An indefinite metric model for interacting quantum fields with non-stationary background gravitation

We consider a relativistic Ansatz for the vacuum expectation values (VEVs) of a quantum field on a globally hyperbolic space-time which is motivated by certain Euclidean field theories. The Yang-Feldman asymptotic condition w.r.t. a "in"-field in a quasi-free representation of the canonic commutation relations (CCR) leads to a solution of this Ansatz for the VEVs. A GNS-like construction on a non-degenerate inner product space then gives local, covariant quantum fields with indefinite metric on a globally hyperbolic space-time. The non-trivial scattering behavior of quantum fields is analyzed by construction of the "out"-fields and calculation of the scattering matrix. A new combined effect of non-trivial quantum scattering and non-stationary gravitational forces is described for this model, as quasi-free "in"- fields are scattered to "out"-fields which form a non quasi-free representations of the CCR. The asymptotic condition, on which the construction is based, is verified for the concrete example of de Sitter space-time

Small-scale dynamos on the solar surface: dependence on magnetic Prandtl number

The question of possible small-scale dynamo action in the surface layers of the Sun is revisited with realistic 3D MHD simulations. As in other MHD problems, dynamo action is found to be a sensitive function of the magnetic Prandtl number ${\rm P_{\rm m} }=\nu/\eta$; it disappears below a critical value ${\rm P_{\rm c}}$ which is a function of the numerical resolution. At a grid spacing of 3.5 km, ${\rm P_{\rm c}}$ based on the hyperdiffusivities implemented in the code (STAGGER) is $\approx 1$, increasing with increasing grid spacing. As in other settings, it remains uncertain whether small scale dynamo action is present in the astrophysical limit where ${\rm P_{\rm m} }<<1$ and magnetic Reynolds number ${\rm R_m}\gg 1$. The question is discussed in the context of the strong effect that external stray fields are observed to have in generating and maintaining dynamo action in other numerical and laboratory systems, and in connection with the type-II hypertransient behavior of dynamo action observed in the absence of such external fields

Brightness of the Sun's small scale magnetic field: proximity effects

The net effect of the small scale magnetic field on the Sun's (bolometric) brightness is studied with realistic 3D MHD simulations. The direct effect of brightening within the magnetic field itself is consistent with measurements in high-resolution observations. The high 'photometric accuracy' of the simulations, however, reveal compensating brightness effects that are hard to detect observationally. The influence of magnetic concentrations on the surrounding nonmagnetic convective flows (a 'proximity effect') reduces the brightness by an amount exceeding the brightening by the magnetic concentrations themselves. The net photospheric effect of the small scale field (~ -0.34% at a mean flux density of 50 G) is thus negative. We conclude that the main contribution to the observed positive correlation between the magnetic field and total solar irradiance must be magnetic dissipation in layers around the temperature minimum and above (not included in the simulations). This agrees with existing inferences from observations

In Honor of Matthew Rabin: Winner of the John Bates Clark Medal

Although there is some evidence that Matthew Rabin existed before 1990, we had the pleasure of discovering him for ourselves when, in the early 1990s, he sent each of us a copy of his manuscript "Incorporating Fairness into Game Theory and Economics" [2]. Matthew was, at this time, an assistant professor in Berkeley's economics department, having recently finished his graduate training at MIT. The paper was remarkable in many ways, and it induced us both to call around and ask: "Who is this guy Rabin?" Now, just a decade later, we find ourselves writing an article in honor of his winning the John Bates Clark award. So, who is this guy

Anomalies: Ultimatums, Dictators and Manners

Economics can be distinguished from other social sciences by the belief that most (all?) behavior can be explained by assuming that agents have stable, well-defined preferences and make rational choices consistent with those preferences in markets that (eventually) clear. An empirical result qualifies as an anomaly if it is difficult to "rationalize" or if implausible assumptions are necessary to explain it within the paradigm. This column will resume, after a long rest, the investigation of such anomalies

Myopic Loss Aversion and the Equity Premium Puzzle

The equity premium puzzle, first documented by Mehra and Prescott, refers to the empirical fact that stocks have greatly outperformed bonds over the last century. As Mehra and Prescott point out, it appears difficult to explain the magnitude of the equity premium within the usual economics paradigm because the level of risk aversion necessary to justify such a large premium is implausibly large. We offer a new explanation based on Kahneman and Tversky's 'prospect theory'. The explanation has two components. First, investors are assumed to be 'loss averse' meaning they are distinctly more sensitive to losses than to gains. Second, investors are assumed to evaluate their portfolios frequently, even if they have long-term investment goals such as saving for retirement or managing a pension plan. We dub this combination 'myopic loss aversion'. Using simulations we find that the size of the equity premium is consistent with the previously estimated parameters of prospect theory if investors evaluate their portfolios annually. That is, investors appear to choose portfolios as if they were operating with a time horizon of about one year. The same approach is then used to study the size effect. Preliminary results suggest that myopic loss aversion may also have some explanatory power for this anomaly.

An Economic Theory of Self-Control

Although many economists, most notably Strotz, have discussed dynamic inconsistency and precommitment, none have dealt directly with the essence of the problem: self-control. This paper attempts to fill that gap by modeling man as an organization. The Strotz model is recast to include the control features missing in his formulation. The organizational analogy permits us to draw on the theory of agency. We thus relate the individual's control problems with those that exist in agency relationships.

Libertarian Paternalism Is Not An Oxymoron

Cass R. Sunstein and Richard H. Thaler assert that while the idea of libertarian paternalism might seem to be an oxymoron, it is both possible and legitimate for private and public institutions to affect behavior while also respecting freedom of choice. Often people's preferences are ill-formed, and their choices will inevitably be influenced by default rules, framing effects, and starting points. In these circumstances, a form of paternalism cannot be avoided. Equipped with an understanding of behavioral findings of bounded rationality and bounded self-control, libertarian paternalists should attempt to steer people's choices in welfare-promoting directions without eliminating freedom of choice. Sunstein and Thaler argue that it is also possible to show how a libertarian paternalist might select among the possible options and to assess how much choice to offer. This paper gives examplesfrom many areas, including savings behavior, labor law, and consumer protection.

Can the Market Add and Subtract? Mispricing in Tech Stock Carve-Outs

Recent equity carve-outs in US technology stocks appear to violate a basic premise of financial theory: identical assets have identical prices. In our 1998-2000 sample, holders of a share of company A are expected to receive x shares of company B, but the price of A is less than x times the price of B. A prominent example involves 3Com and Palm. Arbitrage does not eliminate these blatant mispricing due to short sale constraints, so that B is overpriced but expensive or impossible to sell short. Evidence from options prices shows that shorting costs are extremely high, eliminating exploitable arbitrage opportunities.