Calculation of Connected Green Function

going to the evaluation of the expression (3.91) we se that beyond of terms of the single eorrelation nature given by Eq. (3.96) we need the Green funetion of the harmonic oscillator, whose equation is of (3.78) t5rpe written in real time picture (Putz, 2009b)  

the left side of Eq. (3.106) is formed from the difference of the first derivatives of the solutions (3.101) and (3.104) approaching each other the event times (Putz, 2009b)  

as previously done with the fluctuation paths, the change to the imaginary time picture is done automatically through trigonometric-to-h5 erbolic recipe Table 2.1/Section 2.3 to give 

Expression (3.111) in then employed to the free harmonic limit (3.94) providing the result  

Quantum Nanochemistry—Volume II Quantum Atoms and Periodicity 

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