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Considering the propagation of fields in the spacetime continuum and thewell-defined features of fields with finite degrees of freedom, the wavefunction is expanded in terms of a finite set of basis functions localized inspacetime. This paper presents the analytic eigenenergies derived for aconfined fundamental fermion-antifermion pair under a linear potential obtainedfrom the Wilson loop for the non-Abelian Yang-Mills field. The Hamiltonianmatrix of the Dirac equation is analytically diagonalized using basis functionslocalized in spacetime. The squared lowest eigenenergy (as a function of therelativistic quantum number when the rotational energy is large compared to thecomposite particle masses) is proportional to the string tension and theabsolute value of the Dirac's relativistic quantum number related to the totalangular momentum, consistent with the expectation.

Analytic eigenenergies of the Dirac equation with finite degrees of  freedom under a confining linear potential using basis functions localized in  spacetime