438 research outputs found
Generalized Nonlinear Proca Equation and its Free-Particle Solutions
We introduce a non-linear extension of Proca's field theory for massive
vector (spin ) bosons. The associated relativistic nonlinear wave equation
is related to recently advanced nonlinear extensions of the Schroedinger,
Dirac, and Klein-Gordon equations inspired on the non-extensive generalized
thermostatistics. This is a theoretical framework that has been applied in
recent years to several problems in nuclear and particle physics, gravitational
physics, and quantum field theory. The nonlinear Proca equation investigated
here has a power-law nonlinearity characterized by a real parameter
(formally corresponding to the Tsallis entropic parameter) in such a way that
the standard linear Proca wave equation is recovered in the limit . We derive the nonlinear Proca equation from a Lagrangian that,
besides the usual vectorial field , involves an
additional field . We obtain exact time dependent
soliton-like solutions for these fields having the form of a -plane wave,
and show that both field equations lead to the relativistic energy-momentum
relation for all values of . This suggests
that the present nonlinear theory constitutes a new field theoretical
representation of particle dynamics. In the limit of massless particles the
present -generalized Proca theory reduces to Maxwell electromagnetism, and
the -plane waves yield localized, transverse solutions of Maxwell equations.
Physical consequences and possible applications are discussed
Nonlinear Relativistic and Quantum Equations with a Common Type of Solution
Generalizations of the three main equations of quantum physics, namely, the
Schr\"odinger, Klein-Gordon, and Dirac equations, are proposed. Nonlinear
terms, characterized by exponents depending on an index , are considered in
such a way that the standard linear equations are recovered in the limit . Interestingly, these equations present a common, soliton-like,
travelling solution, which is written in terms of the -exponential function
that naturally emerges within nonextensive statistical mechanics. In all cases,
the well-known Einstein energy-momentum relation is preserved for arbitrary
values of
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