A covariant model based on the Bethe-Salpeter formalism is proposed for investigating the solar proton burning process ppDe⁺ν_e and the near-threshold deuteron disintegration via electromagnetic and weak interactions. Results of numerical calculations of the energy dependence of relevant cross sections and the astrophysical low-energy cross section factor S_pp of the proton burning process are presented. Our results confirm previous canonical values, and the energy dependence of the S_pp factor is rather close to phenomenological extrapolations commonly adopted in computations of solar nuclear reaction rates.