Generalized Nonlinear Proca Equation and its Free-Particle Solutions

摘要: We introduce a non-linear extension of Proca's field theory for massive vector (spin $1$) bosons. The associated relativistic nonlinear wave equation is related to recently advanced extensions the Schroedinger, Dirac, and Klein-Gordon equations inspired on non-extensive generalized thermostatistics. This theoretical framework that has been applied in recent years several problems nuclear particle physics, gravitational quantum theory. Proca investigated here power-law nonlinearity characterized by real parameter $q$ (formally corresponding Tsallis entropic parameter) such way standard linear recovered limit $q \rightarrow 1$. derive from Lagrangian that, besides usual vectorial $\Psi^{\mu}(\vec{x},t)$, involves an additional $\Phi^{\mu}(\vec{x},t)$. obtain exact time dependent soliton-like solutions these fields having form $q$-plane wave, show both lead energy-momentum relation $E^{2} = p^{2}c^{2} + m^{2}c^{4}$ all values $q$. suggests present constitutes new representation dynamics. In massless particles $q$-generalized reduces Maxwell electromagnetism, waves yield localized, transverse equations. Physical consequences possible applications are discussed.