When q=0, The Forced Harmonic Oscillator Isn't

TL;DR

This paper demonstrates that a forced harmonic oscillator quantized with infinite statistics can only be consistent if the forcing term is zero, implying only the free oscillator can be quantized this way.

Contribution

It introduces the restriction that infinite statistics quantization of the harmonic oscillator requires no external forcing, a novel insight into the limitations of this quantization method.

Findings

Forced harmonic oscillator with infinite statistics must have zero forcing term

Only free harmonic oscillators can be consistently quantized with infinite statistics

External forcing invalidates the infinite statistics quantization

Abstract

We consider the forced harmonic oscillator quantized according to infinite statistics ( a special case of the `quon' algebra proposed by Greenberg ). We show that in order for the statistics to be consistently evolved the forcing term must be identically zero for all time. Hence only the free harmonic oscillator may be quantized according to infinite statistics.