Calogero-Vasiliev Oscillator in Dynamically Evolving Curved Spacetime

TL;DR

This paper explores the quantization of a scalar field using Calogero-Vasiliev oscillator algebra in a curved spacetime that evolves over time, revealing new possibilities for statistical conservation and specific mathematical constraints.

Contribution

It introduces the use of Calogero-Vasiliev oscillator algebra for field quantization in dynamic curved spacetime, highlighting novel statistical behaviors and consistency conditions.

Findings

Conservation and anticonservation of statistics are both possible.

The Bogoliubov coefficients satisfy a specific mathematical relation.

The parameter |β_i|^2 must be an integer for consistency.

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 ( $\nu \rightarrow \nu$ ) 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.