Scalar torsion and a new symmetry of general relativity

We reformulate the general theory of relativity in the language of Riemann–Cartan geometry. We start from the assumption that the space-time can be described as a non-Riemannian manifold, which, in addition to the metric field, is endowed with torsion. In this new framework, the gravitational field is represented not only by the metric, but also by the torsion, which is completely determined by a geometric scalar field. We show that in this formulation general relativity has a new kind of invariance, whose invariance group consists of a set of conformal and gauge transformations, called Cartan transformations. These involve both the metric tensor and the torsion vector field, and are similar to the well known Weyl gauge transformations. By making use of the concept of Cartan gauges, we show that, under Cartan transformations, the new formalism leads to different pictures of the same gravitational phenomena. We illustrate this fact by looking at the one of the classical tests of general relativity theory, namely the gravitational spectral shift. Finally, we extend the concept of space-time symmetry to Riemann–Cartan space-times with scalar torsion and obtain the conservation laws for auto-parallel motions in a static spherically symmetric vacuum space-time in a Cartan gauge, whose orbits are identical to Schwarzschild orbits in general relativity.     

On the Interaction of Fermion and Boson Fields with the Gravitational Field

We point out that the gravitational field taken by itself cannot be considered as a gauge field. Only an affinity and not a metric can serve as a gauge field. Originally, metric and affinity are completely independent of each other. This fact allows in a natural way to formulate a restricted principle of relativity, according to which only fermion fields may show that there exist a priori distinguished frames of reference. Furthermore, we can couple the gravitational field to boson and fermion fields such that the flat metric or tetrads orthonormalized with respect to this flat metric appearing in the special relativistic matter Lagrangian, are replaced by a Riemannian metric and tetrads orthonormalized with respect to this metric (principle of most minimal gravitational coupling). This coupling principle is a strong restriction on the existence of independent boson fields. Only scalar and vector fields and their different pseudoquantities are possible as independent fields. Boson fields of higher rank are to be considered as fusions of these (pseudo)scalar and (pseudo)vector fields. Theire field equations follow from those of the (pseudo)scalar and (pseudo)vector fields.     

Field equations for gravity quadratic in the curvature

Vacuum field equations for gravity are studied having their origin in a Lagrangian quadratic in the curvature. The motivation for this choice of the Lagrangian—namely the treating of gravity in a strict analogy to gauge theories of Yang-Mills type—is criticized, especially the implied view of connections as gauge potentials with no dynamical relation to the metric. The correct field equations with respect to variation of the connections and the metric independently are given. We deduce field equations which differ from previous ones by variation of the metric, the torsion, and the nonmetricity from which the connections are built.     

U(4) spin gauge theory over a Riemann-Cartan space-time

A spin gauge theory based on the groupU(4) is investigated in a general relativistic context including the possibility of nonzero torsion. The language of Clifford bundles over a space-time with metric and metric compatible torsion is used as a convenient tool for the study of fields defined on space-time possessing Clifford multiplication properties. A Dirac-type representation is investigated in detail and the geometric implications for spin gauge theory are pointed out.     

Torsional Weyl-Dirac Electrodynamics

Issuing from a geometry with nonmetricity and torsion we build up a generalized classical electrodynamics. This geometrically founded theory is coordinate covariant, as well as gauge covariant in the Weyl sense. Photons having arbitrary mass, intrinsic magnetic currents, (magnetic monopoles), and electric currents exist in this framework. The field equations, and the equations of motion of charged (either electrically or magnetically) particles are derived from an action principle. It is shown that the interaction between magnetic monopoles is transmitted by massive photons. On the other hand, the photon is massive only in the presence of magnetic currents. We obtained a static spherically symmetric solution, describing either the Reissner-Nordstrom metric of an electric monopole, or the metric and field of a magnetic monopole. The latter must be massive. In the absence of torsion and in the Einstein gauge one obtains the Einstein-Maxwell theory.     

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.     

A spherically symmetric vacuum solution of the quadratic Poincaré gauge field theory of gravitation with newtonian and confinement potentials

We derive a stationary spherically symmetric vacuum solution in the framework of the Poincaré gauge field theory with a recently proposed quadratic lagrangian. We find a metric of the Schwarzschild-de Sitter type, both torsion and curvature are non vanishing, with torsion proportional to the mass and curvature proportional to the strong coupling constant κ. The metric exhibits two pieces, a newtonian potential describing the gravitational behavior of macroscopic matter, and a confining potential ～κr² presumably related to the strong-interaction properties of hadrons. To our knowledge this is a new feature of a classical solution of a Yang-Mills type gauge theory.     

Weyl gauging and spontaneously broken Lorentz symmetry: Some alternative models

Some new effective actions are suggested for theories in which the affine connection is not completely specified by the metric. The new actions lead to models in which the metric, torsion, and Weyl vector fields all propagate. The dimensionally reduced versions do not contain third derivatives of the gauge potentials in the field equation. Some simple models which exhibit simultaneous breaking of Weyl andD-dimensional Lorentz symmetry are investigated. It is shown that it is possible for this effect to occur in any model in which the field action contains the Einstein-Hilbert term. This is due to the fact that the contortion occurs in this object as part of an indefinite quadratic form.     

Relativity and equivalence principles in a gauge theory of gravitation

Conclusion The principal difficulty that has obstructed the formulation of gauge gravitation for more than twenty years now is the fact that an Einstein gravitational field represents a metric or a tetradic field, while gauge fields are connections on fiber bundles.The popular approach to the resolution of this problem lies in attempts to represent tetrad fields as gauge fields of the translation subgroup within the framework of the gauge theory of the Poincaré group, but the existing set of variants of the latter theory indicate that it is a long way from completion.Our approach [2, 3] insists that in a gauge theory, apart from gauge fields, the situation of spontaneous breaking of symmetry can also admit Goldstone and Higgs fields, under which is subsumed the metric (tetrad) gravitational field by virtue of the fact that, as we have shown above, the equivalence principle is included in the gauge theory of gravitation.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 79–82, June, 1981.     

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.     

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.     

A new class of exact solutions of the vacuum quadratic Poincaré gauge field theory

A class of algebraically special exact solutions of the vacuum quadratic Poincaré gauge field theory is presented. These solutions are of type III and type N and have a nonexpanding, shear-free and twist-free geodesic repeated principal null congruence. The metric is of Kundt's class, and the torsion components are solutions of certain differential equations. The solutions have been obtained using a generalised spin coefficient formalism.     

Massive, Non-ghost Solutions for the Dirac Field Coupled Self-consistently to Gravity

We present new, massive, non-ghost solutions for the Dirac field coupled self-consistently to gravity. We employ a gauge-theoretic formulation of gravity which automatically identifies the spin of the Dirac field with the torsion of the gauge fields. Homogeneity of the field observables requires that the spatial sections be flat. Expanding and collapsing singular solutions are given, as well as a solution which expands from a singularity before recollapsing. Torsion effects are only important while the Compton wavelength of the Dirac field is larger than the Hubble radius. We study the motion of spinning point-particles in the background of the expanding solution. The anisotropy due to the torsion is manifest in the particle trajectories.     

Reissner--Nordström-de--Sitter-type Solution by a Gauge Theory of Gravity

We use the theory based on a gravitational gauge group （Wu＇s model） to obtain a spherical symmetric solution of the field equations for the gravitational potential on a Minkowski spacetime. The gauge group, the gauge covariant derivative, the strength tensor of the gauge feld, the gauge invariant Lagrangean with the cosmological constant, the field equations of the gauge potentiaIs with a gravitational energy-momentum tensor as well as with a tensor of the field of a point like source are determined. Finally, a Reissner-Nordstrom-de Sitter-type metric on the gauge group space is obtained.     

A charged Taub-NUT metric with torsion: A new axially symmetric solution of the poincare gauge field theory

Within the framework of the Poincaré gauge field theory, McCrea has recently discovered a Taub-NUT-like metric with torsion. The metric is axially symmetric, whereas the torsion turns out to be SO(3)-symmetric. We find the corresponding solution with an additional electric charge.     

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.     

Possible experimental manifestations of the torsion field

The question whether it is possible in principle to obtain experimental evidence of the existence of torsion fields is discussed. Torsion is introduced as an element of the universal gravitational interaction complementary to the metric. An equation is written which is an analog of the Pauli equation in the torsion and electromagnetic external fields. The equations of motion of a weakly relativistic particle in an external torsion field are obtained.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 5–12, March, 1992.     

Gravitational Gauge Interactions of Scalar Field

Quantum gauge theory of gravity is formulated based on gauge principle. Because the Lagrangian has strict local gravitational gauge symmetry, gravitational gauge theory is a perturbatively renormalizable quantum theory. Gravitational gauge interactions of scalar field are studied in this paper. In quantum gauge theory of gravity, scalar field minimal couples to gravitational field through gravitational gauge covariant derivative. Comparing the Lagrangian for scalar field in quantum gauge theory of gravity with the corresponding Lagrangian in quantum fields in curved space-time, the definition for metric in curved space-time in geometry picture of gravity can be obtained, which is expressed by gravitational gauge field. In classical level, the Lagrangian and Hamiltonian approaches are also discussed.     

Stability and decay of the Dirac vacuum in external gauge fields

We consider various gauge fields coupled to the free Dirac equation according to symmetry principles. The gauge fields are treated as classical, unquantized fields. Sufficiently strong time-independent fields may give rise to spontaneous particle creation and to the decay of the symmetric Dirac vacuum into a new ground state with broken symmetry. The vacuum stability of the Dirac field is studied for the cases of external electromagnetic (U(1)), gravitational (Poincaré group including torsion) and Yang-Mills (SU(2)) potentials.