Exoplanet Transit Parallax

The timing and duration of exoplanet transits has a dependency on observer position due to parallax. In the case of an Earth-bound observer with a 2 AU baseline the dependency is typically small and slightly beyond the limits of current timing precision capabilities. However, it can become an important systematic effect in high-precision repeated transit measurements for long period systems due to its relationship to secular perspective acceleration phenomena. In this short paper we evaluate the magnitude and characteristics of transit parallax in the case of exoplanets using simplified geometric examples. We also discuss further implications of the effect, including its possible exploitation to provide immediate confirmation of planetary transits and/or unique constraints on orbital parameters and orientations.Comment: 12 Pages, 3 Figures, Accepted for publication in Ap

Gauge Independence of the S-Matrix in the Causal Approach

The gauge dependence of the time-ordered products for Yang-Mills theories is analysed in perturbation theory by means of the causal method of Epstein and Glaser together with perturbative gauge invariance. This approach allows a simple inductive proof of the gauge independence of the physical S-matrix.Comment: 19 pages, latex, 1 figur

From massive gravity to modified general relativity II

We continue our investigation of massive gravity in the massless limit of vanishing graviton mass. From gauge invariance we derive the most general coupling between scalar matter and gravity. We get further couplings beside the standard coupling to the energy-momentum tensor. On the classical level this leads to a further modification of general relativity.Comment: 12 pages, no figur

The Standard Model and its Generalizations in Epstein-Glaser Approach to Renormalization Theory II: the Fermion Sector and the Axial Anomaly

We complete our study of non-Abelian gauge theories in the framework of Epstein-Glaser approach to renormalization theory including in the model an arbitrary number of Dirac Fermions. We consider the consistency of the model up to the third order of the perturbation theory. In the second order we obtain pure group theoretical relations expressing a representation property of the numerical coefficients appearing in the left and right handed components of the interaction Lagrangian. In the third order of the perturbation theory we obtain the the condition of cancellation of the axial anomaly.Comment: 38 pages, LATEX 2e, extensive rewritting, some errors eliminate

Electron-positron pair production in the external electromagnetic field of colliding relativistic heavy ions

The results concerning the $e^+e^-$ production in peripheral highly relativistic heavy-ion collisions presented in a recent paper by Baltz {\em{et al.}} are rederived in a very straightforward manner. It is shown that the solution of the Dirac equation directly leads to the multiplicity, i.e. to the total number of electron-positron pairs produced by the electromagnetic field of the ions, whereas the calculation of the single pair production probability is much more involved. A critical observation concerns the unsolved problem of seemingly absent Coulomb corrections (Bethe-Maximon corrections) in pair production cross sections. It is shown that neither the inclusion of the vacuum-vacuum amplitude nor the correct interpretation of the solution of the Dirac equation concerning the pair multiplicity is able the explain (from a fundamental point of view) the absence of Coulomb corrections. Therefore the contradiction has to be accounted to the treatment of the high energy limit.Comment: 6 pages, 4 Postscript figures, uses svjour.cls/svepj.cl

Slowly decaying classical fields, unitarity, and gauge invariance

In classical external gauge fields that fall off less fast than the inverse of the evolution parameter (time) of the system the implementability of a unitary perturbative scattering operator ($S$-matrix) is not guaranteed, although the field goes to zero. The importance of this point is exposed for the counter-example of low-dimensionally expanding systems. The issues of gauge invariance and of the interpretation of the evolution at intermediate times are also intricately linked to that point.Comment: 8 pages, no figure

Analysis of Fisher Information and the Cram\'{e}r-Rao Bound for Nonlinear Parameter Estimation after Compressed Sensing

In this paper, we analyze the impact of compressed sensing with complex random matrices on Fisher information and the Cram\'{e}r-Rao Bound (CRB) for estimating unknown parameters in the mean value function of a complex multivariate normal distribution. We consider the class of random compression matrices whose distribution is right-orthogonally invariant. The compression matrix whose elements are i.i.d. standard normal random variables is one such matrix. We show that for all such compression matrices, the Fisher information matrix has a complex matrix beta distribution. We also derive the distribution of CRB. These distributions can be used to quantify the loss in CRB as a function of the Fisher information of the non-compressed data. In our numerical examples, we consider a direction of arrival estimation problem and discuss the use of these distributions as guidelines for choosing compression ratios based on the resulting loss in CRB.Comment: 12 pages, 3figure

Massive gravity as a quantum gauge theory

We present a new point of view on the quantization of the massive gravitational field, namely we use exclusively the quantum framework of the second quantization. The Hilbert space of the many-gravitons system is a Fock space F+ (Hgraviton) where the one-particle Hilbert space Hgraviton carries the direct sum of two unitary irreducible representations of the Poincaré group corresponding to two particles of mass m > 0 and spins 2 and 0, respectively. This Hilbert space is canonically isomorphic to a space of the type Ker(Q)/Im(Q) where Q is a gauge charge defined in an extension of the Hilbert space Hgraviton generated by the gravitational field hμν and some ghosts fields uμ, ũμ (which are vector Fermi fields) and vμ (which is a vector Bose field). Then we study the self interaction of massive gravity in the causal framework. We obtain a solution which goes smoothly to the zero-mass solution of linear quantum gravity up to a term depending on the bosonic ghost field. This solution depends on two real constants as it should be; these constants are related to the gravitational constant and the cosmological constant. In the second order of the perturbation theory we do not need a Higgs field, in sharp contrast to Yang-Mills theor

Massive gravity from descent equations

Both massless and massive gravity are derived from descent equations (Wess-Zumino consistency conditions). The massive theory is a continuous deformation of the massless one.Comment: 8 pages, no figur