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A new perturbative expansion for fermionic functional integrals. (English) Zbl 1452.81149

Summary: We construct a power series representation of certain functional integrals involving Grassmann variables that appear in Euclidean fermionic quantum field theory on a finite lattice in dimensions greater than or equal to 2. Our expansion has a local structure, is clean, and provides an easy alternative to the decoupling expansion and Mayer-type cluster expansions in any analysis. As an example, we show the exponential decay of the two-point truncated correlation function (uniform in volume) in a massive Gross-Neveu model on a unit lattice.
©2020 American Institute of Physics

MSC:

81T10 Model quantum field theories
81T25 Quantum field theory on lattices
14M25 Toric varieties, Newton polyhedra, Okounkov bodies
81V74 Fermionic systems in quantum theory
62H10 Multivariate distribution of statistics
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