Vector fields Yang-Mills equations

In this chapter we discuss the close relationship between the Born-Oppenheimer treatment of molecular systems and field theory as applied to elementary particles. The theory is based on the Born-Oppenheimer non-adiabatic coupling terms which are known to behave as vector potentials in electromagnetic dynamics. Treating the time-dependent Schrodinger equation for the electrons and the nuclei we show that enforcing diabatization produces for non-Abelian time-dependent systems the four-component Curl equation as obtained by Yang and Mills (Phys. Rev. 95, 631 (1954)). 

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