DUFFIN-KEMMER-PETIAU EQUATION: REPRESENTATIONS AND APPLICATIONS TO THE HARMONIC OSCILLATOR BIDIMENSIONAL NUMBER TRANSVERSE MAGNETIC FIELD AND THE POTENTIAL OF MORSE
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This work uses the Duffin-Kemmer-Petiau theory to study the deformations on scalar DKP and Dirac
oscillators, and two-dimensional oscillators immersed in a magnetic field. Inspired in the Tsallis statistics, we
use the non-minimal coupling with a deformed linear momentum operator and investigate the thermodynamics
of relativistic deformed oscillators, mapping them in a relativistic Morse-like potential, recovering S-wave
states in 1D and 3D systems. We revisit the Kemmer 2D oscillator in an external magnetic field and
investigate the result in the scalar and vector sectors, which in the last one we identified a splitting in
the frequencies. We study the thermodynamics for both systems, as well the ocurrence of phase transition
in coupled-free particle systems. We implement in this system the Moyal product, and corroborated the
non-relativistic regime with Galilean covariance. Finally, we approach the Umezawa formalism in Galilean
covariance, finding non-relativistic linear equations, and discussing the Pauli-Lubanski vector with the
projective operators of the Galilean DKP field.