Gaupta-Bleuler triplet for massless spin-3/2 field in de Sitter space

Physicists have been interested in quantization of spinor and vector free fields in 4-dimensional de Sitter space-time,in ambient space notation.The Gupta-Bleuler formalism has been extensively applied to the quantization of gauge invariant theories.The field equation of the massless spin-3/2 fields is gauge invariant in de Sitter space.In this paper,we study the quantization of massless spin-3/2 gauge fields in de Sitter space-time by the Gupta-Bleuler formalism.This triplet carries an indecomposable representation of the de Sitter group.     

Gauge theory of massless spin-(3/2) field in de Sitter space-time

On several levels of theoretical physics, especially particle physics and early universe cosmology, de Sitter space-time has become an attractive possibility. The principle of local gauge invariance governs all known fundamental interactions of elementary particles, from electromagnetism and weak interactions to strong interactions and gravity. This paper presents a procedure for defining the gauge-covariant derivative and gauge invariant Lagrangian density in de Sitter ambient space-time formalism. The gauge invariant field equation is then explicitly calculated in detail for a massless spin-(3/2) gauge field.     

RIGHT TRANSLATION INVARIANT METRICS AND VARIATIONAL PRINCIPLES ON A PRINCIPAL BUNDLE——TREATED AS THE UNION OF SPACE-TIME AND AN INTERNAL SPACE

In this paper, we discuss how to assign a metric on a principal bundle and howto rewrite the variational principles for a particle and for matter fields in an inva-riant from on the bundle in the principal-bundle formulation of gauge theories. Weshow that the right-translation invariant metric on the bundle must contain quantitieswhich transform exactly as gauge potentials, thus providing a new formalism for gaugefields. And we formulate the variational principle for a particle moving in the gaugefield as follows: The particle moves along a horizontal geodesic on the principalbundle. Starting from this we derive the Wong's equations of motion. Moreover, we elucidate the physical view-point which treats the bundle space asthe union of space-time and the internal space. Advantages of this viewpoint for un-derstanding the essentialities of gauge transformations and gauge invariance and forestablishing unified theories of gravitation and gauge fields are also discussed.     

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.     

On the Definition of Gauge Transformations in Gauge Theory

The different types of gauge transformations in gauge theory are discerned and defined in fiber bundle terms. The gauge gravitation case is analysed in order to examine various versions of the gauge gravitation theory.     

Some classical solutions of the sourceless SO(4,1) gauge field equations

Some new classical solutions of the sourceless SO(4,1) gauge field equations are found by identifying the internal symmetry indices with the space-time indices as in the cases of the instanton or the meron solutions. This identification of the internal and the space-time indices takes the simplest form when the gauge field equation is expressed in (4,1) de Sitter space, which is conformal to the Minkowski space having the de Sitter group SO(4,1) as a group of motions. The form of the solutions is close to the de Sitter ‘plane wave’ solutions found recently, i.e. the solutions of the Klein-Gordon, Dirac and Maxwell-Proca equations in de Sitter space. The group theoretical structure of the new solutions is discussed and their relations to the Iwasawa decomposition of the non-compact semisimple group SO(4,1) are pointed out.     

Gauge fields,space-time geometry and gravity

A general framework for the gauge theory of the affine group and its various subgroups in terms of connections on the bundle of affine frames and its subbundles is given, with emphasis on the correct gauging of groups including space-time translations. For consistency of interpretation, the appropriate objects to be identified with gravitational vierbeins in such theories are not the translational gauge fields themselves, but their pull backs,via appropriate bundle homomorphisms, to the bundle of frames. This automatically solves the problems usually encountered in constructing a gauge theory of the conventional sort for groups containing translations. We give a consistent formulation of the Poincare gauge theory and also of the theory based on translational gauge invariance which, in the absence of matter fields with intrinsic spin, gives a local Lorentz invariant theory equivalent to Einstein gravity.     

Electroweak Symmetry on the Tangent Bundle

Various symmetries of elementary particles can be represented by gauge transformations acting on a fiber of the tangent bundle. These are diffeomorphisms of linear groups which act on vertical vector fields. It is shown how the electroweak vector boson potentials and a corresponding Kaluza-Klein-like metric can be obtained by application of SU(2) × U(1) to a tangent fiber. This geometry gives a more unified approach to gravitation and gauge symmetries.     

On the Higgs feature of gravity

The gauge gravitation theory, based on the equivalence principle besides the gauge principle, is formulated in the fibre bundle terms. The correlation between gauge geometry on spinor bundles describing Dirac fermion fields and space-time geometry on a tangent bundle is investigated. We show that field functions of fermion fields in presence of different gravitational fields are always written with respect to different reference frames. Therefore, the conventional quantization procedure is applicable to fermion fields only if gravitational field is fixed. Quantum gravitational fields violate the above mentioned correlation between two geometries.     

Maximal gauged supergravity in three dimensions

We construct maximally supersymmetric gauged N = 16 supergravity in three dimensions, thereby obtaining an entirely new class of anti--de Sitter supergravities. These models apparently cannot be derived from any known higher-dimensional theory and point to the existence of a new type of supergravity beyond D = 11. One of their noteworthy features is a non-Abelian generalization of the duality between scalar and vector fields in three dimensions. Among the possible gauge groups, SO(8) x SO(8) is distinguished as the maximal compact gauge group, but there are also more exotic possibilities such as F(4(-20)) x G2.     

Coupling Between Spin and Gravitational Field and Equation of Motion of Spin

In general relativity, the equation of motion of the spin is given by the equation of parallel transport, which is a result of the space-time geometry. Any result of the space-time geometry cannog be directly applied to gauge theory of gravity. In gauge theory of gravity, based on the viewpoint of the coupling between the spin and gravitational field, an equation of motlon of the spin is deduced. In the post Newtonian approximation, it is proved that this equation gives the same result as that of the equation of parallel transport. So, in the post Newtonian approximation, gauge theory of gravity gives out the same prediction on the precession of orbiting gyroscope as that of general relativity.     

Coupling Between Spin and Gravitational Field and Equation of Motion of Spin

In general relativity, the equation of motion of the spin is given by the equation of parallel transport, which is a result of the space-time geometry. Any result of the space-time geometry cannot be directly applied to gauge theory of gravity. In gauge theory of gravity, based on the viewpoint of the coupling between the spin and gravitational field,an equation of motion of the spin is deduced. In the post Newtonian approximation, it is proved that this equation gives the same result as that of the equation of parallel transport. So, in the post Newtonian approximation, gauge theory of gravity gives out the same prediction on the precession of orbiting gyroscope as that of general relativity.     

A classification of space-time structures

The paper contains a review of various bundles which may be associated to the bundle of linear frames and used to describe properties of space relevant to physics. Restrictions, extensions, prolongations and reductions are defined in terms of morphisms of principal bundles. It is shown that the holonomic prolongation of a G-structure exist iff the corresponding structure function vanishes. G-connections are related to restrictions of the bundle of second-order frames. It is shown that these restrictions may be used to classify theories of space-time and gravitation. A distinction is made between a projective connection and a geodetic structure. In the framework of the Einstein-Cartan theory, the projective connection of a space-time is compatible with its metric tensor iff the spin density is bivector-valued. As an example, we mention a new theory of gravitation and electromagnetism based on the Weyl-Cartan structure of space-time and on the Yang quadratic Lagrangian.     

SO(n)规范势的可分解理论

使用几何代数方法,研究了n维紧致黎曼流形上SO(n)规范势(自旋联络)的一般分解理论,建立了SO(n)规范场用球丛上单位矢量场n分解的一般表达式.由此,分别得到了U(1)规范场和U(2)规范场用单位矢量场n分解的一般形式.     

New massive gravity and AdS(4) counterterms

We show that the recently proposed Dirac-Born-Infeld extension of new massive gravity emerges naturally as a counterterm in four-dimensional anti-de Sitter space (AdS(4)). The resulting on-shell Euclidean action is independent of the cutoff at zero temperature. We also find that the same choice of counterterm gives the usual area law for the AdS(4) Schwarzschild black hole entropy in a cutoff-independent manner. The parameter values of the resulting counterterm action correspond to a c=0 theory in the context of the duality between AdS(3) gravity and two-dimensional conformal field theory. We rewrite this theory in terms of the gauge field that is used to recast 3D gravity as a Chern-Simons theory.     

Broken symmetry of lie groups of transformation generating general relativistic theories of gravitation

Intransitive Lie groups of transformations have invariant varieties which in suitable cases can be considered as space-times of a universe. The physical laws in the latter are expressed in terms of group theoretical notions. Theorems on the coincidences of group trajectories and geodesics are derived. The groups of linear transformations of the space of basis vectors are used as gauge groups to break the symmetry of the group of transformations and of their natural metric. It is shown that in case of the de Sitter group and its adjoint group as gauge group, one obtains in this way general relativistic theories of gravitation, especially Einstein's theory. More general aspects of the formalism are discussed.Article written in memoriam of B. Jouvet of the Collège de France     

Cosmological term in the general theory of relativity and localization of the de Sitter and Einstein groups

The theory of a gauge gravitational field with localization of the de Sitter group is formulated. Starting from the tetradic components of the de Sitter universe, a relationship is established between the Riemannian metric and the de Sitter gauge field. It is shown that the general theory of relativity with the cosmological term is the simplest variant of the de Sitter gauge theory of gravitation, which transforms in the limit of an infinite radius of curvature of the de Sitter universe into the Poincaré-invariant GTR without the cosmological term. A theory of a gauge gravitational field with localization of Einstein's group of motions of the uniform static universe (the Einstein group R × S0 (4)) is formulated in an analogous manner.Translated from Izvestiya Vysshykh Uchebnykh Zavedenii, Fizika, No. 8, pp. 86–90, August, 1984.