Reduction formula for Fermion loops and density correlations of the \(1\)D Fermi gas

DOI10.1023/A:1004546206544zbMATH Open0988.82009arXivcond-mat/9904113OpenAlexW3100234600MaRDI QIDQ1964525

Arne Neumayr, Walter Metzner

Publication date: 20 February 2000

Published in: Journal of Statistical Physics (Search for Journal in Brave)

Abstract: Fermion N-loops with an arbitrary number of density vertices N > d+1 in d spatial dimensions can be expressed as a linear combination of (d+1)-loops with coefficients that are rational functions of external momentum and energy variables. A theorem on symmetrized products then implies that divergencies of single loops for low energy and small momenta cancel each other when loops with permuted external variables are summed. We apply these results to the one-dimensional Fermi gas, where an explicit formula for arbitrary N-loops can be derived. The symmetrized N-loop, which describes the dynamical N-point density correlations of the 1D Fermi gas, does not diverge for low energies and small momenta. We derive the precise scaling behavior of the symmetrized N-loop in various important infrared limits.

Full work available at URL: https://arxiv.org/abs/cond-mat/9904113

zbMATH Keywords

surface fluctuationsFeynman amplitudesFermi systemsdensity correlations

Mathematics Subject Classification ID

Phase transitions (general) in equilibrium statistical mechanics (82B26) Quantum equilibrium statistical mechanics (general) (82B10)

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