Perturbation Theory for Path Integrals of Stiff Polymers

نویسنده

  • H. Kleinert
چکیده

The wormlike chain model of stiff polymers is a nonlinear σ-model in one spacetime dimension in which the ends are fluctuating freely. This causes important differences with respect to the presently available theory which exists only for periodic and Dirichlet boundary conditions. We modify this theory appropriately and show how to perform a systematic large-stiffness expansions for all physically interesting quantities in powers of L/ξ, where L is the length and ξ the persistence length of the polymer. This requires special procedures for regularizing highly divergent Feynman integrals which we have developed in previous work. We show that by adding to the unperturbed action a correction term Acorr, we can calculate all Feynman diagrams with Green functions satisfying Neumann boundary conditions. Our expansions yield, order by order, properly normalized end-to-end distribution function in arbitrary dimensions d, its even and odd moments, and the two-point correlation function.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Non-perturbative double scaling limits

Recently, the author has proposed a generalization of the matrix and vector models approach to the theory of random surfaces and polymers. The idea is to replace the simple matrix or vector (path) integrals by gauge theory or non-linear σ model (path) integrals. We explain how this solves one of the most fundamental limitation of the classic approach: we automatically obtain non-perturbative de...

متن کامل

Path Integrals and Perturbative Expansions for Non-Compact Symmetric Spaces

We show how to construct path integrals for quantum mechanical systems where the space of configurations is a general non-compact symmetric space. Associated with this path integral is a perturbation theory which respects the global structure of the system. This perturbation expansion is evaluated for a simple example and leads to a new exactly soluble model. This work is a step towards the con...

متن کامل

Symbolic Summation and Higher Orders in Perturbation Theory

Higher orders in perturbation theory require the calculation of Feynman integrals at multiple loops. We report on an approach to systematically solve Feynman integrals by means of symbolic summation and discuss the underlying algorithms. Examples such as the non-planar vertex at two loops, or integrals from the recent calculation of the three-loop QCD corrections to structure functions in deep-...

متن کامل

Integrals over Products of Distributions from Manifest Coordinate Invariance of Perturbation Expansions of Path Integrals in Curved Space

– We show that the requirement of manifest coordinate invariance of perturbatively defined quantum-mechanical path integrals in curved space leads to an extension of the theory of distributions by specifying unique rules for integrating products of distributions. The rules are derived using equations of motion and partial integration, while keeping track of certain minimal features stemming fro...

متن کامل

Perturbation theory via Feynman diagrams in classical mechanics

In this paper we show how Feynman diagrams, which are used as a tool to implement perturbation theory in quantum field theory, can be very useful also in classical mechanics, provided we introduce also at the classical level concepts like path integrals and generating functionals.

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2005