De Sitter gauge theories of gravity

The two types of de Sitter gravities are constructed with the fiber bundle technique and some special cases are discussed. Relations among de Sitter, Poincaré, and Lorentz gravity are discussed and the contraction from the de Sitter bundle to the Poincaré bundle is demonstrated. Two types of gravitational gauge field equations are obtained by using the de Sitter-Poincaré and de Sitter-Lorentz actions. The de Sitter effect occurring in the field equations is discussed.     

Asymptotic freedom in gauge theories and quantum gravity

Restrictions on the structure of a gauge theory which follow from the requirement of asymptotic freedom with respect to all coupling constants are studied. One-loop counterterms for renormalizable gravity with matter are computed. It is shown that for the group O(N), taking into account the contribution of quantum R²-gravity allows one to construct new, asymptotically free gauge theories with a reduced number of spinor multiplets. The results are compared with those obtained earlier for conformal gravity with matter.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 36–41, January, 1990.The authors thank A. O. Barvinskii, I. L. Bukhbinder, and E. S. Fradkin for the discussions.     

Propagating modes in gauge field theories of gravity

The particle content of the most general quadratic field Lagrangian for Poincaré gauge field theories is examined and restrictions on the coupling constants for absence of ghosts and tachyons are derived. Our final field Lagrangian contains three coupling constants, the usual gravitational constant in front of an Einsteinian part and two other constants governing pure torsion terms.     

On higher derivatives in 3D gravity and higher-spin gauge theories

The general second-order massive field equations for arbitrary positive integer spin in three spacetime dimensions, and their “self-dual” limit to first-order equations, are shown to be equivalent to gauge-invariant higher-derivative field equations. We recover most known equivalences for spins 1 and 2, and find some new ones. In particular, we find a non-unitary massive 3D gravity theory with a 5th order term obtained by contraction of the Ricci and Cotton tensors; this term is part of an N=2 super-invariant that includes the “extended Chern-Simons” term of 3D electrodynamics. We also find a new unitary 6th order gauge theory for “self-dual” spin 3.     

Progress in metric-affine gauge theories of gravity with local scale invariance

Einstein's general relativity theory describes very well the gravitational phenomena in themacroscopic world. In themicroscopic domain of elementary particles, however, it does not exhibit gauge invariance or approximate Bjorken type scaling, properties which are believed to be indispensible for arenormalizable field theory. We argue that thelocal extension of space-time symmetries, such as of Lorentz and scale invariance, provides the clue for improvement. Eventually, this leads to aGL(4, R)-gauge approach to gravity in which the metric and the affine connection acquire the status ofindependent fields. The Yang-Mills type field equations, the Noether identities, and conformal models of gravity are discussed within this framework. After symmetry breaking, Einstein's GR surfaces as an effective low-energy theory.Based on a plenary talk given by one of us (EWM) at the 53rd annual meeting of the Deutsche Physikalische Gesellschaft in Bonn on March 14, 1989.Supported by the German-Israeli Foundation for Scientific Research and Development (GIF), Jerusalem and Munich.Supported by the Deutsche Forschungsgemeinschaft (DFG), Bonn, project He 528/12-1.Supported in part by DOE Grant DE-FG05-85-ER40200.     

Radiation zeros and gravity

The existence of spin independent zeros in every tree approximated radiation amplitude in gauge theories is examined when quantum gravity is included. Using a direct evaluation of the relevant transition amplitudes a series of results is proven. They are mostly negative showing that there is no general mechanism of cancellation when quantum gravity is present. The question of gravitational radiation zeros is also addressed and their absence is inferred.     

Complex zeros of the partition function for two-dimensionalU(N) lattice gauge theories

The complex zeros of the partition function for the two-dimensionalU(N) lattice gauge model in the variable β or ξ=N/β are calculated analytically for large β and numerically. The zeros formN trajectories which forN→∞ fill a domain of the ξ plane densely. This domain touches the real ξ axis at ξ=1 with a kink that causes the Gross-Witten phase transition.     

Charges in gauge theories

In this article we investigate charged particles in gauge theories. After reviewing the physical and theoretical problems, a method to construct charged particles is presented. Explicit solutions are found in the abelian theory and a physical interpretation is given. These solutions and our interpretation of these variables as the true degrees of freedom for charged particles, are then tested in the perturbative domain and are demonstrated to yield infra-red finite, on-shell Green’s functions at all orders of perturbation theory. The extension to collinear divergences is studied and it is shown that this method applies to the case of massless charged particles. The application of these constructions to the charged sectors of the standard model is reviewed and we conclude with a discussion of the successes achieved so far in this programme and a list of open questions. An erratum to this article is available at .     

Distribution of zeros in Ising and gauge models

We discuss some features of Ising and gauge systems in the complex temperature plane. The distribution of zeros of the partition function enables one to study critical properties in a way complementary to the methods using real values. Data on small lattices confirm this picture. Nearby complex singularities seem to exhibit a universal behavior which might have some relation with a model of random surfaces.     

Non-abelian gauge couplings in thermal gauge field theories

Properties of the effective gauge couplings renormalized at finite temperature and density in thermal non-abelian gauge field theories are studied within one-loop approximations. Strong and severe vertex dependence is shown to come out both in the temperature and chemical potential dependences. Difficulties appearing in the perturbative calculation of physical quantities, indicated by the above disaster, are discussed. Also discussed is what insight might be gained from the present analysis into the “magnetic” screening of effective charge.     

Quark fragmentation in gauge theories

A theory of quark fragmentation is based on the phenomenon of spontaneous pair creation in a strong Coulomb field, applied to the color field surrounding the leading quarks.     

Soliton quantization in gauge theories

We study the quantization of the SO₃ gauge theory which possesses the 't Hooft-Polyakov monopole as a classical solution. The one-monopole sector of this model is constructed in lowest-order perturbation theory, with \(\sqrt \hbar \) as expansion parameter. Explicit expressions for the fields are given and their properties discussed. We use a manifestly covariant formalism.