2005/11/02 by J. F. Corney, J F Corney, P. D. Drummond +1
Physics and Astronomy · #Basis (linear algebra) #Cold Atom Physics and Bose-Einstein Condensates #Completeness (order theory) #Fermi Gamma-ray Space Telescope #Fermion #Gaussian #Operator (biology) #Phase space #Physics of Superconductivity and Magnetism #Quantum many-body systems #Representation (politics) #Superselection #quant-ph
paper · pdf · doi:10.1088/0305-4470/39/2/001
published as J. Phys. A: Math. Gen. 39, 269 (2006).
arxiv created 2005/11/02 · openalex publication_date 2005/12/14 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We formulate a general multi-mode Gaussian operator basis for fermions, to enable a positive phase-space representation of correlated Fermi states. The Gaussian basis extends existing bosonic phase-space methods to Fermi systems and thus allows first-principles dynamical or equilibrium calculations in quantum many-body Fermi systems. We prove the completeness of the basis and derive differential forms for products with one- and two-body operators. Because the basis satisfies fermionic superselection rules, the resulting phase space involves only c -numbers, without requiring anticommuting Grassmann variables. Furthermore, because of the overcompleteness of the basis, the phase-space distribution can always be chosen positive. This has important consequences for the sign problem in fermion physics.