Abstract:
The difference between Einstein's general relativity and its Cartan extension is analyzed within the scenario of asymptotic safety of quantum gravity. In particular, we focus on the four-fermion interaction which distinguishes the Einstein-Cartan theory from its Riemannian limit. 1. Introduction In the coupling of gravity to Dirac type spinor fields [1], it is at times surmised that the Einstein-Cartan (EC) theory [2] is superior to standard General Relativity (GR), inasmuch as the involved torsion tensor of Cartan [3, 4] can accommodate the spin of fundamental Fermions of electrons and quarks in gravity. However, classically,the effects of spin and torsion cannot be detected by Lageos or Gravity Probe B [5] and would be significant only at densities of matter that are very high but nevertheless smaller than the Planck density at which quantum gravitational effects are believed to dominate. It was even claimed [6] that EC theory may avert the problem of singularities in cosmology, but for a coupling to Dirac fields, the opposite happens [7–9]. Recently, it has been stressed by Weinberg [10–12] that the Riemann-Cartan (RC) connection , a one-form, is just a deformation of the Christoffel connection by the (con-)tortion tensor-valued one-form , at least from the field theoretical point of view. Although algebraically complying with [13], this argument has been refuted [14] on the basis of the special geometrical interpretation [15, 16] of Cartan’s torsion. It is well-known [17, 18] that EC theory coupled to the Dirac field is effectively GR with an additional four-fermion (FF) interaction. However, such contact interactions are perturbatively nonrenormalizable in without Chern-Simons (CS) terms [19], which was one of the reasons for giving up Fermi’s theory of the beta decay. Since GR with a cosmological constant appears to be asymptotically safe, in the scenario [20] first devised by Weinberg [21], one may ask [22] what the situation in EC theory is, where Cartan’s algebraic equation relates torsion to spin, that is, to the axial current in the case of Dirac fields, on dimensional grounds coupled with gravitational strength. 2. Dirac Fields in Riemann-Cartan Spacetime In our notation [13, 23–25], a Dirac field is a bispinor-valued zero-form for which denotes the Dirac adjoint and is the exterior covariant derivative with respect to the RC connection one-form , providing a minimal gravitational coupling. In the manifestly Hermitian formulation, the Dirac Lagrangian is given by the four-form where is the Clifford algebra-valued coframe, obeying , and is

Abstract:
In Riemann-Cartan spacetimes with torsion only its axial covector piece $A$ couples to massive Dirac fields. Using renormalization group arguments, we show that besides the familiar Riemannian term only the Pontrjagin type four-form $dA\wedge dA$ does arise additionally in the chiral anomaly, but not the Nieh-Yan term $d^\star A$, as has been claimed in a recent paper [PRD 55, 7580 (1997)].

Abstract:
Similarily as in the Ashtekar approach, the translational Chern-Simons term is, as a generating function, instrumental for a chiral reformulation of simple (N=1) supergravity. After applying the algebraic Cartan relation between spin and torsion, the resulting canonical transformation induces not only decomposition of the gravitational fields into selfdual and antiselfdual modes, but also a splitting of the Rarita-Schwinger fields into their chiral parts in a natural way. In some detail, we also analyze the consequences for axial and chiral anomalies.

Abstract:
Wave packets are considered as solutions of the Maxwell equations in a reduced waveguide exhibiting tunneling due to a stepwise change of the index of refraction. We discuss several concepts of “tunneling time” during the propagation of an electromagnetic pulse and analyze their compatibility with standard relativity. 1. Introduction Tunneling is often regarded as a quantum effect. Among the many recent applications is the scanning tunneling microscope exhibiting also phonon tunneling [1]. However, in optics, it was discovered already by Newton as frustrated total reflection of light, compare [2]. In physics, it is largely accepted that there is some time scale [3] associated with the duration of any tunneling process [4]. In fact, it has been directly measured, for instance, with microwaves [5–8]. However, there is a lack of consensus what is the exact nature of this “tunneling time,” and a unique and simple expression [9] is still missing. Here, we will recapitulate some introductional material about its classical aspects and discuss the consequences for propagating electromagnetic waves in undersized waveguides. Our main objective is to confront them with standard relativity [10]. Recently, modern versions [11] of the Michelson-Morley experiment have provided the bound of for the isotropy of the velocity of light in vacuum, one of the most stringent experimental limits in physics. The wave operator of Jean-Baptiste le Rond d’Alembert is invariant under the general Lorentz transformations where is the radius vector of an event and the Lorentz factor. It is quite remarkable that Riemann [12] proposed already in 1858 an invariant wave equation for the electromagnetic potential in an attempt to accommodate—within his scalar electrodynamics—the 1855 experiments of Kohlrausch and Weber [13]. He estimated correctly the velocity of light in vaccum from the then known values the electromagnetic units. In 1886, Voigt [14] anticipated to some extent the invariance of the d’Alembertian (1) under what is now called a Lorentz boost (2). 2. Electromagnetic Plane Waves Let us consider the electromagnetic field in a waveguide [15, 16]. To this end, we depart from the Maxwell equations of the Appendix which imply the wave equations for the electric and magnetic field. The refractive index is given in terms of the relative permittivity or dielectric constant and permeability of a medium. Let us restrict ourselves first to a plane wave solution written in the complex form where is the wave vector determining the direction of the wave propagation and the amplitudes and

Abstract:
The mechanism of the initial inflation of the universe is based on gravitationally coupled scalar fields $\phi$. Various scenarios are distinguished by the choice of an {\it effective self--interaction potential} $U(\phi)$ which simulates a {\it temporarily} non--vanishing {\em cosmological term}. Using the Hubble expansion parameter $H$ as a new ``time" coordinate, we can formally derive the {\it general} Robertson--Walker metric for a {\em spatially flat} cosmos. Our new method provides a classification of allowed inflationary potentials and is broad enough to embody all known {\it exact} solutions involving one scalar field as special cases. Moreover, we present new inflationary and deflationary exact solutions and can easily predict the influence of the form of $U(\phi)$ on density perturbations.

Abstract:
Using the Hubble parameter as new `inverse time' coordinate ($H$-formalism), a new method of reconstructing the inflaton potential is developed also using older results which, in principle, is applicable to any order of the slow-roll approximation. In first and second order, we need three observational data as inputs: the scalar spectral index $n_s$ and the amplitudes of the scalar and the tensor spectrum. We find constraints between the values of $n_s$ and the corresponding values for the wavelength $\lambda $. By imposing a dependence $\lambda (n_s)$, we were able to reconstruct and visualize inflationary potentials which are compatible with recent COBE and other astrophysical observations. >From the reconstructed potentials, it becomes clear that one cannot find only one special value of the scalar spectral index $n_s$.

Abstract:
By using the rather stringent nonlinear second order slow-roll approximation, we reconsider the nonlinear second order Abel equation of Stewart and Lyth. We determine a new blue eigenvalue spectrum. Some of the discrete values of the spectral index $n_s$ have consistent fits to the cumulative COBE data as well as to recent ground-base CMB experiments.

Abstract:
The present surge for the astrophysical relevance of boson stars stems from the speculative possibility that these compact objects could provide a considerable fraction of the non-baryonic part of dark matter within the halo of galaxies. For a very light `universal' axion of effective string models, their total gravitational mass will be in the most likely range of \sim 0.5 M_\odot of MACHOs. According to this framework, gravitational microlensing is indirectly ``weighing" the axion mass, resulting in \sim 10^{-10} eV/c^2. This conclusion is not changing much, if we use a dilaton type self-interaction for the bosons. Moreover, we review their formation, rotation and stability as likely candidates of astrophysical importance.

Abstract:
The canonical theory of (N=1) supergravity, with a matrix representation for the gravitino covector-spinor, is applied to the Bianchi class A spatially homogeneous cosmologies. The full Lorentz constraint and its implications for the wave function of the universe are analyzed in detail. We found that in this model no physical states other than the trivial "rest frame" type occur.

Abstract:
Boson stars are descendants of the so-called geons of Wheeler, except that they are built from scalar particles instead of electromagnetic fields. If scalar fields exist in nature, such localized configurations kept together by their self-generated gravitational field can form within Einstein's general relativity. In the case of complex scalar fields, an absolutely stable branch of such non-topological solitons with conserved particle number exists. Our present surge stems from the speculative possibility that these compact objects could provide a considerable fraction of the non-baryonic part of dark matter. In any case, they may serve as a convenient "laboratory" for studying numerically rapidly rotating bodies in general relativity and the generation of gravitational waves.