Hamiltonian structure and gauge symmetries of Poincaré gauge theory

This is a review of the constrained dynamical structure of Poincaré gauge theory which concentrates on the basic canonical and gauge properties of the theory, including the identification of constraints, gauge symmetries and conservation laws. As an interesting example of the general approach, we discuss the teleparallel formulation of general relativity.     

Tetrad fields and metric tensor in the gauge theory of gravitation

The most relevant geometrical aspects of the gauge theory of gravitation are considered. A global definition of the tetrad fields is given and emphasis is placed on their role in defining an isomorphism between the tangent bundle of space-time and an appropriate vector bundle B associated to the gauge bundle. It is finally shown how to construct the fundamental geometrical objects on space-time, starting from B.     

Yang-Mills gauge theory and gravitation

We point out that Yang's and Einstein's gravitational equations can be obtained from a geometric approach of Yang-Mills gauge theory in a sourceless case, under a decomposition of the Poincaré algebra. Otherwise, Einstein's equations cannot be derived from a Yang-Mills gauge equation when sources are inserted in the rotational sector of that algebra. A gauge Lagrangian structure is also discussed.     

Restrictions on gauge theory of gravitation

I discuss geometric aspects - causality, conformal structure, and spinor structure - of a “gauge” type theory of gravitation, proposed by Stephenson, later independently presented by Yang, then criticized by many people, cautioned by Fairchild, and recently advocated for microphysical systems by Hehl, Kerlick, and Heyde. I find that in macrophysical and microphysical systems the affine connexion cannot be nonmetric but is very likely to be metric.     

Canonical structure of the theory of gauge fields interacting with matter fields

The dynamics of gauge-field interacting with matter field is discussed. It is shown that the dynamics is a symplectic relation in a certain symplectic space. Momenta canonically conjugate to both gauge-field and matter field are found. It is shown that the gauge invariance of the theory implies the existence of constraints and vice-versa.     

Phase coupling gravitation: Symmetries and gauge fields

We consider possible generalizations of phase coupling gravitation, a relativistic theory introduced to account for the astrophysical missing mass problem in the framework of departures from newtonian gravitation. We show that pure phase coupled gravitation cannot be gauged. However, the theory can be extended by modifying the interactions. It is then endowed with a continuous global symmetry which can be gauged.     

A unified gauge and gravity theory with only matter fields

We propose a purely fermionic action with gauge and general relativistic invariances. This implies a unified treatment of gravity and gauge theories without elementary metric tensor and gauge boson fields. At the quantum level this scale-invariant theory generates, as vacuum properties, both a metric and a scale Λ which becomes related to the Planck mass. The analysis of the spectrum displays, besides the original fermions, massless composite vierbein and gauge bosons, as well as a set of states with masses of order Λ. In a low-energy regime in which these heavy modes are not excited, the light sector is shown to be governed by a phenomenological action which coincides with the conventional gravity-gauge-matter theory without cosmological term and with a Newton constant and gauge couplings determined by Λ. For increasing energies, the gauge interactions are predicted to grow towards their merging with gra Λ, the theory differs substantially from the conventional one, not even allowing a definition of a space-time metric and providing hints for a milder ultraviolet behaviour.     

Poincaré gauge theory with coupled even and odd parity spin‐0 modes: Cosmological normal modes

We are investigating the dynamics of a new Poincaré gauge theory of gravity model, which has cross coupling between the spin‐0⁺ and spin‐0^‐ modes. To this end we are considering a very appropriate situation – homogeneous‐isotropic cosmologies – which is relatively simple, and yet all the modes have non‐trivial dynamics which reveals physically interesting and possibly observable results. More specifically we consider manifestly isotropic Bianchi class A cosmologies. Here the first order equations obtained from an effective Lagrangian are linearized and the normal modes are found. These turn out to control the asymptotic late time cosmological normal modes. Numerical evolution confirms the late time asymptotic approximation and shows the expected effects of the cross parity pseudoscalar coupling.     

Inflation in Poincaré gauge gravitation theory

Exponential inflation and power-law inflation are studied in the Poincaré gauge gravitation theory for a Robertson-Walker metric.     

A spontaneously broken conformal gauge theory of gravitation

In a fusing of a few attractive ingredients, we consider a spontaneously broken conformal gauge theory of gravitation, with an underlying Riemann-Cartan-Weyl geometry. The theory contains no intrinsic dimensional parameters, is unitary, and has the Schwarzschild metric as the unique spherically symmetric solution of the vacuum field equation (thus guaranteeing agreement with observed gravitational phenomena). The particle content of the theory consists of a massless 2^. graviton, and a super-massive 1^? “conformon”.     

Unified theory of weak,strong, and electromagnetic interactions: Gauge transformation groups and gauge fields

An attempt is made to construct a unified theory of the weak, strong, and electro-magnetic interactions, based on a generalization of the Weinberg-Salam theory [1]. The groups of gauge transformations leaving the Lagrangian of the bispinor field invariant are discussed. It is shown that in order to preserve this invariance in transition from global to local transformations it is necessary to introduce seven gauge compensation fields.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 19–23, May, 1982.     

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.     

The linear theory of gravitation in the radiation gauge

A global gauge for the linear theory of gravity is given which avoids the (In(R))/R problem of harmonic coordinates. Consequently it is possible to do 1/R expansions for precisely those null sources which lead to difficulties in the harmonic gauge. This is important, for example, in second order calculations where the first order field is a gravitational wave. This gauge makes manifest the two degrees of freedom for the dynamic fields. In it the second time derivative of the metric itself has physical significance since R _oioj=–1/2h_ij.Work supported in part by NSF Grant No. GP-13959.     

On the renormalizability of a gauge theory of gravitation

One-loop divergences in gauge theory of gravitation with a quadratic Lagrangian are computed. The renormalizability of the theory in the case of Riemannian background is shown.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 43–49, December, 1984.     

Double duality and hidden gauge freedom in the poincaré gauge theory of gravitation

We investigate the double duality ansatz of the Poincaré gauge theory of gravitation. It is shown that many known exact solutions belong, as special cases, to larger families of solutions. These families of solutions include several arbitrary functions and can be generated by a transformation which is a Lorentzian rotation of the connection with fixed tetrad. Several new spherically symmetric and wavelike exact solution are presented.     

Motion of matter in metric-affine theory of gravitation

Based on the Lie derivative technique in a general space with affine connection (L₄, g), we show that in the metric-affine theory of gravitation, the law of conservation of the energy-momentum tensor for matter and consequently also the equations of motion for matter stemming from this law are (as in the general theory of relativity) a consequence of the gravitational field equations. We derive the hydrodynamic equation of motion for an ideal Weyssenhoff—Raabe spin fluid in Weyl space. We discuss the possibilities for observation of space—time nonmetricity.Moscow State Pedagogical University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 76–82, January, 1994.     

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.