English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

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

Generalized Nonlinear Proca Equation and its Free-Particle Solutions