On the Use of Lie Group Homomorphisms for Treating Similarity Transformations in Nonadiabatic Photochemistry

Table 8

Similarity transforms of Gell-Mann matrices through elementary rotations.

𝐇	𝑒^𝑖𝜑𝝀2𝐇𝑒^−𝑖𝜑𝝀2	𝑒^𝑖𝜒𝝀7𝐇𝑒^−𝑖𝜒𝝀7	𝑒^−𝑖𝜓𝝀5𝐇𝑒^𝑖𝜓𝝀5
𝝀1	cos2𝜑𝝀1+sin2𝜑𝝀3	cos𝜒𝝀1−sin𝜒𝝀4	sin𝜓𝝀6+cos𝜓𝝀1
𝝀2	𝝀2	cos𝜒𝝀2−sin𝜒𝝀5	−sin𝜓𝝀7+cos𝜓𝝀2
𝝀4	cos𝜑𝝀4−sin𝜑𝝀6	sin𝜒𝝀1+cos𝜒𝝀4	cos2𝜓𝝀4+sin2𝜓𝝀^−3
𝝀5	cos𝜑𝝀5−sin𝜑𝝀7	sin𝜒𝝀2+cos𝜒𝝀5	𝝀5
𝝀6	sin𝜑𝝀4+cos𝜑𝝀6	cos2𝜒𝝀6+sin2𝜒𝝀^+3	cos𝜓𝝀6−sin𝜓𝝀1
𝝀7	sin𝜑𝝀5+cos𝜑𝝀7	𝝀7	cos𝜓𝝀7+sin𝜓𝝀2
𝝀3	−sin2𝜑𝝀1+cos2𝜑𝝀3
𝝀8	𝝀8
𝝀^−3			−sin2𝜓𝝀4+cos2𝜓𝝀^−3
𝝀^−8			𝝀^−8
𝝀^+3		−sin2𝜒𝝀6+cos2𝜒𝝀^+3
𝝀^+8		𝝀^+8