Eur. Phys. J. B 9, 679-683 (1999)
https://doi.org/10.1007/s100510050812

The thermal Green functions in nonextensive quantum statistical mechanics

College of Science and Technology, Nihon University, Funabashi, Chiba 274-8501, Japan

Corresponding author: ^a sabe@penta.ge.cst.nihon-u.ac.jp

Received: 30 September 1998
Published online: 15 June 1999

Abstract

The thermal Green functions of the quantum-mechanical harmonic oscillator are constructed within the framework of nonextensive statistical mechanics with normalized q-expectation values. For the Tsallis index q greater than unity, these functions are found to be expressed analytically in terms of the Hurwitz zeta function. It is found that influence of the nonextensivity on the time-ordered thermal propagator is relevant only at the "on-shell" states. In particular, the finite-temperature contribution to the thermal propagator becomes enhanced for the strong nonextensivity.