Global existence in the critical space for the Thirring and Gross-Neveu models coupled with the electromagnetic field

We prove global well-posedness for the coupled Maxwell-Dirac-Thirring-Gross-Neveu equations in one space dimension, with data for the Dirac spinor in the critical space $L^2(\R)$. In particular, we recover earlier results of Candy and Huh for the Thirring and Gross-Neveu models, respectively, without the coupling to the electromagnetic field, but the function spaces we introduce allow for a greatly simplified proof. We also apply our method to prove local well-posedness in $L^2(\R)$ for a quadratic Dirac equation, improving an earlier result of Tesfahun and the author.Comment: 15 page

An Aconceptual View of Mind and World

In Mind and World (1994/1996), John McDowell follows Donald Davidson in claiming that the world is a conceptually laden structure. A (conceptual) language and tradition constitutes the world, and our (conceptual) "openness to the world� (ibid, p.155). This means that the condition for access to the world is a clear subject – object split, and a clear split between content and the way the content is presented. With this view as the basis he criticizes the idea of a non-conceptual1 experience and non-conceptual content, starting from the demand that (conceptual) thinking must be constrained by, and rationally answerable to the empirical world (ibid p.xii)