SU(2) gauge theory of gravity with topological invariants

The most general gravity Lagrangian in four dimensions contains three topological densities, namely Nieh-Yan, Pontryagin and Euler, in addition to the Hilbert-Palatini term. We set up a Hamiltonian formulation based on this Lagrangian. The resulting canonical theory depends on three parameters which are coefficients of these terms and is shown to admit a real SU(2) gauge theoretic interpretation with a set of seven first-class constraints. Thus, in addition to the Newton's constant, the theory of gravity contains three (topological) coupling constants, which might have non-trivial imports in the quantum theory.Comment: Based on a talk at Loops-11, Madrid, Spain; To appear in Journal of Physics: Conference Serie

Inmarsat aeronautical mobile satellite system: Internetworking issues

The Inmarsat Aeronautical Mobile Satellite System (AMSS) provides air-ground and air-air communications services to aero-mobile users on a global basis. Communicating parties may be connected either directly, or more commonly, via interconnecting networks to the Inmarsat AMSS, in order to construct end-to-end communications circuits. The aircraft earth station (AES) and the aeronautical ground earth station (GES) are the points of interconnection of the Inmarsat AMSS to users, as well as to interconnecting networks. This paper reviews the internetworking aspects of the Inmarsat AMSS, by introducing the Inmarsat AMSS network architecture and services concepts and then discussing the internetwork address/numbering and routing techniques

On the Kolmogorov--Wiener--Masani spectrum of a multi-mode weakly stationary quantum process

We introduce the notion of a $k$-mode weakly stationary quantum process $\varrho$ based on the canonical Schr\"odinger pairs of position and momentum observables in copies of $L^2(\mathbb{R}^k)$, indexed by an additive abelian group $D$ of countable cardinality. Such observables admit an autocovariance map $\widetilde{K}$ from $D$ into the space of real $2k \times 2k$ matrices. The map $\widetilde{K}$ on the discrete group $D$ admits a spectral representation as the Fourier transform of a $2k \times 2k$ complex Hermitain matrix-valued totally finite measure $\Phi$ on the compact character group $\widehat{D}$, called the Kolmogorov-Wiener-Masani (KWM) spectrum of the process $\varrho$. Necessary and sufficient conditions on a $2k \times 2k$ complex Hermitian matrix-valued measure $\Phi$ on $\widehat{D}$ to be the KWM spectrum of a process $\varrho$ are obtained. This enables the construction of examples. Our theorem reveals the dramatic influence of the uncertainty relations among the position and momentum observables on the KWM spectrum of the process $\varrho$. In particular, KWM spectrum cannot admit a gap of positive Haar measure in $\widehat{D}$. The relationship between the number of photons in a particular mode at any site of the process and its KWM spectrum needs further investigation.Comment: 17 pages, added Theorem 4.2 and some remarks. Comments welcome. Keywords: Weakly stationary quantum process, Kolmogorov-Wiener-Masani spectrum, autocovariance map, spectral representation, uncertainty relation

Did Prepayments Sustain the Subprime Market?

This paper demonstrates that the reason for widespread default of mortgages in the subprime market was a sudden reversal in the house price appreciation of the early 2000's. Using loan-level data on subprime mortgages, we observe that the majority of subprime loans were hybrid adjustable rate mortgages, designed to impose substantial financial burden on reset to the fully indexed rate. In a regime of rising house prices, a financially distressed borrower could avoid default by prepaying the loan and our results indicate that subprime mortgages originated between 1998 and 2005 had extremely high prepayment rates. Most important, prepayment rates on subprime mortgages were extremely high (i) not just for ARMs but FRMs as well, (ii) even before the reset dates on hybrid-ARMs and (iii) despite prepayment penalties on the contract. However, a sudden reversal in house price appreciation increased default in this market because it made this prepayment exit option cost-prohibitive. In short, prepayments sustained the subprime boom and the extremely high default rates on 2006-2007 vintages were largely due to the inability of these mortgages to prepay (an option that was available for mortgages of earlier vintages).mortgages;subprime;refinance;prepayment;crisis

Fock spaces corresponding to positive definite linear transformations

Suppose $A$ is a positive real linear transformation on a finite dimensional complex inner product space $V$. The reproducing kernel for the Fock space of square integrable holomorphic functions on $V$ relative to the Gaussian measure $d\mu_A(z)=\frac {\sqrt {\det A}} {\pi^n}e^{-{\rm Re}} dz$ is described in terms of the holomorphic--antiholomorphic decomposition of the linear operator $A$. Moreover, if $A$ commutes with a conjugation on $V$, then a restriction mapping to the real vectors in $V$ is polarized to obtain a Segal--Bargmann transform, which we also study in the Gaussian-measure setting