3 research outputs found
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