Discrete symmetries and the reduction of the two-body Dirac equations with interactions

We consider two-particle relativistic equations with scalar, pseudoscalar, vector and oscillator-like interactions. These basic equations describing the steady states of the system are [1], [2] (1)Liψ=[α1p1+α2p2+(β1+β2)m+Ui]ψ=Eiψ,       i=1,2,3,4,https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780367812027/499b2676-17a6-4805-9fd8-78c8baf0b813/content/eq1120.tif"/>