Análise das singularidades da função de dois pontos do campo quântico escalar localizado tipo-string

Abstract

As is well-known, the quantum fields studied in QFT satisfy the principle of locality according to points in space-time. However, the principles of physics also admit quantum fields that satisfy a condition of locality determined by strings2, which are rays (semi axes) in space-time starting from some point (event) and extending in some space-like direction. Due to this notion of locality via string, we say that such fields are string-localized. On the other hand, we refer to fields whose locality is characterized by points in space-time, saying that they are localized on points. The interest in string localization is the possibility that fields with such kind of localization present a less singular UV behaviour, that is, at high energy, than that of fields localized on points, and then permitting the construction of more interacting models. String-localized free quantum fields have been constructed for many particles types [1, 2], from which one can construct interacting models. However, in order to do this, that is, to construct interacting models from the free fields, it is necessary to analyse the two point function of the corresponding free fields. At this point we have to use some concepts and tools - for example: singular support, wave front set and scaling degree - to analyse the two point function. In this text we introduce these concepts and tools. Moreover, we consider a string-localized free scalar quantum field model for a massive spin zero particle, for which we present and analyse the singularity structure of the corresponding two point function, giving a interpretation in terms of strings.