Renormalization of a model for spin-1 matter fields
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Regular Article - Theoretical Physics
Renormalization of a model for spin-1 matter fields Ailier Rivero-Acosta1,2,a , Carlos A. Vaquera-Araujo1,3,b 1
Departamento de Física, DCI, Campus León, Universidad de Guanajuato, Loma del Bosque 103, Lomas del Campestre, C.P. 37150 León, Guanajuato, Mexico 2 Laboratorio de Ciencia Planetaria, Departamento de Física, Universidad Central de Las Villas, Santa Clara, C.P. 54830 Villa Clara, Cuba 3 Consejo Nacional de Ciencia y Tecnología, Av. Insurgentes Sur 1582, Colonia Crédito Constructor, Del. Benito Juárez, C.P. 03940 Ciudad de Mexico, Mexico
Received: 22 March 2020 / Accepted: 27 June 2020 © The Author(s) 2020
Abstract In this work, the one-loop renormalization of a theory for fields transforming in the (1, 0) ⊕ (0, 1) representation of the Homogeneous Lorentz Group is studied. The model includes an arbitrary gyromagnetic factor and selfinteractions of the spin 1 field, which has mass dimension one. The model is shown to be renormalizable for any value of the gyromagnetic factor.
1 Introduction In the Standard Model of particle physics, only fields transforming in the (0, 0), (1/2, 0), (0, 1/2) and (1/2, 1/2) representations of the Homogeneous Lorentz Group (HLG) are needed. There is however no guiding principle restricting the possible representations, and indeed high spin fields naturally appear in Hadron physics and in Beyond the Standard Model (BSM) scenarios like supergravity and superstrings. In an attempt to better understand the physics of fields transforming in different representations of the HLG, a series of works have been carried [1–8] based on the projection onto subspaces of the Poincaré group. In this formalism, it has been shown that the gyromagnetic factor of spin 3/2 fields is connected with their causal propagation in an electromagnetic background [1], and with the unitarity of the Compton scattering amplitude in the forward direction [2]. The formalism can also be applied to lower spins, for example, in the spin 1 case, a similar connection between the unitarity of Compton scattering in the forward direction and the gyromagnetic factor of the field exists, which is also related to the electric quadrupole moment [3]. When the Poincaré projector method is applied to spin 1/2 fields transforming in the (1/2, 0) ⊕ (0, 1/2) representation a e-mail:
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b e-mail:
[email protected] (corresponding author)
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[6,7], the resulting Lagrangian is a generalized version of the original second order Feynman-Gell-Man formalism [9], enhanced with an arbitrary gyromagnetic factor and fermion self interactions. The second order fermions studied in these works are conceptually different to Dirac ones, as the former propagate 8 dynamical degrees of freedom instead of 4. As shown in [6,7], there is a consistent reduction of dynamical degrees of freedom and a direct connection between the renormalization group equations for the second order fermions and the Dirac formalism if the gyromagnetic (or chromomagnetic) factor is s
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