J F Corney and P D Drummond 2006 J. Phys. A: Math. Gen. 39 269 doi:10.1088/0305-4470/39/2/001
J F Corney and P D Drummond
Show affiliationsWe 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.
81Qxx General mathematical topics and methods in quantum theory
81V70 Many-body theory; quantum Hall effect
47F05 Partial differential operators (See also 35Pxx, 58Jxx)
Quantum gases, liquids and solids
Issue 2 (13 January 2006)
Received 3 August 2005
Published 14 December 2005
J F Corney and P D Drummond 2006 J. Phys. A: Math. Gen. 39 269
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