Are the String and Einstein Frames Equivalent

The low energy physics as predicted by strings can be expressed in two (conformally related) different variables, usually called {\em frames}. The problem is raised as to whether it is physically possible in some situations to tell one from the other.Comment: 12 pages, LaTe

Local supersymmetry without SUSY partners

A gauge theory for a superalgebra that includes an internal gauge (G) and local Lorentz algebras, and that could describe the low energy particle phenomenology is constructed. These two symmetries are connected by fermionic supercharges. The system includes an internal gauge connection 1-form $A$, a spin-1/2 Dirac spinor $\psi$, the Lorentz connection $\omega$, and the vielbein $e$. The connection one-form is in the adjoint representation of G, while $\psi$ is in the fundamental. In contrast to standard supergravity, the metric is not a fundamental field and is in the center of the superalgebra: it is not only invariant under the internal gauge group and under Lorentz transformations, but is also invariant under supersymmetry. The features of this theory that mark the difference with standard supersymmetry are: A) The number of fermionic and bosonic states is not necessarily the same; B) There are no superpartners with equal mass, "bosoninos", sleptons and squarks are absent; C) Although this supersymmetry originates in a local gauge theory and gravity is included, there is no gravitino; D) Fermions acquire mass from their coupling to the background or from self-couplings, while bosons remain massless. In odd dimensions, the Chern-Simons form provides an action that is quasi-invariant under the entire superalgebra. In even dimensions, the Yang-Mills form $$ is the only natural option, and the symmetry breaks down to [G x SO(1,D-1)]. In 4D, the construction follows the Townsend - Mac Dowell-Mansouri approach. Due to the absence of osp(4|2)-invariant traces in four dimensions, the resulting Lagrangian is only invariant under [U(1) x SO(3,1)], and includes a Nambu--Jona-Lasinio term. In this case, the Lagrangian depends on a single dimensionful parameter that fixes Newton's constant, the cosmological constant and the NJL coupling.Comment: 24 pages, no figures. Title changed in journal version to "Unconventional supersymmetry and its breaking". Few references added and some paragraphs rewritten from v.1. This version includes two appendices that are not found in the journal versio

Urban Growth and Long-Term Transformations in Spanish Cities Since the Mid-Nineteenth Century: A Methodology to Determine Changes in Urban Density.

The current work models urban growth in the continuous built-up areas of 47 Spanish cities from the mid-nineteenth century through to the present day. We did this by compiling a comprehensive Geographic Information System (GIS) dataset, based on a series of historic maps and aerial images, and then used this to study urban growth and to make spatial comparisons. Our chosen indicator of expansion: population density, was calculated by dividing the total population of each city (based on its municipal area) by its built-up area during each period. Our results revealed four different stages of growth, each of which was characterised by a certain political and economic reality. They showed the clogging up of the walled city, the shaping of the urban ensanches, the maturity of the compact city and the process of metropolisation

Vassiliev invariants: a new framework for quantum gravity

We show that Vassiliev invariants of knots, appropriately generalized to the spin network context, are loop differentiable in spite of being diffeomorphism invariant. This opens the possibility of defining rigorously the constraints of quantum gravity as geometrical operators acting on the space of Vassiliev invariants of spin nets. We show how to explicitly realize the diffeomorphism constraint on this space and present proposals for the construction of Hamiltonian constraints.Comment: 15 pages, several figures included with psfi

Carnation Co. v. Commissioner, 640 F.2d 1010 (9th Cir. 1981)

Income Tax-FOREIGN INCOME-INSURANCE PAYMENTS TO WHOLLY-OWNED FOREIGN CAPTIVE INSURANCE COMPANY ARE RECAST AS CAPITAL CONTRIBUTION

Murry v. Commissioner, 601 F.2d 892 (5th Cir. 1979)

Income Tax-CONDOMINIUM RECREATION FACILITIES-EXCESS RENTAL PAYMENTS TO OWNERS OF RECREATIONAL FACILITIES NOT INCLUDIBLE IN DEVELOPER\u27S SALES INCOM