Gauge theories of weak and strong gravity

A review of some recent papers on gauge theories of weak and strong gravity is presented. For weak gravity, SL(2, C) gauge theory along with tetrad formulation is described which yields massless spin-2 gauge fields (quanta gravitons). Next a unified SL(2n,C) model is discussed along with Higgs fields. Its internal symmetry is SU(n). The free field solutions after symmetry breaking yield massless spin-1 (photons) and spin-2 (gravitons) gauge fields and also massive spin-1 and spin-2 bosons. The massive spin-2 gauge fields are responsible for short range superstrong gravity. Higgs-fermion interaction can lead to baryon and lepton number non-conservation. The relationship of strong gravity with other forces is also briefly considered.     

Local currents for the GL(N,C) self-dual Yang-Mills equation

By using a simple Bäcklund-like transformation which linearizes the GL(N, C) self-dual Yang-Mills equation, an infinite number of local conservation laws for this equation are constructed. In the SL(N, C) case, the currents become trivial, which explains why these currents are not found in SU(N) gauge theory.     

Relativistic spin on the Poincaré group

Classical spinning particles are interpreted in terms of an underlying geometric theory. They are described by trajectories on the Poincaré group. Upon quantization an eleven-dimensional Kaluza-Klein type theory is obtained which incorporates spin and isospin in a local SL(2, C)×U(1)×SU(2) gauge theory, unifying gravity and the pre-Higgs standard model. The relation to parametrized relativistic quantum theory is discussed.     

Limitations on the existence of massless composite states

Massless particles represented by the fields with mixed spinor indices of SL(2,C) are generally shown to be forbidden in covariant field theory under the assumptions of positivity and covariiance alone. This remains true also in gauge theory (in which a negative metric appears) as far as the particles are gauge invariant. This in particular implies that any dynamical “gauge-type particle” (such as vector A_μ, Rarita-Schwinger ψ_μ etc.) cannot appear unless the system has a corresponding local invariance from the outset.     

The gauge theory of dislocations: conservation and balance laws

We derive conservation and balance laws for the translational gauge theory of dislocations by applying Noether's theorem. We present an improved translational gauge theory of dislocations including the dislocation density tensor and the dislocation current tensor. The invariance of the variational principle under the continuous group of transformations is studied. Through Lie's infinitesimal invariance criterion we obtain conserved translational and rotational currents for the total Lagrangian made up of an elastic and dislocation part. We calculate the broken scaling current. Looking only on one part of the whole system, the conservation laws are changed into balance laws. Because of the lack of translational, rotational and dilatation invariance for each part, a configurational force, moment and power appears. The corresponding J , L and M integrals are obtained. Only isotropic and homogeneous materials are considered and we restrict ourselves to a linear theory. We choose constitutive laws for the most general linear form of material isotropy. Also we give the conservation and balance laws corresponding to the gauge symmetry and the addition of solutions. From the addition of solutions we derive a reciprocity theorem for the gauge theory of dislocations. Also, we derive the conservation laws for stress-free states of dislocations.     

Quantal Conserved Charges in Gauge Theory

Starting from the configuration-space generating functional for gauge theory obtained by using the Faddeev-Popov method,the conservation laws at the quantum level for the gauge-invariant system are derived.Appling to non-Abel Chern-Simons(CS)theory,the quantum BRS conserved charge and quantuml conserved angular momentum for the non-Abelian CS fields coupled to Fermion field are deduced.The property of fractional spin in CS theory is discussed.     

Vector and Spinor Decomposition of SU（2） Gauge Potential, Their Equivalence, and Knot Structure in SU（2） Chern-Simons Theory

In this paper, spinor and vector decompositions of SU（2） gauge potential are presented and their equivalence is constructed using a simply proposal. We also obtain the action of Faddeev nonlinear 0（3） sigma model from the SU（2） mass/ve gauge field theory, which is proposed according to the gauge invariant principle. At last, the knot structure in SU（2） Chern-Simons filed theory is discussed in terms of the Φ-mapping topological current theory, The topological charge of the knot is characterized by the Hopf indices and the Brouwer degrees of Φ-mapping.     

Affine Defects and Gravitation

We argue that the structure general relativity (GR) as a theory of affine defects is deeper than the standard interpretation as a metric theory of gravitation. Einstein–Cartan theory (EC), with its inhomogeneous affine symmetry, should be the standard-bearer for GR-like theories. A discrete affine interpretation of EC (and gauge theory) yields topological definitions of momentum and spin (and Yang–Mills current), and their conservation laws become discrete topological identities. Considerations from quantum theory provide evidence that discrete affine defects are the physical foundation for gravitation.     

Micromorphic Electromagnetic Theory and Waves

This paper introduces a continuum microelectromagnetic theory (also called micromorphic electromagnetic theory), to discuss electromagnetic phenomena in bodies with microstructures. Balance laws of microelectromagnetic media of the first-grade are given. Constitutive equations are developed. The field equations are obtained . It has been shown that, this theory gives rise to several new vector and tensor waves. A theorem of conservation of energy (Poynting type) is proved. Dispersion relations are obtained for both vector and tensor waves. Relations of tensor waves to microscopic phenomena (such as spin waves) are discussed.     

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.     

Bianchi identities and the automatic conservation of energy-momentum and angular momentum in general-relativistic field theories

Automatic conservation of energy-momentum and angular momentum is guaranteed in a gravitational theory if, via the field equations, the conservation laws for the material currents are reduced to the contracted Bianchi identities. We first execute an irreducible decomposition of the Bianchi identities in a Riemann-Cartan space-time. Then, starting from a Riemannian space-time with or without torsion, we determine those gravitational theories which have automatic conservation: general relativity and the Einstein-Cartan-Sciama-Kibble theory, both with cosmological constant, and the nonviable pseudoscalar model. The Poincaré gauge theory of gravity, like gauge theories of internal groups, has no automatic conservation in the sense defined above. This does not lead to any difficulties in principle. Analogies to 3-dimensional continuum mechanics are stressed throughout the article.     

Grand unification of effective gauge theories

An effective non-renormalizable SU(3)×SU(2)×U(1) invariant gauge theory results at ordinary energies when superheavy fields are integrated out from a grand unified theory based on a simple gauge group G. The solutions of the second-order renormalization-group equations for the gauge coupling constants of the effective theory are examined. General formulae for the superheavy vector boson mass and for sin²θ near M_W are given in this approach to grand unification. The superheavy vector boson mass is plotted against the QCD scale parameter Λ for a certain set of grand unified models. Corrections to the prediction when the set of models is enlarged are discussed, and illustrated with examples from G≡SU(5) and O(10).     

The conservation of source strength in linear field theories and the superpotentials

In linear field theories for vector potentialsAi and tensor potentialsgik=gki, the Maxwell and the linearized Einstein equations are the only field equations from which true conservation laws result for each gauge of the field equations.     

Gauged N = 8 supergravity in five dimensions

We construct gauged N = 8 supergravity theories in five dimensions. Instead of the twenty-seven vector fields of the ungauged theory, the gauged theories contain fifteen vector fields and twelve second-rank antisymmetric tensor fields satisfying self-dual field equations. The fifteen vector fields can be used to gauge any of the fifteen-dimensional semisimple subgroups of SL(6,R), specially SO(p, 6?p) for p = 0, 1, 2, 3. The gauged theories also have a physical global SU(1,1) symmetry which survives from the E₆₍₆₎ symmetry of the ungauged theory. This SU(1,1) for the SO(6) gauging is presumably related to that of the chiral N = 2 theory in ten dimensions. In our formalism we maintain a composite local USp(8) symmetry analogous to SU(8) in four dimensions.     

Extended antifield formalism

The antifield formalism is extended so as to incorporate the rigid symmetries of a given theory. To that end, it is necessary to introduce global ghosts not only for the given rigid symmetries, but also for all the higher order conservation laws, associated with conserved antisymmetric tensors j^μ₁3μ_k fulfilling _μ1j^μ₁3μ_k 2˜ 0. Otherwise, one may encounter obstructions of the type discussed in by the authors. These higher order conservation laws are shown to define additional rigid symmetries of the master equation and to form — together with the standard symmetries — an interesting algebraic structure. They lead furthermore to independent Ward identities which are derived in the standard manner, because the resulting master (“Zinn-Justin”) equation capturing both the gauge symmetries and the rigid symmetries of all orders takes a known form. Issues such as anomalies or consistent deformations of the action preserving some set of rigid symmetries can be also systematically analysed in this framework.     

THE GAUGE OPERATORS FOR PSEUDOSCALAR FIELDS AND THE BAKER-HAUSDORFF FORMULA

In this paper, we present the explicit expressions of the gauge operators for pseudoscslar fields in a gauge theory coupled vector and axial-vector fields with the aid of the method of operator algebras.The gauge operators of the pure gauge field theory under the chiral group SU(N)×SU(N) are also presented. P9oreover, the explicit expression of the Baker-Hausdorff formula is obtained for a special case and the general situation is discussed.     

Gauge covariant formulation of the generating operator. 2. Systems on homogeneous spaces

A gauge covariant approach to the operator Λ, generating the n-wave type equations on homogeneous spaces is proposed. The operator Λ̃ for the gauge equivalent equations is explicitly constructed. The main results (such as conservation laws, hierarchies of hamiltonian structures, etc.) for the n-wave type equations and their gauge equivalent ones are formulated in terms of Λ and Λ̃ respectively.     

<Emphasis Type="Italic">SL(2; R)</Emphasis> Duality of the Noncommutative DBI Lagrangian

We study the action of the SL(2; R) group on the noncommutative DBI Lagrangian. The symmetry conditions of this theory under the above group will be obtained. These conditions determine the extra U(1) gauge field. By introducing some consistent relations we observe that the noncommutative (or ordinary) DBI Lagrangian and its SL(2; R) dual theory are dual of each other. Therefore, we find some SL(2; R) invariant equations. In this case the noncommutativity parameter, its T -dual and its SL(2; R) dual versions are expressed in terms of each other. Furthermore, we show that on the effective variables, T -duality and SL(2; R) duality do not commute. We also study the effects of the SL(2; R) group on the noncommutative Chern–Simons action.     

Dijet production at large rapidity separation in N = 4 supersymmetric Yang-Mills theory

Ratios of azimuthal angle correlations between two jets produced at large rapidity separation are studied in the N = 4 maximally supersymmetric Yang-Mills (MSYM) theory. It is shown that these observables, which directly prove the SL(2,C) symmetry present in gauge theories in the Regge limit, exhibit an excellent perturbative convergence. They are compared to those calculated in QCD for different renormalization schemes concluding that the momentum-substraction scheme with the Brodsky-Lepage-Mackenzie scale-fixing procedure captures the bulk of the MSYM results.     

Quantisation of 2D- gravity with Weyl and area- preserving diffeomorphism invariances

The constraint structure of the induced 2D-gravity with the Weyl and area-preserving diffeomorphism invariances is analysed in the ADM formulation. It is found that when the area-preserving diffeomorphism constraints are kept, the usual conformal gauge does not exist, whereas there is the possibility to choose the so-called “quasi-light-cone” gauge, in which besides the area-preserving diffeomorphism invariance, the reduced Lagrangian also possesses the SL(2, R) residual symmetry. This observation indicates that the claimed correspondence between the SL(2, R) residual symmetry and the area-preserving diffeomorphism invariance in both regularisation approaches does not hold. The string-like approach is then applied to quantise this model, but a fictitious non-zero central charge in the Virasoro algebra appears. When a set of gauge-independent SL(2, R) current-like fields is introduced instead of the string-like variables, a consistent quantum theory is obtained, which means that the area-preserving diffeomorphism invariance can be maintained at the quantum level.