Classical and Quantum Field-Theoretical approach to the non-linear q-Klein-Gordon Equation

Abstract

In the wake of efforts made Nobre and Rego-Monteiro in EPL, 97 (2012) 41001 and J. Math. Phys., 54 (2913) 103302, we extend them here by developing the conventional Lagrangian treatment of a classical field theory (FT) to the q-Klein-Gordon equation advanced in Phys. Rev. Lett., 106 (2011) 140601 and J. Math. Phys., 54 (2913) 103302 by the same authors, and the quantum theory corresponding to q = 3 2 . This makes it possible to generate a putative conjecture regarding black matter. Our theory reduces to the usual FT for q → 1.