(Pre-)Hilbert spaces in twistor quantization

In twistor theory, the canonical quantization procedure, called twistor quantization, is performed with the twistor operators represented as \hat{Z}^{A}=Z^{A}(\in C) and \hat{\bar{Z}}_{A}=-\frac{\partial}{\partial Z^{A}}. However, it has not been clarified what kind of function spaces this representation is valid in. In the present paper, we try to find appropriate (pre-)Hilbert spaces in which the above representation is realized as an adjoint pair of operators. To this end, we define an inner product for the helicity eigenfunctions by an integral over the product space of the circular space S^{1} and the upper half of projective twistor space. Using this inner product, we define a Hilbert space in some particular case and indefinite-metric pre-Hilbert spaces in other particular cases, showing that the above- mentioned representation is valid in these spaces. It is also shown that only the Penrose transform in the first particular case yields positive-frequency massless fields without singularities, while the Penrose transforms in the other particular cases yield positive-frequency massless fields with singularities.Comment: Typos correcte

Simon Grant, Monti, Martin Osherson, Daniel

The classical theory of preference among monetary bets represents people as expected utility maximizers with nondecreasing concave utility functions. Critics of this account often rely on assumptions about preferences over wide ranges of total wealth. We derive a prediction of the theory that bears on bets at any fixed level of wealth, and test the prediction behaviorally. Our results are discrepant with the classical account. Competing theories are also examined in light of our data.

A Note on Infinities in Eternal Inflation

In some well-known scenarios of open-universe eternal inflation, developed by Vilenkin and co-workers, a large number of universes nucleate and thermalize within the eternally inflating mega-universe. According to the proposal, each universe nucleates at a point, and therefore the boundary of the nucleated universe is a space-like surface nearly coincident with the future light cone emanating from the point of nucleation, all points of which have the same proper-time. This leads the authors to conclude that at the proper-time t = t_{nuc} at which any such nucleation occurs, an infinite open universe comes into existence. We point out that this is due entirely to the supposition of the nucleation occurring at a single point, which in light of quantum cosmology seems difficult to support. Even an infinitesimal space-like length at the moment of nucleation gives a rather different result -- the boundary of the nucleating universe evolves in proper-time and becomes infinite only in an infinite time. The alleged infinity is never attained at any finite time.Comment: 13 pages and 6 figure

Note by Note

My poster describes the initial goals and functions of a new organization that I am starting. The organization, Note by Note, is a local program that aims to engage children in the arts. Its current activities include providing enriching performances to younger students in the district 200 area. Every year, kids drop out of performing arts programs for a variety of reasons. This limits the important benefits provided by learning music. The main goal of this organization is to keep more students in the arts programs because of the benefits it has on child education and quality of life

Spinor and Twistor Formulations of Tensionless Bosonic Strings in Four Dimensions

Spinor and twistor formulations of tensionless bosonic strings in 4-dimensional Minkowski space are constructed. We begin with a first-order action that is equivalent to the Nambu-Goto action in the tensionful case and that leads to a spinorial action in the tensionless case. From this spinorial action, we find an alternative spinorial action useful for constructing a simple twistor formulation of tensionless strings. The twistor formulation is steadily constructed in accordance with a fundamental concept of twistor theory. We investigate local internal symmetries inherent in the twistorial action for a tensionless string and carry out some classical analyses of the tensionless string expressed in a twistorial form.Comment: 30 pages, no figures, minor corrections, a footnote added, published versio

Case Note: Germany

GmS-OGB 1/98 in Gemeinsamer Senat der obersten Gerichtshöfe des Bundes (Joint Senate of the Federal High Courts). Order from 5 April 2000

Reflections on Meaningfulness and its Social Relevance

Philosophers who write about the meaning of life are few nowadays. Thesubject has lost its attractiveness. Perceived from a viewpoint of logical positivism or language philosophy, the whole issue of meaningfulness seems rather pointless. It is often considered to be related to metaphysics, making it less suitable for philosophical inquiry. The topic of meaningfulness seems too intangible. Indeed, the few philosophers that have embarked on examining meaningfulness have proven to be well aware of the challenges this poses. At times they acknowledge that the more they concentrate on the subject, the more it seems to fall apart into unintelligible pieces about whichnothing of philosophical value can be said