A Unified Invariant Formulation, by Frames, from General Relativity to the Atomic Scale

The aim of this article is the formulation of the basic laws of Physics by frames, i.e. quadruples of exterior differential one forms. The basic operator is a modification of the Hodge-de Rham Laplacian d*d*+*d*d, where * is the hyperbolic star. In this article it is modified depending on the frame. The modified * is invariant w.r. to any diffeomorphism. Consequently, the modified Laplavian is invariant. The field equation developed in this article is a complete alternative to the field equation of General Relativity in vacuum. The frame-field equation yields a derivation of Newtonian (Einstein) law of attraction without recourse to the geodesic postulate. Coulomb law is also derived. Invariant formulation of Maxwell equations is exhibited. Then first order linear approximation is considered. It is used to derive invariant formulation of Schroedinger equation (classical and relativistic) and Dirac equation all of which are linear. The lhs of the field equation, defined on a four dimensional manifold, is the same for all bodies. Thus hopefully, it may set the foundation for a field theory. The interaction of the particles has to be worked out. The basic equation of this article is motivated by the Einstein equation in nonempty space.Comment: Several changes of the sig

The Newtonian limit of the relativistic Boltzmann equation

The relativistic Boltzmann equation for a constant differential cross section and with periodic boundary conditions is considered. The speed of light appears as a parameter $c>c_0$ for a properly large and positive $c_0$. A local existence and uniqueness theorem is proved in an interval of time independent of $c>c_0$ and conditions are given such that in the limit $c\to +\infty$ the solutions converge, in a suitable norm, to the solutions of the non-relativistic Boltzmann equation for hard spheres.Comment: 12 page

Individual Investor Sentiment and Stock Returns

This paper investigates a unique dataset that enables us to determine the aggregate buy and sell volume of individual investors for a large cross-section of NYSE stocks. We find that individuals trade as if they are contrarians, and that the stocks that individuals buy exhibit positive excess returns in the following month. These patterns are consistent with the idea that risk-averse individuals provide liquidity to meet institutional demand for immediacy. We further examine the relation between individual investor sentiment and short-horizon (weekly) return reversals that have been documented in the literature. Our results reveal that individual investor sentiment predicts future returns, and that the information content of investor sentiment is distinct from that of past returns or past volume. Furthermore, the trading of individuals predicts weekly returns in the post-2000 era for stocks of all sizes, while past return seems to have lost its predictive power for all but small stocks over the same time period. Lastly, we note that there is very little cross-sectional correlation of our individual sentiment measure across the stocks in our sample

Coframe teleparallel models of gravity. Exact solutions

The superstring and superbrane theories which include gravity as a necessary and fundamental part renew an interest to alternative representations of general relativity as well as the alternative models of gravity. We study the coframe teleparallel theory of gravity with a most general quadratic Lagrangian. The coframe field on a differentiable manifold is a basic dynamical variable. A metric tensor as well as a metric compatible connection is generated by a coframe in a unique manner. The Lagrangian is a general linear combination of Weitzenb\"{o}ck's quadratic invariants with free dimensionless parameters \r_1,\r_2,\r_3. Every independent term of the Lagrangian is a global SO(1,3)-invariant 4-form. For a special choice of parameters which confirms with the local SO(1,3) invariance this theory gives an alternative description of Einsteinian gravity - teleparallel equivalent of GR. We prove that the sign of the scalar curvature of a metric generated by a static spherical-symmetric solution depends only on a relation between the free parameters. The scalar curvature vanishes only for a subclass of models with \r_1=0. This subclass includes the teleparallel equivalent of GR. We obtain the explicit form of all spherically symmetric static solutions of the ``diagonal'' type to the field equations for an arbitrary choice of free parameters. We prove that the unique asymptotic-flat solution with Newtonian limit is the Schwarzschild solution that holds for a subclass of teleparallel models with \r_1=0. Thus the Yang-Mills-type term of the general quadratic coframe Lagrangian should be rejected.Comment: 28 pages, Latex error is fixe

The Importance of Being an Optimist: Evidence from Labor Markets

Dispositional optimism is a personality trait associated with individuals who believe, either rightly or wrongly, that in general good things tend to happen to them more often than bad things. Using a novel longitudinal data set that tracks the job search performance of MBA students, we show that dispositional optimists experience significantly better job search outcomes than pessimists with similar skills. During the job search process, they spend less effort searching and are offered jobs more quickly. They are choosier and are more likely to be promoted than others. Although we find optimists are more charismatic and are perceived by others to be more likely to succeed, these factors alone do not explain away the findings. Most of the effect of optimism on economic outcomes stems from the part that is not readily observed by one's peers.