The Spinning Particles as a Nonlinear Realizations of the Superworldline Reparametrization Invariance

The superdiffeomorphisms invariant description of $N$ - extended spinning particle is constructed in the framework of nonlinear realizations approach. The action is universal for all values of $N$ and describes the time evolution of $D+2$ different group elements of the superdiffeomorphisms group of the $(1,N)$ superspace. The form of this action coincides with the one-dimensional version of the gravity action, analogous to Trautman's one.Comment: 4 pages, RevTe

On the extension of the concept of Thin Shells to The Einstein-Cartan Theory

This paper develops a theory of thin shells within the context of the Einstein-Cartan theory by extending the known formalism of general relativity. In order to perform such an extension, we require the general non symmetric stress-energy tensor to be conserved leading, as Cartan pointed out himself, to a strong constraint relating curvature and torsion of spacetime. When we restrict ourselves to the class of space-times satisfying this constraint, we are able to properly describe thin shells and derive the general expression of surface stress-energy tensor both in its four-dimensional and in its three-dimensional intrinsic form. We finally derive a general family of static solutions of the Einstein-Cartan theory exhibiting a natural family of null hypersurfaces and use it to apply our formalism to the construction of a null shell of matter.Comment: Latex, 21 pages, 1 combined Latex/Postscript figure; Accepted for publication in Classical and Quantum Gravit

Space-time defects :Domain walls and torsion

The theory of distributions in non-Riemannian spaces is used to obtain exact static thin domain wall solutions of Einstein-Cartan equations of gravity. Curvature $\delta$-singularities are found while Cartan torsion is given by Heaviside functions. Weitzenb\"{o}ck planar walls are caracterized by torsion $\delta$-singularities and zero curvature. It is shown that Weitzenb\"{o}ck static thin domain walls do not exist exactly as in general relativity. The global structure of Weitzenb\"{o}ck nonstatic torsion walls is investigated.Comment: J.Math.Phys.39,(1998),Jan. issu

Matrix geometries and fuzzy spaces as finite spectral triples

A class of real spectral triples that are similar in structure to a Riemannian manifold but have a finite-dimensional Hilbert space is defined and investigated, determining a general form for the Dirac operator. Examples include fuzzy spaces defined as real spectral triples. Fuzzy 2-spheres are investigated in detail, and it is shown that the fuzzy analogues correspond to two spinor fields on the commutative sphere. In some cases it is necessary to add a mass mixing matrix to the commutative Dirac operator to get a precise agreement for the eigenvalues.Comment: 39 pages, final versio

Perfect fluid and test particle with spin and dilatonic charge in a Weyl-Cartan space

The equation of perfect dilaton-spin fluid motion in the form of generalized hydrodynamic Euler-type equation in a Weyl-Cartan space is derived. The equation of motion of a test particle with spin and dilatonic charge in the Weyl-Cartan geometry background is obtained. The peculiarities of test particle motion in a Weyl-Cartan space are discussed.Comment: 25 July 1997. - 9 p. Some corrections in the text and formulars (2.4) and (2.8) are perfomed, the results being unchange

The variational theory of the perfect dilaton-spin fluid in a Weyl-Cartan space

The variational theory of the perfect fluid with intrinsic spin and dilatonic charge (dilaton-spin fluid) is developed. The spin tensor obeys the classical Frenkel condition. The Lagrangian density of such fluid is stated, and the equations of motion of the fluid, the Weyssenhoff-type evolution equation of the spin tensor and the conservation law of the dilatonic charge are derived. The expressions of the matter currents of the fluid (the canonical energy-momentum 3-form, the metric stress-energy 4-form and the dilaton-spin momentum 3-form) are obtained.Comment: 25 July 1997. - 10 p. The variational procedure is improved, the results being unchange

Perfect hypermomentum fluid: variational theory and equations of motion

The variational theory of the perfect hypermomentum fluid is developed. The new type of the generalized Frenkel condition is considered. The Lagrangian density of such fluid is stated, and the equations of motion of the fluid and the Weyssenhoff-type evolution equation of the hypermomentum tensor are derived. The expressions of the matter currents of the fluid (the canonical energy-momentum 3-form, the metric stress-energy 4-form and the hypermomentum 3-form) are obtained. The Euler-type hydrodynamic equation of motion of the perfect hypermomentum fluid is derived. It is proved that the motion of the perfect fluid without hypermomentum in a metric-affine space coincides with the motion of this fluid in a Riemann space.Comment: REVTEX, 23 pages, no figure

On Some Stability Properties of Compactified D=11 Supermembranes

We desribe the minimal configurations of the bosonic membrane potential, when the membrane wraps up in an irreducible way over $S^{1}\times S^{1}$. The membrane 2-dimensional spatial world volume is taken as a Riemann Surface of genus $g$ with an arbitrary metric over it. All the minimal solutions are obtained and described in terms of 1-forms over an associated U(1) fiber bundle, extending previous results. It is shown that there are no infinite dimensional valleys at the minima.Comment: 12 pages,Latex2e lamuphys, Invited talk at International Seminar "Supersymetry and Quantum Symmetries", Dubn

Gauge-potential approach to the kinematics of a moving car

A kinematics of the motion of a car is reformulated in terms of the theory of gauge potentials (connection on principal bundle). E(2)-connection originates in the no-slipping contact of the car with a road.Comment: 13 pages, AmsTe

The Einstein 3-form G_a and its equivalent 1-form L_a in Riemann-Cartan space

The definition of the Einstein 3-form G_a is motivated by means of the contracted 2nd Bianchi identity. This definition involves at first the complete curvature 2-form. The 1-form L_a is defined via G_a = L^b \wedge #(o_b \wedge o_a). Here # denotes the Hodge-star, o_a the coframe, and \wedge the exterior product. The L_a is equivalent to the Einstein 3-form and represents a certain contraction of the curvature 2-form. A variational formula of Salgado on quadratic invariants of the L_a 1-form is discussed, generalized, and put into proper perspective.Comment: LaTeX, 13 Pages. To appear in Gen. Rel. Gra