Pseudoscalar interaction of coupled quantum‐mechanical oscillators with independent Fermi systems
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Using the techniques of constructive quantum field theory we analyze the dynamics of a cubic lattice of quantum mechanical oscillators with nearest-neighbor coupling that interact with a corresponding lattice of finite-volume truncations of independent relativistic Fermi fields. Since the model is nonrelativistic, we rely on a nonrelativistic version of the Osterwalder-Schrader (OS) reconstruction theorem. Also, the absence of Nelson's symmetry in the (un)Euclidean picture is not serious because the transfer matrix in a given space direction is simple enough to make the verification of spatial OS positivity easy. After establishing for our model many of the basic results that hold for the more standard models, we give a proof of the Fortuin-Kasteleyn-Ginibre (FKG) inequality that is essentially independent of the dimension of the Fermi systems. © 1982 American Institute of Physics.
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