The Thirring model in spaces of analytic functions (Q1747876)

The chief aim of this article is the analyticity of solutions to a Cauchy problem that arises for a model in quantum field theory; in particular, the Thirring model. The Cauchy problem is posed in Gevrey spaces, where it is shown that the analyticity of solutions persists for a short time. The Gevrey spaces under consideration contain those functions which satisfy, for \(\sigma>0\) and \(s\in\mathbb{R}\), \[ \|f\|_{G^{\sigma,s}} = \|e^{\sigma|\xi|}(1+|\xi|^2)^{s/2}\hat f(\xi)\|_{L^2_\xi} <\infty. \] Here, \(\hat f\) is the Fourier transform of \(f\). The second main result concerns whether analytic solutions can persist for all time. On this, a general sufficient condition (rather, for all time in which the solution to the associated Cauchy problem remains finite) is used to provide analyticity for all time \(t>0\).