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Functional Integrals and their Applications
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Introduction These lectures are concerned with the analysis and applications of functional integrals de ned by small perturbations of Gaussian measures The central topic is the renormalization group Following Wilson and Polchinski an e ective po tential is studied as a function of an ultra violet cuto By changing the cuto in a continuous manner one obtains a di erential equation for the e ective potential It is shown that by converting this equation to an integral equation and generat ing an iterative solution one obtains the Mayer expansion of classical statistical mechanics Some results on the convergence of such an expansion are deduced with applications to Coulomb and Yukawa gases However this method of solv ing for the e ective potential turns out to be of limited value due to large eld problems which we explain To achieve better results we abandon the e ective action and represent the partition function as a polymer gas The polymer gas representation has enough in common with the e ective action that we are able to exactly repeat the previous method of iterating an integral equation concluding with the ow of the activities of the polymers given by cluster expansions This is expounded in considerable detail using as illustration the example of dipole gases In addition there are two introductory sections independent of the other lectures in which as a motivation problems in the theory of Coulomb gases and polymer physics are shown to be related to functional integrals of the type studied here In particular a heuristic discussion is presented on how quantum e ects can destroy Debye screening 下载地址：http://www.isload.com.cn/store/sbb5esqjip2bf [ Last edited by zhq025 on 2008-1-16 at 10:38 ] |
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