Campos quânticos livres massivos localizados tipo-string para spin arbitrário

Abstract

It is well known that quantum fields studied in the quantum theory of fields satisfy the locality principle, this means that if x1 and x2 are space-like separated, then ᵩ (x1) and ᵩ (x2) (anti-) commute. They are referred to as fields that have point-like localization. In this thesis, we will construct free quantum fields with arbitrary spin for the cases of integer (bosons) and semi-integer (fermions) spin, with a "string-like"location 2. In contrast to the usual fields living in space-time points, they live in strings "Formula disponibilizado no texto completo" e, that are rays that begins at a certain point x in Minkowski's space and extends to infinity in a certain space-like direction e. These fields satisfy the string-like locality principle, in the sense that if "Formula disponibilizado no texto completo" are causally separated, then ᵩ x1;e1 and ᵩ x2;e2 (anti-) commute. Such location is allowed by the principles of relativistic quantum physics, since the fields admit the construction of local observables. A (point-localized) free quantum field for massive particles with spin s acting in a Hilbert space has, at best, scaling dimension (Ds) = s + 1, which excludes its use in the perturbative construction of renormalizable interacting models for higher spin (s ≥ 1). Up to date, such models have been constructed only in the context of gauge theory, at the cost of introducing additional unphysical (ghost) fields and an unphysical (indefinite metric) state space. The unphysical degrees of freedom are divided out by requiring gauge (or BRST) invariance. We then construct free quantum fields for higher spin particles, where, for any integer spin, we have the same good UV behavior as the scalar field (s = 0), namely, have scaling dimension 1. For fields with arbitrary semi-integer spin, we have the same UV behavior of the Dirac field " Formula disponibilizado no texto completo " , namely, a scaling dimension " Formula disponibilizado no texto completo " , and at the same time, they act on a Hilbert space without ghosts. They are localized on semi-infinite strings extending to space-like infinity, but are linearly related to their point-local counterparts. We argue that this is suficient locality for a perturbative construction of interacting models of gauge theory type, with a string-independent S-matrix and point-localized interacting observable fields. The usual principle of gauge invariance is here replaced by the (deeper) principle of locality.