A Note on Quantum Field Theories with a Minimal Length Scale

The aim of this note is to address the low energy limit of quantum field theories with a minimal length scale. The essential feature of these models is that the minimal length acts as a regulator in the asymptotic high energy limit which is incorporated through an infinite series of higher order derivatives. If one investigates a perturbative expansion in inverse powers of the Planck mass, one generically obtains extra poles in the propagator, and instabilities connected with the higher order derivative Lagrangian, that are however artifacts of truncating the series

Dynamics with Infinitely Many Derivatives: The Initial Value Problem

Differential equations of infinite order are an increasingly important class of equations in theoretical physics. Such equations are ubiquitous in string field theory and have recently attracted considerable interest also from cosmologists. Though these equations have been studied in the classical mathematical literature, it appears that the physics community is largely unaware of the relevant formalism. Of particular importance is the fate of the initial value problem. Under what circumstances do infinite order differential equations possess a well-defined initial value problem and how many initial data are required? In this paper we study the initial value problem for infinite order differential equations in the mathematical framework of the formal operator calculus, with analytic initial data. This formalism allows us to handle simultaneously a wide array of different nonlocal equations within a single framework and also admits a transparent physical interpretation. We show that differential equations of infinite order do not generically admit infinitely many initial data. Rather, each pole of the propagator contributes two initial data to the final solution. Though it is possible to find differential equations of infinite order which admit well-defined initial value problem with only two initial data, neither the dynamical equations of p-adic string theory nor string field theory seem to belong to this class. However, both theories can be rendered ghost-free by suitable definition of the action of the formal pseudo-differential operator. This prescription restricts the theory to frequencies within some contour in the complex plane and hence may be thought of as a sort of ultra-violet cut-off.Comment: 40 pages, no figures. Added comments concerning fractional operators and the implications of restricting the contour of integration. Typos correcte

Systematic documentation and analysis of human genetic variation in hemoglobinopathies using the microattribution approach

We developed a series of interrelated locus-specific databases to store all published and unpublished genetic variation related to hemoglobinopathies and thalassemia and implemented microattribution to encourage submission of unpublished observations of genetic variation to these public repositories. A total of 1,941 unique genetic variants in 37 genes, encoding globins and other erythroid proteins, are currently documented in these databases, with reciprocal attribution of microcitations to data contributors. Our project provides the first example of implementing microattribution to incentivise submission of all known genetic variation in a defined system. It has demonstrably increased the reporting of human variants, leading to a comprehensive online resource for systematically describing human genetic variation in the globin genes and other genes contributing to hemoglobinopathies and thalassemias. The principles established here will serve as a model for other systems and for the analysis of other common and/or complex human genetic diseases