5 papers
Magnetic forces in the absence of a classical magnetic field
Ismael L. Paiva, Yakir Aharonov, Jeff Tollaksen +1
It is shown that, in some cases, the effect of discrete distributions of flux lines in quantum mechanics can be associated with the effect of continuous distributions of magnetic f…
Topological bound states for quantum charges
Ismael L. Paiva, Yakir Aharonov, Jeff Tollaksen +1
We discuss how, in appropriately designed configurations, solenoids carrying a semifluxon can be used as topological energy barriers for charged quantum systems. We interpret this…
A general setting for functions of Fueter variables: differentiability, rational functions, Fock module and related topics
Daniel Alpay, Ismael L. Paiva, Daniele C. Struppa
We develop some aspects of the theory of hyperholomorphic functions whose values are taken in a Banach algebra over a field -- assumed to be the real or the complex numbers -- and…
Positivity, rational Schur functions, Blaschke factors, and other related results in the Grassmann algebra
Daniel Alpay, Ismael L. Paiva, Daniele C. Struppa
We begin a study of Schur analysis in the setting of the Grassmann algebra, when the latter is completed with respect to the -norm. We focus on the rational case. We start with…
Distribution spaces and a new construction of stochastic processes associated with the Grassmann algebra
Daniel Alpay, Ismael L. Paiva, Daniele C. Struppa
We associate with the Grassmann algebra a topological algebra of distributions, which allows the study of processes analogous to the corresponding free stochastic processes with st…