Nonlinear gauge theory of Poincaré gravity

A Poincaré affine frame bundle (M) and its associated bundleÊ are established. Using the connection theory of fiber bundles, nonlinear connections on the bundleÊ are introduced as nonlinear gauge fields. An action and two sets of gauge field equations are presented.     

Effective Einsteinian gravity from Poincaré gauge field theory

The Poincaré gauge theory of gravity should apply in the microphysical domain. Here we investigate its implications for macrophysics. Weakly self double dual Riemann-Cartan curvature is assumed throughout. It is shown that the metrical background is then determined by Einstein's field equations with the Belinfante-Rosenfeld symmetrized energy-momentum current amended by spin squared terms. Moreover, the effective cosmological constant can be reconciled with the empirical data by absorbing the corresponding constant curvature part into the dynamical torsion of recently found exact solutions. Macroscopically this extra torsion remains undetectable.     

A magnetic-monopole-type solution in the Poincaré gauge field theory of gravity

In a microscopical theory of gravity the coupling of internal gauge degrees of freedom to those of space-time are studied. A magnetic-monopole-type solution for the coupledSO(3) Yang-Mills-Higgs system in a space-time with curvature and torsion is derived. The coupling constant of the Lorentz gauge bosons can be related directly to the (constant) Higgs field and to the cosmological constant which is induced by the quadratic curvature terms in the Lagrangian. This reveals a new interpretation of the parameters entering the general Lagrangian density of the Poincaré gauge field theory (PG).     

All torsion-free spherical vacuum solutions of the quadratic Poincaré gauge theory of gravity

We find all torsion-free, spherically symmetric, vacuum solutions to the theory of gravity recently proposed by Hehl, Ne'eman, Nitsch, and von der Heyde. There are three classes of solutions: (A) the Schwarzschild metrics with arbitrary mass,M, and arbitrary cosmological constant, ; (B) the Nariai-Bertotti metrics with arbitrary positive cosmological constant, ; and (C) the conformally flat metrics whose conformai factor is ²/ ² where is a function of only the time coordinate , and the radial coordinate, and satisfies the wave equation in these variables. Hence there is no Birkhoff theorem for this theory. In fact, solutions (C) include some asymptotically flat but nonstationary solutions. On the other hand, solutions (A) include a gravitational confinement potential, as was sought by Hehl et al., since when <0, the weak field limit of the Schwarzschild metric becomes a harmonic oscillator potential. We also discuss the relationship of this theory to the Eddington theory, the Lichnerowicz-Kilmister-Newman-Yang theory, the Nordström theory and the Einstein theory with a cosmological constant.     

Geometrical meaning of the Poincaré group gauge theory

We find a condition (6) under which a gauge theory of the Poincaré group is equivalent to the Einstein-Cartan theory of gravitation.     

On the difference between Poincaré and Lorentz gravity

The Poincaré invariance of GR is usually interpreted as Lorentz invariance plus diffeomorphism invariance. In this paper, by introducing the local inertial coordinates (LIC), it is shown that a theory with Lorentz and diffeomorphism invariance is not necessarily Poincaré invariant. Actually, the energy–momentum conservation is violated there. On the other hand, with the help of the LIC, the Poincaré invariance is reinterpreted as an internal symmetry. In this formalism, the conservation law is derived, which has not been sufficiently explored before.     

Mechanical systems with Poincaré invariance

Some years ago Ruijsenaars and Schneider initiated the study of mechanical systems exhibiting an action of the Poincaré algebra. The systems they discovered were far richer: their models were actually integrable and possessed a natural quantum version. We follow this early work finding and classifying mechanical systems with such an action. New solutions are found together with a new class of models exhibiting an action of the Galilean algebra. These are related to the functional identities underlying the various Hirzebruch genera. The quantum mechanics is also discussed.     

Bound states in gauge theories as the Poincaré group representations

The bound-state generating functional is constructed in gauge theories. This construction is based on the Dirac Hamiltonian approach to gauge theories, the Poincaré group classification of fields and their nonlocal bound states, and the Markov-Yukawa constraint of irreducibility. The generating functional contains additional anomalous creations of pseudoscalar bound states: para-positronium in QED and mesons inQCDin the two-gamma processes of the type of γ + γ → π ₀ +para-positronium. The functional allows us to establish physically clear and transparent relations between the perturbativeQCD to its nonperturbative low-energy model by means of normal ordering and the quark and gluon condensates. In the limit of small current quark masses, the Gell-Mann-Oakes-Renner relation is derived from the Schwinger-Dyson and Bethe-Salpeter equations. The constituent quark masses can be calculated from a self-consistent nonlinear equation.     

Conserved charges of Kerr–Ads spacetime using Poincaré gauge version

The process of covariant conserved charge of gravitational theory, which is covariant under general coordinate and local Lorentz transformations, has been applied to many tetrad fields, which reproduce Kerr-Ads spacetime, to calculate their conserved charges. It is shown that this process gives an infinite value of the conserved charges for Kerr–Ads spacetime. Therefore, the method of “regularization through relocalization”, i.e., modification of the Lagrangian of the gravitational field through a total derivative, is used. This method gaves a finite and a consistent result of total energy and angular momentum for Kerr–Ads spacetime.     

Yukawa-type potential besides newtonian potential in Poincaré gauge theory of gravitation

It is shown that the spin gauge fields with non-zero mass mediate the Yukawa-type interactions besides the short-range spin-spin interactions in the Poincaré gauge theory of gravitation. The interaction range of spin gauge fields is determined from the coupling constants. The coupling constant in front of the R(W) term is bounded by the requirement of a non-oscillating solution.     

Poincaré vortices

Traditional interferometric methods for measuring the vortex structure of complex wave fields suffer from many intrinsic problems and seldom yield results of any accuracy. Using the unique properties of what I call Poincaré vortices, I develop a radically different method based on Stokes parameters that offers many practical advantages. The theory of this new method is discussed, and its unique capabilities are illustrated by reconstruction with high accuracy of the vortex structure of a simulated random field containing numerous vortices, including several closely spaced vortex pairs that would be difficult, if not impossible, to resolve by traditional means.     

Relativistic Chaplygin Gas with Field-Dependent Poincaré Symmetry

The relativistic generalization of the Chaplygin gas, put forward by Jackiw and Polychronakos, is derived in Duval's Kaluza–Klein framework, using a universal quadratic Lagrangian. Our framework yields a simplified proof of the field-dependent Poincaré symmetry. Our action is related to the usual Nambu–Goto action [world volume] of d-branes in the same way as the Polyakov and the Nambu action are in string theory.     

Gravity as an internal Yang-Mills gauge field theory of the Poincaré group

In the framework of affine bundles we present gravity as an internal gauge field theory of the Poincaré group. The resulting geometry is a Riemann-Cartan space-time carrying torsion and curvature. In order to admit a nontrivial action of the translation group we formally extend the matter Lagrangian to affine field variables. Finally, we establish the relation of our approach with the formalism of Hehl et al.     

A classical particle in a Poincaré gauge field as a model for the gravitational interaction

The geometrical and mechanical aspects of a particle interacting with a Poincaré gauge field are considered and the relation with a gravitational interaction is studied.     

A remark on the axisymmetric Chen et al. solution of the Poincaré gauge theory

Recently the search for exact solutions of the Poincaré gauge theory of gravity was highlighted by the independent discovery of two Kerr-type solutions with dynamic torsion. Some properties of these axisymmetric solutions, found by Chen et al. and by McCrea et al., are compared and put into proper perspective. In particular we show that the Chen et al., solution, in marked contrast to the more general McCrea et al. solution, belongs to a class of quadratic Poincaé gauge lagrangians of a highly degenerate nature, which admits non-unique solutions already in the limit of spherical symmetry.