## SciPost Submission Page

# Newton series expansion of bosonic operator functions

### by Jürgen König, Alfred Hucht

### Submission summary

As Contributors: | Fred Hucht |

Arxiv Link: | https://arxiv.org/abs/2008.11139v1 (pdf) |

Date submitted: | 2020-08-26 11:56 |

Submitted by: | Hucht, Fred |

Submitted to: | SciPost Physics |

Discipline: | Physics |

Subject area: | Quantum Physics |

Approach: | Theoretical |

### Abstract

We show how series expansions of functions of bosonic number operators are naturally derived from finite-difference calculus. The scheme employs Newton series rather than Taylor series known from differential calculus, and also works in cases where the Taylor expansion fails. For a function of number operators, such an expansion is automatically normal ordered. Applied to the Holstein-Primakoff representation of spins, the scheme yields an exact series expansion with a finite number of terms. As a second example, we show that factorial moments and factorial cumulants arising in the context of photon or electron counting are a natural consequence of Newton series expansions.

###### Current status:

Editor-in-charge assigned