Harmonizing Europe’s payment systems: an uphill battle?

A model is introduced to analyze the effect of network effects and transactions patterns on the decision by banks (not) to standardize payment systems both domestically and across borders. If only a small share of all transactions is cross-border, banks have strong incentives to maintain incompatible standards across countries. The model is applied to the case of harmonizing Europe’s payment networks.economics of technology ;

Quantum Gauge Equivalence in QED

We discuss gauge transformations in QED coupled to a charged spinor field, and examine whether we can gauge-transform the entire formulation of the theory from one gauge to another, so that not only the gauge and spinor fields, but also the forms of the operator-valued Hamiltonians are transformed. The discussion includes the covariant gauge, in which the gauge condition and Gauss's law are not primary constraints on operator-valued quantities; it also includes the Coulomb gauge, and the spatial axial gauge, in which the constraints are imposed on operator-valued fields by applying the Dirac-Bergmann procedure. We show how to transform the covariant, Coulomb and spatial axial gauges to what we call ``common form,'' in which all particle excitation modes have identical properties. We also show that, once that common form has been reached, QED in different gauges has a common time-evolution operator that defines time-translation for states that represent systems of electrons and photons. By combining gauge transformations with changes of representation from standard to common form, the entire apparatus of a gauge theory can be transformed from one gauge to another.Comment: Contribution for a special issue of Foundations of Physics honoring Fritz Rohrlich; edited by Larry P. Horwitz, Tel-Aviv University, and Alwyn van der Merwe, University of Denver (Plenum Publishing, New York); 40 pages, REVTEX, Preprint UCONN-93-3, 1 figure available upon request from author