ISSN:
1089-7658
Source:
AIP Digital Archive
Topics:
Mathematics
,
Physics
Notes:
This is the continuation of notes written for the NATO-ASI conference in Il Ciocco (September 96) consisting of the analysis of the links between estimating the splitting between the two first eigenvalues for the Schrödinger operator H and the proof of infrared estimates for quantities attached to Gaussian-type measures. These notes were mainly reporting on the "old" contributions of Dyson, Fröhlich, Glimm, Jaffe, Lieb, Simon, and Spencer (in the 1970s) in connection with more recent contributions of Pastur, Khoruzhenko, Barbulyak, and Kondrat'ev which treat in general more sophisticated models. Here we concentrate on the simplest model related to field theory and extend the results of Barbulyak and Kondrat'ev by mixing ideas coming from Pastur and Khozurenko related to the use of Bogolyubov's inequality with classical inequalities due to Ginibre, Lebowitz, Sokal, and others, or, in the case when the temperature T is zero, by applying rather elementary estimates on Schrödinger operators, in order to find lower bounds for second-order moments attached to the measure φ(functional relationship right)Trφ exp−βH/Tr exp−βH with β=1/T. This question was "left to the reader" in lectures given by J. Fröhlich in 1976 [Acta Phys. Austriaca, Suppl. XV, 133–269 (1976)], but we think that it is worthwhile to do this "homework" carefully. © 1998 American Institute of Physics.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.532351
Permalink
