Campo eletromagnético acoplado a um campo de Rarita-Schwinger de spin 3/2

Abstract

The field of Rarita-Schwinger (RS) is widely used in the context of supergravity and particle physics. Its Lagrangian, which results in Dirac’s equation for spin 3/2, has a generic expression that depends on a parameter A, except for the value A = −1/2. Supergravity is described by A = −1, in which the Lagrangian appropriately maintains gauge and Lorentz symmetry. However, for other values of A, e.g., A = −1/3 (Lagrangian proposed by Rarita-Schwinger) and A = 0 (simpler Lagrangian), these symmetries are violated in certain ways. In this monograph, we will study the quantum corrections of the RS Lagrangian coupled to the gauge field Aµ, up to the four-point function. We note that, for A = −1, the gauge symmetry is respected; however, for A = −1/3 and A = 0, there are terms present that can induce the violation of this symmetry, and thus, the violation of Lorentz symmetry.