Calogero-Vasiliev Oscillator in Dynamically Evolving Curved Spacetime

In a recent work, the consequences of quantizing a real scalar field $\Phi$ according to generalized ``quon'' statistics in a dynamically evolving curved spacetime (~which, prior to some initial time and subsequent to some later time, is flat~) were considered. Here a similar calculation is performed; this time we quantize $\Phi$ via the Calogero-Vasiliev oscillator algebra, described by a real parameter $\nu > -1/2$. It is found that both conservation ( $\nu \rightarrow \nu$ ) and anticonservation ( $\nu \rightarrow - \nu$ ) of statistics is allowed. We find that for mathematical consistency the Bogoliubov coefficients associated with the $i$'th field mode must satisfy $|\alpha_i |^2 - | \beta_i |^2 = 1$ with $| \beta_i |^2$ taking an integer value.Comment: 11 pages ( no figures ), RevTex - To appear in Physics Letters

The Canonical Partition Function for Quons

We calculate the canonical partition function $Z_N$ for a system of $N$ free particles obeying so-called `quon' statistics where $q$ is real and satisfies $|q|<1$ by using simple counting arguments. We observe that this system is afflicted by the Gibbs paradox and that $Z_N$ is independent of $q$. We demonstrate that such a system of particles obeys the ideal gas law and that the internal energy $U$ ( and hence the specific heat capacity $C_V$ ) is identical to that of a system of $N$ free particles obeying Maxwell-Boltzmann statistics.Comment: 12 pages RevTex, NCL94-TP5 ( To be published in Physics Letters A