Аңдатпа
Klein–Gordon and Dirac oscillators are formulated on the constant-curvature spacetime g μ ν = s − 2 ( t ) η μ ν generated by the Fock–Lorentz conformal factor s ( t ) = 1 + c t / R , a conformal Poincaré patch of de Sitter spacetime. This metric is a geometric postulate rather than a consequence of the Fock–Lorentz transformations, whose projective map pulls Minkowski space back to a flat metric. In the ordinary cotangent-bundle phase space, ( E 2 − p 2 c 2 ) s 2 = m 0 2 c 4 is the conformal-coordinate representation of the covariant mass shell, not a deformed dispersion relation. Covariant actions yield the canonically rescaled scalar equation, including its order- R − 2 term, and the Dirac equation with m app ( t ) = m 0 / s ( t ) . The oscillator couplings are coordinate-defined simplified models. Two Klein–Gordon factor orderings give alternative oscillator models, not independent physical sectors of one scalar field; their conditional fixed-time spectra and the Dirac-oscillator spectrum are obtained analytically. In the stable domain κ ξ 2 > 0 with positive squared instantaneous eigenvalues, the Klein–Gordon modes are treated as a second-order adiabatic system with both level and particle–antiparticle gaps. Changing the trap-frequency prescription removes the leading coordinate spectral drift after eigenvalue rescaling, but the rescaled eigenvalue is not a locally measured energy.