Metric projective geometry, BGG detour complexes and partially massless gauge theories

A projective geometry is an equivalence class of torsion free connections sharing the same unparametrised geodesics; this is a basic structure for understanding physical systems. Metric projective geometry is concerned with the interaction of projective and pseudo-Riemannian geometry. We show that the BGG machinery of projective geometry combines with structures known as Yang-Mills detour complexes to produce a general tool for generating invariant pseudo-Riemannian gauge theories. This produces (detour) complexes of differential operators corresponding to gauge invariances and dynamics. We show, as an application, that curved versions of these sequences give geometric characterizations of the obstructions to propagation of higher spins in Einstein spaces. Further, we show that projective BGG detour complexes generate both gauge invariances and gauge invariant constraint systems for partially massless models: the input for this machinery is a projectively invariant gauge operator corresponding to the first operator of a certain BGG sequence. We also connect this technology to the log-radial reduction method and extend the latter to Einstein backgrounds.Comment: 30 pages, LaTe

Quantum Gravity and Causal Structures: Second Quantization of Conformal Dirac Algebras

It is postulated that quantum gravity is a sum over causal structures coupled to matter via scale evolution. Quantized causal structures can be described by studying simple matrix models where matrices are replaced by an algebra of quantum mechanical observables. In particular, previous studies constructed quantum gravity models by quantizing the moduli of Laplace, weight and defining-function operators on Fefferman-Graham ambient spaces. The algebra of these operators underlies conformal geometries. We extend those results to include fermions by taking an osp(1|2) "Dirac square root" of these algebras. The theory is a simple, Grassmann, two-matrix model. Its quantum action is a Chern-Simons theory whose differential is a first-quantized, quantum mechanical BRST operator. The theory is a basic ingredient for building fundamental theories of physical observables.Comment: 4 pages, LaTe

Development of biaxial test fixture includes cryogenic application

Test fixture has the capability of producing biaxial stress fields in test specimens to the point of failure. It determines biaxial stress by dividing the applied load by the net cross section. With modification it can evaluate materials, design concepts, and production hardware at cryogenic temperatures

Gravitational- and self-coupling of partially massless spin 2

We show that higher spin systems specific to cosmological spaces are subject to the same problems as models with Poincaré limits. In particular, we analyze partially massless (PM) spin 2 and find that both its gravitational coupling and nonlinear extensions suffer from the usual background- and self-coupling difficulties: Consistent free field propagation does not extend beyond background Einstein geometries. Then (using conformal, Weyl, gravity, which contains relative ghost PM and graviton excitations) we find that avoiding graviton ghosts restricts Weyl-generated PM self-couplings to the usual, leading, safe, Noether current cubic ones

The Comparative Predictive Abilities Of Accrual Earnings And Cash Flows In Periods Of Economic Turbulence: The Case Of The IT Bubble

As set forth in SFAC No. 1, a primary objective of financial reporting is to provide information useful to decision makers. Predicting future cash flows represents a major goal of investors and creditors, and accrual and cash flow accounting information present two alternative factors useful in such predictions. The current research investigates the comparative abilities of accrual basis net income and historical cash flows from operations as predictors of future cash flows during both the economic boom leading up to the IT Bubble and the period of economic duress following the burst of that Bubble. Generally, results indicate that historical cash flows outperform accrual net income in predicting future cash flows during these periods of economic turbulence.  Additionally, the evidence reveals great variability in the predictive ability of accrual earnings during the time period studied, suggesting that accrual accounting estimates lose some of their precision during periods of extreme economic fluctuation

Bertrand Oligopoly And Factors Markets With Scarcity And Price Controls

In an earlier article, we reported the results of a classroom experiment simulating price competition in an oligopoly with differentiated goods. That study raised some questions that we were unable to address at that time. For this current study, we have adapted the experiment to further explore the effects of scarcity in the input markets, and to study the effects of price controls in these markets. We find that scarcity in an input market has the expected directional effect on prices in both input and output markets, but not necessarily the magnitude expected; we further find that price controls have only some of the effects expected. In the current experiment, we increased the number of rounds of the game to allow more opportunity for convergence to a stable outcome, and to allow for three distinct phases of the game: initial rounds in which inputs were abundantly available, subsequent rounds in which one input’s supply was dramatically reduced, and final rounds in which a price floor was established on the one input which remained abundant. As expected, firms played Nash/Bertrand strategies in the early rounds. However, the shock caused by reducing the availability of capital took many rounds for full adjustment, with both output prices and the equilibrium rental rate of capital rising consistently and gradually toward their projected equilibria over ten rounds, although even then capital prices did not rise enough to absorb all firm profits. Surprisingly, establishing a minimum wage did not have the anticipated effect of balancing payments between labor and capital; instead, the minimum wage completely disrupted the trend of an increasing rental price of capital and reduced it to zero, while creating volatility in profits without consistently eliminating them. Overall, we find that most of our anticipated results ultimately obtain, but adjustments to variations in market conditions are neither immediate nor perfectly consistent with the predictions of theory

Quantum Darboux theorem

The problem of computing quantum mechanical propagators can be recast as a computation of a Wilson line operator for parallel transport by a flat connection acting on a vector bundle of wave functions. In this picture, the base manifold is an odd-dimensional symplectic geometry, or quite generically a contact manifold that can be viewed as a "phase-spacetime,"while the fibers are Hilbert spaces. This approach enjoys a "quantum Darboux theorem"that parallels the Darboux theorem on contact manifolds which turns local classical dynamics into straight lines. We detail how the quantum Darboux theorem works for anharmonic quantum potentials. In particular, we develop a novel diagrammatic approach for computing the asymptotics of a gauge transformation that locally makes complicated quantum dynamics trivial

Evolution of inflation accounting in the U.S.

This article presents a discussion of the development of the need for inflation accounting, the history of official pronouncements addressing inflation accounting, and a summary of research studies dealing with reporting the effects of changing prices. Not only does this analysis reveal the continuity, depth, and complexity of the issues facing the FASB, but it also facilitates an understanding of how and why the FASB determined that presentation of supplmentary price-level adjusted information should be voluntary

Experiments In Bertrand Competition With Factor Markets

We present a classroom experiment which introduces product differentiation and factor markets into the traditional Bertrand framework.  We find that student behavior converges toward the market outcomes predicted by theory.  We also find that the experiment enhances student understanding of Bertrand price competition in a market with product differentiation and factor markets, and also appears to increase student satisfaction