de Sitter gauge theories and induced gravities

The European Physical Journal C - Pure de Sitter, anti de Sitter, and orthogonal gauge theories in four-dimensional Euclidean spacetime are studied. It is shown that, if the theory is...     

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.     

Gravitational theories with de Sitter constant vacuum solution

We consider a large class of geometric Lagrangian forms defined in the manifold of the reference frames. The theories described by those Lagrangians are such that, in an empty region, the manifold can be identified with one of the de Sitter groups. The Lagrangian forms are classified according to their symmetry properties with respect to transformation groups acting on the linear space of the infinitesimal transformations of the frames. Requiring invariance with respect to aSO(3) group and a reasonable physical behavior under space reflections, we obtain only three different theories. Then we show that every Lagrangian form of the kind we are considering, is equivalent to anSO(3)-invariant one.     

Infrared behavior and gauge artifacts in de Sitter spacetime: the photon field

We study the infrared (long-distance) behavior of the free photon field in de Sitter spacetime. Using a two-parameter family of gauge-fixing terms, we show that the infrared (IR) behavior of the two-point function is highly gauge-dependent and ranges from vanishing to growing. This situation is in disagreement with its counterpart in flat spacetime, where the two-point function vanishes in the IR region for any choice of the gauge-fixing parameters. A criterion to isolate the physical part of the two-point function is given and is shown to lead to a well-behaved two-point function in the IR region.     

A gauge field theory of spacetime based on the de Sitter group

A new theory of spacetime is proposed in which translations are considered as a part of the de Sitter gauge group. The theory is built along the general principles of classical gauge field theories, which are outlined. Applications of gauge principles to linear and affine connections are also given in order to make the presentation self-sufficient. A de Sitter invariant Lagrangian is constructed, which yields approximately Einstein's vacuum equations when it is subjected to variation with respect to gauge potentials and the result expressed in a specific gauge class. As a difference from the usual use of de Sitter groups, the radius of its translations must be small in the present approach, which probably has the meaning of an elementary subatomic length. The solution of the equations describing flat spacetime is not the trivial zero-curvature connection of the conventional approach.     

Theory of a gravitational gauge field with localization of the de Sitter group

A de Sitter-invariant gauge theory is formulated for the case where a 40-component de Sitter A-field is present. It is shown that the theory coincides with the Poincare-invariant gauge theory in a space with torsion with a cosmological term. Two other versions of a de Sitter-invariant theory are also discussed: the first is a metric theory of gravitation in a Riemann space; the second is a de Sitter-invariant generalization of the tetrad theory of gravitation in a space of absolute parallelism.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 50–53, November, 1986.     

On the weak field approximation of the de Sitter gauge theory of gravity

The weak field approximation of a model of de Sitter gauge theory of gravity is studied in two cases. Without torsion and spin current, the model cannot give the right non-relativistic approximation unless the density is a constant. With small torsion, a satisfactory Newtonian approximation can be obtained.     

De Sitter and conformal field theories

After a brief review of conformal gravity and conformal anomalies in field theories, this paper deals with elementary particles and quantum field theories in 3 + 2 de Sitter space and in conformal space. The importance of working in realistic space-time rather than Euclidean or spherical models, is demonstrated. The parton-like representations Di and Rac give rise to gauge theories of scalar and spinor fields, and a theory of interacting massless particles with all spins. This theory (in 4-dimensional de Sitter space) is constructed on the basis cf a conformally invariant field theory in 3-dimensional space-time. Conformally invariant field theories in 3 and 4 dimensional are reviewed and examined, and new proposals are made for the interpretation of massless field theories in general.Invited talk presented at the International Symposium Selected Topics in Quantum Field Theory and Mathematical Physics, Bechyn, Czechoslovakia, June 14–19, 1981.     

On torsion-free vacuum solutions of the model of de Sitter gauge theory of gravity

It is shown that all vacuum solutions of Einstein field equation with a positive cosmological constant are the solutions of a model of dS gauge theory of gravity. Therefore, the model is expected to pass the observational tests on the scale of solar systems and explain the indirect evidence of gravitational wave from the binary pulsars PSR1913+16.      

On torsion-free vacuum solutions of the model of de Sitter gauge theory of gravity

It is shown that all vacuum solutions of Einstein field equation with a positive cosmological constant are the solutions of a model of dS gauge theory of gravity. Therefore, the model is expected to pass the observational tests on the scale of solar systems and explain the indirect evidence of gravitational wave from the binary pulsars PSR1913+16.     

de Sitter QED

Attention is called to the fact that the well-known and straightforward generalization of electrodynamics to de Sitter space is incompatible with conformal invariance. In addition, there is difficulty in reconciling the space of one-photon states in de Sitter QED, for which the field carries no degree of freedom related to helicity, with that of flat space QED in which both signs of the helicity appear. The requirement of conformal invariance leads to the introduction of two vector potentials in de Sitter electrodynamics and resolves the helicity problem. A conformally invariant, indefinite metric quantization is carried out, and the nature of the flat space limit is clarified. Implications for a theory of composite massless particles are discussed, as well as applications to supersymmetry and supergravity.     

Beltrami-de Sitter时空和de Sitter不变的狭义相对论

分析了在相对论体系中狭义相对性原理和宇宙学原理之间的关系以及Beltrami-de Sitter -陆启铿疑难.指出可以把狭义相对性原理推广到非零常曲率时空，在具有Beltrami度规 的de Sitter/反de Sitter时空中建立狭义相对论的运动学和粒子动力学. 在这类狭义相对 论中,相对于Beltrami坐标同时性，Beltrami坐标系就是惯性坐标系，相应的观测者为惯 性观测者; 对于自由粒子和光讯号, 惯性定律成立;可以定义可观测量,它们不但守恒而且还 满足推广的爱因斯坦关系.除了Beltrami坐标时同时性之外，对于共动观测, 还可以取固 有时同时性;此时，Beltrami度规成为Robertson-Walker型的度规，其3维空间是闭的,对 于平坦的偏离为宇宙学常数的量级.这表明,在这类狭义相对论中,相对性原理与“完美”宇 宙学原理之间存在内在联系,并不存在那些问题.进而,基于最新观测事实，重述了Mach原 理；指出对于Beltrami-de Sitter/反de Sitter时空，宇宙学常数恰恰给出惯性运动的起 源. 关键词： 狭义相对性原理 宇宙学原理 de Sitter不变的狭义相对论 Beltrami-de Sitter时空 同时性 Mach原理     

Lorentz boosts in de Sitter and anti-de Sitter space-times

Symmetries of de Sitter and anti-de Sitter space-times are discussed. In particular, Lorentz boosts, which appear to be given previously only in the infinitesimal form, are presented here in closed finite forms.Dedicated to the memory of Professor Jozef Kvasnica.I would like to thank Prof. Jií Biák and Dr. Hans-Jürgen Schmidt for useful discussions.     

Kamlah expansion and gauge theories

In Yang-Mills theories, variational calculations of the Rayleigh-Ritz type face the problem that on the one hand, calculability puts severe constraints on the space of test wave functionals; on the other hand, the test wave functionals have to be gauge invariant. The conflict between the two requirements can be resolved by introducing a projector. In this paper, we present an approach to approximating the projector in a way known and successfully employed in nuclear physics: the Kamlah expansion. We discuss it both for electrodynamics and for Yang-Mills theories to leading order in a perturbative expansion, and demonstrate that the results are compatible with what one would expect from perturbation theory.     

Extended supersymmetry and gauge theories

A formulation of gauge theories with an extended supersymmetry for N = 2 is given in terms of superfields. The Lagrangian is expressed in terms of superfields and component fields as well.     

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.