The infinite-spin representations of the Poincaré group

All particles inside the Standard Model fall inside some of these representations, which are labelled by the value of a continuous parameter called mass m and by the value of the spin s in the massive case or by the value of the helicity h in the massless case. But the most general type of massless particles allowed included the so-called infinite-spin representations which are characterized by a dimensionful scale K and reduce to familiar helicity particles only in the limit K -> 0. These particles are also called continuous spin particles (CSP). The scope of the thesis is to study the general form of quantum (free) fields for CSP, particularly focusing on the structure of the intertwiners (the coefficients of the annihilation and creation operators in the mode expansion of the fields). I will first establish, parametrizing directly the orbits of the little group for massless particles E(2), a new way to find the "smooth" and "singular" solutions of Schuster and Toro papers. Then I will make a deep connection between the general structure of Mund-Schroer-Yngvason intertwiners with Schuster-Toro smooth wavefunctions via Gaussian integration. Moreover I will emphasize the role of localization for infinite-spin intertwiners, considering both Mund-Schroer-Yngvas on and Schuster and Toro's works from different perspectives. The Mund-Schroer-Yngvason bound regards the admissible class of infinite-spin intertwiners. We will give an estimate about a special type of intertwiner, showing that it will fulfill the Mund-Schroer-Yngvason bound if it is multiplied by a suitable factor. Finally I will discuss the properties of the 2-point function using the general structure of infinite-spin intertwiners.