Useful Bounds on Interesting Quantities by Path Integrals
In these lectures I shall discuss some interesting consequences of the representation of Green’s functions by means of path integrals. First we shall discuss a lower bound for the partition function of a system that follows from this representation, and show how it may be used to discuss the density of energy levels of a model disordered system. Second a very natural upper bound will be discussed, and it will be shown that special cases of this comprise all the well-known “isoperimetric inequalities” of physics and geometry.
KeywordsPartition Function Thermodynamic Limit Path Integral Isoperimetric Inequality Skin Depth
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