Abstract
We discuss upper bounds for density matrices for a particle, that occur in potential theory, and as a result of averaging over other degrees of freedom. The Weiner path integral representation is used. A basic technique of Symanzik is generalized in a variety of ways to a series of sharper upper bounds. There are distinct ways of applying the technique to the two-parameter integrals that describe averaged density matrices. A single-parameter application of the Symanzik technique leads to a temperature-dependent potential problem. The nature of the bounds is illustrated for two-parameter integrals by studying a soluble quadratic action, a one-dimensional delta correlation function action and shell correlation functions. The dependence on dimension is studied in the latter case.
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Gross, E.P. Upper bounds for density matrices using path integrals. J Stat Phys 30, 45–66 (1983). https://doi.org/10.1007/BF01010868
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DOI: https://doi.org/10.1007/BF01010868