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The covering of the affine symmetry group, a semidirect product of translations and special linear transformations, in $D \geq 3$ dimensional spacetime is considered. Infinite dimensional spinorial representations on states and fields are presented. A Dirac-like affine equation, with infinite matrices generalizing the $\gamma$ matrices, is constructed.
Comment: 18 pages
A generic-curved spacetime Dirac-like equation in 3D is constructed. It has, owing to the $\bar{SL}(n,R)$ group deunitarizing automorphism, a physically correct unitarity and flat spacetime particle properties. The construction is achieved by embedding $\bar{SL}(3,R)$ vector operator $X_{\mu}$, that plays a role of Dirac's $\gamma_{\mu}$ matrices, into $\bar{SL}(4,R)$. Decomposition of the unitary irreducible spinorial $\bar{SL}(4,R)$ representations gives rise to an explicit form of the infinite $X_{\mu}$ matrices.
Comment: 10 pages, LaTeX2e, Workshop on "Gauge Theories of Gravitation" Jadwisin, Poland, 4-10 Sept. 1997
Previous work on the IR regime approximation of QCD in which the dominant contribution comes from a dressed two-gluon effective metric-like field $G_{\mu\nu} = g_{ab} A^{a}_{\mu} A^{b}_{\nu}$ ($g_{ab}$ a color SU(3) metric) is reviewed. The QCD gauge is approximated by effective "chromodiffeomorphisms", i.e. by a gauge theory based on a pseudo-diffeomorphisms group. The second-quantized $G_{\mu\nu}$ field, together with the Lorentz generators close on the $\bar{SL}(4,R)$ algebra. This algebra represents a spectrum generating algebra for the set of hadron states of a given flavor - hadronic "manifields" transforming w.r.t. $\bar{SL}(4,R)$ (infinite-dimensional) unitary irreducible representations. The equations of motion for the effective pseudo-gravity are derived from a quadratic action describing Riemannian pseudo-gravity in the pr...
The questions of the existence, basic algebraic properties and relevant constraints that yield a viable physical interpretation of world spinors are discussed in details. Relations between spinorial wave equations that transform respectively w.r.t. the tangent flat-space (anholonomic) Affine symmetry group and the world generic-curved-space (holonomic) group of Diffeomorphisms are presented. A geometric construction based on an infinite-component generalization of the frame fields (e.g. tetrads) is outlined. The world spinor field equation in 3D is treated in more details.
Comment: Invited talk at the III Summer School in Modern Mathematical Physics
Embedding of a Green-Schwarz superbrane into a generic curved target space in a general covariant way is considered. It is demonstrated explicitely, that the customary superbrane formulation based on finite-component spinors extends to a superspaces of restricted curving only, with the General Coordinate Transformations realized nonlinearly over its orthogonal type subgroups. Infinite-component, world, spinors and a recently constructed corresponding Dirac-like equation, enable a possibility of a manifestly covariant generic curved target space superbrane formulation.
Comment: 13 pages, Plain Tex
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