Hermitian analyticity versus Real analyticity in two-dimensional factorised S-matrix theories

The constraints implied by analyticity in two-dimensional factorised S-matrix theories are reviewed. Whenever the theory is not time-reversal invariant, it is argued that the familiar condition of `Real analyticity' for the S-matrix amplitudes has to be superseded by a different one known as `Hermitian analyticity'. Examples are provided of integrable quantum field theories whose (diagonal) two-particle S-matrix amplitudes are Hermitian analytic but not Real analytic. It is also shown that Hermitian analyticity is consistent with the bootstrap equations and that it ensures the equivalence between the notion of unitarity in the quantum group approach to factorised S-matrices and the genuine unitarity of the S-matrix.Comment: 9 pages, LaTeX file. The comments about unitarity in affine Toda theories have been improved. The basis dependence of the Hermitian analyticity conditions is discusse

Local analytic regularity in the linearized Calder\'on problem

We consider the linearization of the Dirichlet-to-Neumann (DN) map as a function of the potential. We show that it is injective at a real analytic potential for measurements made at an open subset of analyticity of the boundary. More generally, we relate the analyticity up to the boundary of the variations of the potential to the analyticity of the symbols of the corresponding variations of the DN-map.Comment: A gap in the proof of Lemma 1.2 in v1 prompted us to remove that lemma, causing a superficial change in the formulation of the main resul

From 2D conformal to 4D self-dual theories: quaternionic analyticity

It is shown that self-dual theories generalize to four dimensions both the conformal and analytic aspects of two-dimensional conformal field theories. In the harmonic space language there appear several ways to extend complex analyticity (natural in two dimensions) to quaternionic analyticity (natural in four dimensions). To be analytic, conformal transformations should be realized on $CP^3$, which appears as the coset of the complexified conformal group modulo its maximal parabolic subgroup. In this language one visualizes the twistor correspondence of Penrose and Ward and consistently formulates the analyticity of Fueter.Comment: 24 pages, LaTe

Psychosemantic analyticity

It is widely agreed that the content of a logical concept such as and is constituted by the inferences it enters into. I argue that it is impossible to draw a principled distinction between logical and non-logical concepts, and hence that the content of non-logical concepts can also be constituted by certain of their inferential relations. The traditional problem with such a view has been that, given Quine’s arguments against the analytic-synthetic distinction, there does not seem to be any way to distinguish between those inferences that are content constitutive and those that are not. I propose that such a distinction can be drawn by appealing to a notion of ‘psychosemantic analyticity’. This approach is immune to Quine’s arguments, since ‘psychosemantic analyticity’ is a psychological property, and it is thus an empirical question which inferences have this property

Analycity and smoothing effect for the coupled system of equations of Korteweg - de Vries type with a single point singularity

We study that a solution of the initial value problem associated for the coupled system of equations of Korteweg - de Vries type which appears as a model to describe the strong interaction of weakly nonlinear long waves, has analyticity in time and smoothing effect up to real analyticity if the initial data only has a single point singularity at $x=0.