THERMAL COHERENT STATES,A BROADER CLASS OF MIXED COHERENT STATES, ANDGENERALIZED THERMO-FIELD DYNAMICS

摘要

We introduce coherent mixed states (or thermal coherent states) associated with thedisplaced harmonic oscillator at nonzero temperature (T≠ 0), as a "random" (or "ther-mal" or "noisy") basis in Hilbert space. A resolution of the identity for these states isproven and is used to generalize the usual pure (T=0) coherent state formalism tothe mixed (T≠0) case. This new formalism for thermal coherent states is then furthergeneralized to a broader class of so-called negative-binomial mixed states. It is knownthat the negative-binomial distribution is itself intimately related to the discrete series ofSU(1,1) representations. We consider the pure SU(1,1) coherent states in the two-modeharmonic oscillator space, and show how our negative-binomial mixed states arise fromtaking the partial trace with respect to one of these two modes. This observation is thenused to show how the formalism of thermo-field dynamics may be generalized to a cor-respondingly much broader negative-binomial-field dynamics, which we expect to havemany uses.