Tsallis’ quantum q-fields

Abstract

We generalize several well known quantum equations to a Tsallis' qscenario, and provide a quantum version of some classical fields associated to them in recent literature. We refer to the q-Schrödinger, q-Klein-Gordon, q-Dirac, and q-Proca equations advanced in, respectively, [Phys. Rev. Lett. 106, 140601 (2011), EPL 118, 61004 (2017 and references therein]. Also, we introduce here equations corresponding to q-Yang-Mills fields, both in the Abelian and not-Abelian instances. We show how to define the q-Quantum Field Theories corresponding to the above equations, introduce the pertinent actions, and obtain motion equations via the minimum action principle. These q-fields are meaningful at very high energies (TeVs) for q = 1.15, high ones (GeVs) for q = 1.001, and low energies (MeVs)for q = 1.000001 [Nucl. Phys. A 955 (2016) 16 and references therein]. (See the Alice experiment of LHC). Surprisingly enough, these q-fields are simultaneously q-exponential functions of the usual linear fields' logarithms.

Lorentzian solitary wave in a generalised nonlinear Schrödinger equation

“…The density of energy consistent with this generalised NLSE (6) is obtained from classical field theory (16). For specific values of the constants of this solution, the density of energy (18) behaves as a Lorentzian solitary wave (22) of total energy E s = 2 1+q 2 k 2 2m , with q > −1, q = 1, and momentum P s = k. Notice that the total energy of this solution as well as the velocity of the solitary wave depends on the value of q. Moreover, we have also shown the conservation of momentum (29).…”

“…Thus the energy of the solution in eqs. (12) and (13) with constant c in eq. (21) is a Lorentzian solitary wave with total energy…”

“…Finally, it is simple to realise that inserting the solutions eqs. (12) and (13), for the values which give the Lorentzian solitary waves in eqs. (20) and (21), into the density eq.…”

Thermoelectric properties of BiSbTe alloy nanofilms produced by DC sputtering: experiments and modeling

“…In the literature, several generalized statistical models have been intensively investigated [25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41] .…”

Critical exponents and amplitude ratios of scalar nonextensive q -field theories

“…Corresponding quantum q-field theories were designed [4]. This nonextensive generalization of quantum field theory leads to nonlinear equations [5] and then one needs to consider the physics of nonlinear phenomena, for example the physical behavior of solitons and breathers [6][7][8][9][10].…”