with torsion, transforming when the gauge fields are switched off into the Christoffel connection of Einstein's universe, is found. It is shown that in the limit of infinite radius of curvature of Einsteinr's universe, the given Einstein-invariant gauge theory transforms into the tetradic theory of gravitation with localized triadic rotations. Exact solutions are obtained in the form of nonsingular cosmological models.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 68–73, July, 1985.     

RIEMANNIAN STRUCTURE ON GAUGE GROUP AND METRIC COMPATIBLE YANG-MILLS THEORY

A gauge theory with gauge potentials that are compatible with right invariant metric of the gauge group is presented. It is shown that in the metric compatible torsion free gauge theory, gauge potentials can acquire the mass, without introducing the tliggs field. A plane-wave exact solution in vacuum is obtained.