Matsubara Harmonic Partition Function

With the quantum path decomposition (2.19) the Feynman path integral measure in Eq. (2.21) factorizes accordingly (Putz, 2009) 

Firstly, let s separately compute the kinetic and harmonic quantum path terms appearing under the integral (2.23). For kinetic term we successively get  

Quantum Nanochemistry—Volume II Quantum Atoms and Periodicity 

Once calculated, the Riemann series (2.33) is replaced in Eq. (2.32) which, at its turn, is employed in the integral manner 

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We have now all prerequisites to compute the Matsubara harmonic partition function (2.28) aiming to find out the Matsubara normalization of periodic path integrals. This will be addressed in the sequel. 

Turning to the Matsubara harmonic partition function algorithm (2.28)-(2.34) one successively has (Putz, 2009) ... 

Releasing the Matsubara partition function for the harmonic motion by replacing function (2.50) into expression (2.28) ... 

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