Glauber P-representations for fermions

Barnett, S. M. and Dalton, B. J. (2023) Glauber P-representations for fermions. Physica Scripta, 98(4), 044006. (doi: 10.1088/1402-4896/acc432)

Abstract

The Glauber-Sudarshan P-representation for bosons is well-known within quantum optics, and is widely applied to problems involving photon statistics. Less familiar, perhaps, is its fermionic counterpart, introduced by Cahill and Glauber. We present a derivation of both the bosonic and fermionic distributions and, in doing so, demonstrate the reason for the existence of two distinct fermionic forms and the relationship between these. We consider both single mode systems and also multiparticle systems with many modes. Expressions for the moments involving products of mode annihilation and creation operators are obtained. For simplicity only one type of boson or fermion will be considered, but generalising to more types is straightforward.

• Item Type: Articles
• Keywords: Paper, Glauber-Sudarshan, P-representations, fermions, Grassmann calculus, quantum statistics.
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Barnett, Professor Stephen and Dalton, Professor Bryan
• Authors: Barnett, S. M., and Dalton, B. J.
• College/School: College of Science and Engineering > School of Physics and Astronomy
• Journal Name: Physica Scripta
• Publisher: IOP Publishing
• ISSN: 0031-8949
• ISSN (Online): 1402-4896
• Published Online: 23 March 2023
• Copyright Holders: Copyright © 2023 The Authors
• First Published: First published in Physica Scripta 98(4): 044006
• Publisher Policy: Reproduced under a Creative Commons License

Project Code	Award No	Project Name	Principal Investigator	Funder's Name	Funder Ref	Lead Dept
173378		Astronomy and physics, theoretical physics and application physics / Quantum Theory. Royal Society Research Professorship.	Stephen Barnett	The Royal Society (ROYSOC)	RP150122	P&S - Physics & Astronomy