The Canonical Structure of a Classical Theory, Quantization Procedures and Non-Equilibrium Quantum Statistical Mechanics

  • K. Jezuita
Conference paper
Part of the Few-Body Systems book series (FEWBODY, volume 15/1976)


The aim of this lecture is to show that the harmonic oscillator model of the non-equilibrium quantum statistical mechanics which was presented by Emch [1] we can obtain by the natural quantization of the two interesting transformations in the phase-space of the one-dimensional classical harmonic oscillator:
$$ \Pi _{\beta /2} :\left[ {\begin{array}{*{20}c} z \hfill \\ {z^* } \hfill \\ \end{array} } \right] \to \left[ {\begin{array}{*{20}c} {e^{ - \frac{{\beta \omega }} {2}} \;\;z} \hfill \\ {e^{\frac{{\beta \omega }} {2}} \;\;z*} \hfill \\ \end{array} } \right]$$
$$ \gamma (s):\left[ {\begin{array}{*{20}c} z \hfill \\ {z*} \hfill \\ \end{array} } \right]\,\, \to \,\,\left[ {_{e^{ - \lambda s} \,\,\,z*}^{e^{ - \lambda s} \,\,\,z} } \right]\,\,\,\,,\,s \geqslant 0$$
where z= ω1/2q + iω −1/2p, the physical constants n = 1, k = 1, and β is the inverse temperature.


Harmonic Oscillator Weyl Group Heisenberg Picture Quantum Harmonic Oscillator Cyclic Representation 
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Copyright information

© Springer-Verlag 1976

Authors and Affiliations

  • K. Jezuita
    • 1
  1. 1.Institute of Nuclear ResearchWarsawPoland

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