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Different aspects of the self-dual (anti-self-dual) action of the Ashtekar canonical formalism are discussed. In particular, we study the equivalences and differences between the various versions of such an action. Our analysis may be useful for the development of an Ashtekar formalism in eight dimensions., Comment: 10 pages, Latex, minor corrections

We investigate the possibility of extending the Ashtekar theory to eight dimensions. Our approach relies on two notions: the octonionic structure and the MacDowell-Mansouri formalism generalized to a spacetime of signature 1+7. The key mathematical tool for our construction is the self-dual (antiself-dual) four-rank fully antisymmetric octonionic tensor. Our results may be of particular interest in connection with a possible formulation of M-theory via matroid theory., Comment: 15 pages, Latex, minor changes, to appear in Class. Quantum Grav

We prove that 1+1 and 2+2 target `spacetimes' of a 0-brane are exceptional signatures. Our proof is based on the requirement of SL(2,R) and `Lorentz' symmetries of a first order lagrangian. Using a special kind of 0-brane called `quatl', we also show that the exceptional signatures 1+1 and 2+2 are closely related. Moreover, we argue that the 2+2 target `spacetime' can be understood either as 2+2 worldvolume `spacetime' or as `1+1-matrix-brane'. The possibility that the exceptional 2+2-signature implies an exceptional chirotope is briefly outlined., Comment: 16 pages, Latex

We explicitly construct in the (1/2,1/2)X(1/2,1/2) representation space the operator of the squared Pauli-Lubanski vector and derive from it that the -6m^{2}eigensubspace (spin 2 in the rest frame), with well defined parity, is pinned down by the one sole equation, [\epsilon_{\mu\alpha\beta\sigma} \epsilon^{\mu}_{\nu\delta\rho}p^{\sigma}p^{\rho}-m^{2}g_{\alpha\beta}g_{\nu\del ta}]h^{\beta\delta}=0$., Comment: 5 pages

We argue that the chirotope concept of oriented matroid theory may be found in different scenarios of physics, including classical mechanics, quantum mechanics, gauge field theory, p-branes formalism, two time physics and Matrix theory. Our observations may motivate the interest of possible applications of matroid theory in physics., Comment: 19 pages, Latex

We discuss the relativistic top theory from the point of view of the de Sitter (or anti de Sitter) group. Our treatment rests on Hanson-Regge's spherical relativistic top lagrangian formulation. We propose an alternative method for studying spinning objects via Kaluza-Klein theory. In particular, we derive the relativistic top equations of motion starting with the geodesic equation for a point particle in 4+N dimensions. We compare our approach with the Fukuyama's formulation of spinning objects, which is also based on Kaluza-Klein theory. We also report a generalization of our approach to a 4+N+D dimensional theory., Comment: 25 pages, Latex,commnets and references added

We develop a Born-Infeld type theory for gravity in any dimension. We show that in four dimensions our formalism allows a self-dual (or anti-self dual) Born-Infeld gravity description. Moreover, we show that such a self-dual action is reduced to both the Deser-Gibbons and the Jacobson-Smolin-Samuel action of Ashtekar formulation. A supersymmetric generalization of our approach is outlined., Comment: 5 pages, REVeX4, additional comments, minor typos corrected

It is shown that, with the only exception of $n=2$, the Einstein-Hilbert action in $n+D+d$ dimensions, with $n$ times, is invariant under the duality transformation $a\to \frac{1}{a}$ and $b\to \frac{1}{b}$, where $a$ is a Friedmann-Robertson-Walker scale factor in $D$ dimensions and $b$ a Brans-Dicke scalar field in $d$ dimensions respectively. We investigate the $2+D+d$ dimensional cosmological model in some detail., Comment: 23 pages, Latex

We discuss linearized gravity from the point of view of a gauge theory. In (3+1)-dimensions our analysis allows to consider linearized gravity in the context of the MacDowell-Mansouri formalism. Our observations may be of particular interest in the strong-weak coupling duality for linearized gravity, in Randall-Sundrum brane world scenario and in Ashtekar formalism., Comment: Latex, 13 pages

A link between matroid theory and $p$-branes is discussed. The Schild type action for $p$-branes and matroid bundle notion provide the two central structures for such a link. We use such a connection to bring the duality concept in matroid theory to $p$-branes physics. Our analysis may be of particular interest in M-theory and in matroid bundle theory., Comment: 12 pages, Latex, the formulae (30) and (31)have been added; the equations (32)-(38) and the references [12]-[15] have been added. Minor typos corrected

By using the relativistic top theory, we derive a relativistic top deviation equation. This equation turns out to be a generalization of the geodesic deviation equation for a pair of nearby point particles. In fact, we show that when the spin angular momentum tensor associated to the top vanishes, such a relativistic top deviation equation reduces to the geodesic deviation equation for spinless point particles. Just as the geodesic deviation equation for spinless particles can be used to investigate the detection of gravitational waves, our generalized formula for a relativistic top can be used to study the gravitational wave background. Our formulation may be of special interest to detect the inflationary gravitational waves via the polarization of the cosmic background radiation., Comment: 19 pages LaTex, references added

By combining the concepts of graviton and matroid, we outline a new gravitational theory which we call gravitoid theory. The idea of this theory emerged as an attempt to link the mathematical structure of matroid theory with M-theory. Our observations are essentially based on the formulation of matroid bundle due to MacPherson and Anderson-Davis. Also, by considering the oriented matroid theory, we add new observations about the link between the Fano matroid and D=11 supergravity which was discussed in some of our recent papers. In particular we find a connection between the affine matroid AG(3,2) and the $G_ {2}-$symmetry of D=11 supergravity., Comment: 21 pages, Latex; minor typos corrected

We make a number of observations about matter-ghost string phase, which may eventually lead to a formal connection between matroid theory and string theory. In particular, in order to take advantage of the already established connection between matroid theory and Chern-Simons theory, we propose a generalization of string theory in terms of some kind of Kahler metric. We show that this generalization is closely related to the Kahler-Chern-Simons action due to Nair and Schiff. In addition, we discuss matroid/string connection via matroid bundles and a Schild type action, and we add new information about the relationship between matroid theory, D=11 supergravity and Chern-Simons formalism., Comment: 28 pages, LaTex, section 6 and references added

A mechanism to find different Weyl invariant p-branes and Dp-branes actions is explained. Our procedure clarifies the Weyl invariance for such systems. Besides, by considering gravity-dilaton effective action in higher dimensions we also derive a Weyl invariant action for p-branes. We argue that this derivation provides a geometrical scenario for the Weyl invariance of p-branes. Our considerations can be extended to the case of super-p-branes., Comment: 18 pages, Latex

We investigate the analogue of S-duality for 2-d gravity. Our analysis is based in a partition function associated to the Katanaev-Volovich type action for 2-d gravity. We find a S-dual 2-d gravitational action which is related to the original 2-d gravitational action by strong-weak duality transformation., Comment: 15 pages, Latex

Using a special ansatz for the metric, by straightforward computation we prove that gravi-dilaton effective action in higher dimensions is reduced to the p-brane action. The dual symmetry of the generic type $%a\longleftrightarrow \frac 1a$ is an important symmetry of the reduced action., Comment: 7 pages, Latex, the last four sentences were dropped

By using tensor analysis, we find a connection between normed algebras and the parallelizability of the spheres S$^1$, S$^3$ and S$^7.$ In this process, we discovered the analogue of Hurwitz theorem for curved spaces and a geometrical unified formalism for the metric and the torsion. In order to achieve these goals we first develope a proof of Hurwitz theorem based in tensor analysis. It turns out that in contrast to the doubling procedure and Clifford algebra mechanism, our proof is entirely based in tensor algebra applied to the normed algebra condition. From the tersor analysis point of view our proof is straightforward and short. We also discuss a possible connection between our formalism and the Cayley-Dickson algebras and Hopf maps., Comment: slightly changed content

It is shown that matroid theory may provide a natural mathematical framework for a duality symmetries not only for quantum Yang-Mills physics, but also for M-theory. Our discussion is focused in an action consisting purely of the Chern-Simons term, but in principle the main ideas can be applied beyond such an action. In our treatment the theorem due to Thistlethwaite, which gives a relationship between the Tutte polynomial for graphs and Jones polynomial for alternating knots and links, plays a central role. Before addressing this question we briefly mention some important aspects of matroid theory and we point out a connection between the Fano matroid and D=11 supergravity. Our approach also seems to be related to loop solutions of quantum gravity based in Ashtekar formalism., Comment: 18 pages, Latex

We develope the analogue of S-duality for linearized gravity in (3+1)-dimensions. Our basic idea is to consider the self-dual (anti-self-dual) curvature tensor for linearized gravity in the context of the Macdowell-Mansouri formalism. We find that the strong-weak coupling duality for linearized gravity is an exact symmetry and implies small-large duality for the cosmological constant., Comment: 18 pages, Latex, to be published in Phys. Lett. A

In this work we propose an action which unifies self-dual gravity and self-dual Yang-Mills in the context of the Macdowell-Mansouri formalism. We claim that such an action may be used to find the S-dual action for both self-dual gravity and self-dual Yang-Mills., Comment: 8 pages, Revtex, no figures, submitted to Phys. Rev. D

In this work we present a new hidden symmetry in gravity for the scale factor in the FRW model, for $k=0$. This exact symmetry vanishes the cosmological constant. We interpret this hidden symmetry as a dual symmetry in the sense that appears in the string theory., Comment: 7 pages, no figures, work sent to Class. Quantum Grav

In this work, we consider matroid theory. After presenting three different (but equivalent) definitions of matroids, we mention some of the most important theorems of such theory. In particular, we note that every matroid has a dual matroid and that a matroid is regular if and only if it is binary and includes no Fano matroid or its dual. We show a connection between this last theorem and octonions which at the same time, as it is known, are related to the Englert's solution of D = 11 supergravity. Specifically, we find a relation between the dual of Fano matroid and D = 11 supergravity. Possible applications to M-theory are speculated upon., Comment: 8 pages, Revtex, to appear in Rev. Mex. Fis. 1998

In this work we raise the question whether nonsymmetric gravity and string theory are related. We start making the observation, that the gravitational field $ g_{\mu\nu}$ and the nonsymmetric gauge field $ A_{\mu\nu}$ arising in the low energy limit in the string theory are exactly the same two basic fields used in four dimensions in nonsymmetric gravity. We argue, that this connection between nonsymmetric gravity and string theory at the level of the gauge fields $ g_{\mu\nu}$ and $ A_{\mu\nu}$ is not, however, reflected at the level of the corresponding associated actions. In an effort to find a connection between such an actions we discover a new gravitational action, which suggests an alternative version of the bosonic string in which the target and the world-volume metrics are unified., Comment: 11 pages, no figures, revtex macros

We present the results of an isophotal shape analysis of three samples of galaxies in the Coma cluster. Quantitative morphology, together with structural and photometric parameters, is given for each galaxy. Special emphasis has been placed on the detailed classification of early-type galaxies. The three samples are: i) a sample of 97 early-type galaxies brighter than m$_B$ = 17.00 falling within one degree from the center of the Coma cluster; these galaxies were observed with CCD cameras, mostly in good to excellent resolution conditions; ii) a magnitude complete sample of 107 galaxies of all morphological types down to m$_B$ = 17.00 falling in a circular region of 50 arcmin diameter, slightly offcentered to the North-West of the cluster center; the images for this and the next sample come from digitized photographic plates; iii) a complete comparison sample of 26 galaxies of all morphological types down to m$_R$ = 16.05 (or m$_B$ $\simeq$ 17.5), also in a region of 50 arcmin diameter, but centered 2.6 degrees West of the cluster center. The reliability of our morphological classifications and structural parameters of galaxies, down to the adopted magnitude limits, is assessed by comparing the results on those galaxies for which we had images taken with different instrumentation and/or seeing conditions, and by comparing our results with similar data from other observers., Comment: 22 pages, including 4 figures and 4 tables, uuencoded, gzipped postscript

A relation between the MacDowell-Mansouri theory of gravity and the Pontrjagin toplogical invariant in $(3+1)$ dimensions is discussed. This relation may be of especial interest in the quest of finding a mechanism to go from non-dynamical to dynamical gravity., Comment: 9 pages, TeX

Using a classical action associated to a point-particle in (1+1)-dimensions the classical string theory is derived. In connection with this result two aspects are clarified: First, the point particle in (1+1)-dimensions is not an ordinary relativistic system, but rather a some kind of a relativistic top; and second, through the quantization of such a kind of top the ordinary string theory is not obtained, but rather a $\sigma$-model associated to a non-compact group which may be understood as an extended string theory., Comment: 12 pages, no figures, file in TEX. E-mail: nie@zeus.ccu.umich.mx

A non-minimal coupling for spin $3/2$ fields is obtained. We use the fact that the Rarita-Schwinger field equations are the square root of the full linearized Einstein field equations in order to investigate the form of the interaction for the spin $3/2$ field with gauge fields. We deduce the form of the interaction terms for the electromagnetic and non-Abelian Yang-Mills fields by implementing appropiate energy momentum tensors on the linearized Einstein field equations. The interaction found for the electromagnetic case happens to coincide with the dipole term found by Ferrara {\it et al} by a very different procedure, namely by demanding $g=2$ at the tree level for the electromagnetic interaction of arbitrary spin particles. The same interaction is found by using the resource of linearized Supergravity N=2. For the case of the Yang-Mills field Supergravity N=4 is linearized, providing the already foreseen interaction., Comment: 16 pages, Latex

By adding the Pontrjagin topological invariant to the gauge theory of the de Sitter group proposed by MacDowell and Mansouri we obtain an action quadratic in the field-strengths, of the Chern-Simons type, from which the Ashtekar formulation is derived., Comment: 9 pages

Sub-arcsecond imagery (HRCAM, 0".35 - 0".57 FWHM) and two-dimensional spectrography (TIGER, 0".9 FWHM) of the central nucleus of M31 have been obtained at CFHT. The photometric data clearly show the double-peaked nucleus, in excellent agreement with a recent HST image by Lauer et al. 1993. We built deconvolved surface brightness models, using the multi-Gaussian expansion method. We then perform a detailed morphological analysis of the three central photometric components (bulge, nucleus and bright secondary peak) and derive various spatial luminosity models (oblate and triaxial). Stellar velocity and velocity dispersion fields were derived from the TIGER data: the former displays an extremely rapid rotation around the true center of the galaxy, while the latter exhibits a peaked structure offset in the opposite direction of the brightest light peak. Neglecting these offsets,both extended versions of the virial theorem and detailed hydrodynamical models confirm the classical strong central mass concentration, perhaps a supermassive black hole of about 7.10**7 Msun, as well as a large excess of circular motions. These offsets, however, suggest that the nucleus presently undergoes a strong stellar oscillation, with non-stationary, non-axisymmetric dynamics. This too reopens the case for a strong central mass concentration., Comment: (to appear in AA), 26 pages and 28 figures (available on anonymous FTP: orion.univ-lyon1.fr in pub/m31), LaTeX file and laa.sty, OL-36