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R. SCHRADER and R. SEILER, A Uniform Lower Bound on the Renormalized Euclidean Functional Determinant, to appear in Commun.math.Phys.
H. HESS, R. SCHRADER, D.A. UHLENBROCK, Kato's Inequality and Spectral Distribution of Laplace Operators on Compact Riemannian Manifolds, to appear in Journ.Diff.Geom.
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Using Fermion functional integration and a lattice cutoff, a proof of the paramagnetic inequality (4) was given by D. Bridges, J. Fröhlich and E. Seiler; On the Construction of Quantized Gauge Fields. I. General Results; IHES Preprint June 1978. The proof works as yet up to dimension three. A particular case of our conjecture has been demonstrated by E. Lieb, private communication. He has shown for the case of a constant magnetic field and an arbitrary potential V in three dimensions that the groundstate is lowered by the magnetic field. In fact, this particular case was the subject of an independent conjecture by I. Herbst, J. Avron and B. Simon in their article “Schrödinger Operators with Magnetic Fields. I, General Interactions; to appear in Duke Math. Journ. 1978, Princeton University Preprint, where also the argument by Lieb can be found. Lieb's argument can be extended to the case of nonconstant magnetic fields, see J. Avron and R. Seiler, Paramagnetism for Nonrelativistic Electrons and Euclidean Massless Dirac Particles, Preprint 7B/P.1038, CNRS Marseille.
H. HOGREVE, R. SCHRADER and R. SEILER; A Conjecture on the Spinor Functional Determinant, to appear in Nucl. Phys. B, FUB-HEP Preprint, April 1978.
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See e.g. H. ARAKI and E. LIEB, Entropy Inequalities, Commun.math.Phys. 18, 160–170 (1970).
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Hogreve, H., Schrader, R., Seiler, R. (1979). Bounds on the Euclidean functional determinant. In: Albeverio, S., et al. Feynman Path Integrals. Lecture Notes in Physics, vol 106. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-09532-2_82
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DOI: https://doi.org/10.1007/3-540-09532-2_82
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