Calogero-Vasiliev Oscillator in Dynamically Evolving Curved Spacetime

Abstract

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 ( $\nu \to \nu$ ) and anticonservation ( $\nu \to -\nu$ ) 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.

11 pages ( no figures ), RevTex - To appear in Physics Letters B

References in corpus (4)

• Exchange Operator Formalism for Integrable Systems of Particles
• Explicit Solution to the N-Body Calogero Problem
• Hidden algebra of the $N$-body Calogero problem
• No generalized statistics from dynamics in curved spacetime

Cited by in corpus (2)

• Recursively minimally-deformed oscillators
• On Spin-Statistics and Bogoliubov Transformations in Flat Spacetime With Acceleration Conditions