Functional Integration Stiff Polymer Chains

INTRODUCTION TO FUNCTIONAL INTEGRATION STIFF POLYMER CHAINS 

Thus far we have the functional integral representation for the distribution functions involved in the configurational statistics of flexible polymers. By considering the polymer in the presence of an external field, we are able to relate the configurations of a polymer to the paths of a particle when this particle is undergoing Brownian or diffusive motion, or when it is evolving according to the laws of quantum mechanics. This establishes connections with other familiar concepts. 

In this section we consider functional Integral representations for the distribution functions for stiff polymer chains. Aside from providing a class of useful models of stiff polymer chains, these results illustrate the following  

They provide functional integrals which can be evaluated directly. 

They give some examples in which the derivation of the equation of motion analogous to (3.21) becomes interesting. 

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V. INTRODUCTION TO FUNCTIONAL INTEGRATION STIFF POLYMER CHAINS... 

Therefore, in an attempt to obtain simple analytic expressions for the distribution functions of stiff polymer chains, condition (5.2a) is relaxed. The relaxation of this condition is in the original spirit of the use of Wiener integrals. If this condition were imposed for flexible polymer chains, the Wiener measure would be 2[t s)] exp (—3L/2/) and would give equal weight (measure) to all continuous configurations of the polymer. Thus the use of (5.2a) would not yield the correct gaussian distribution for flexible chains. 

The techniques of functional integration are naturally introduced into the study of the statistical mechanics of polymer systems because they are ideally suited to the description of simple generic models of flexible and stiff ideal polymer chains. Thus we discuss ideal polymer chains to introduce the simple generic models which then naturally lead to the use of functional integrals. 

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