Narrow Results

We construct in a rigorous mathematical way interacting quantum field theories on a $p$-adic spacetime. The main result is the construction of a measure on a function space which allows a rigorous definition of the partition function. The advantage of the approach presented here is that all the perturbation calculations can be carried out in the standard way using functional derivatives, but in a mathematically rigorous way.

We examine several widely used statistical field theoretic methods in theoretical polymer physics. A systematic derivation for the polymer field theoretic model is given within the framework of the effective Landau theory. After constructing the field theoretic model, we perform a perturbative expansion of the model, and then the mean-field approximation and the Gaussian fluctuation approximation are introduced into the treatment of the model in order. We also outline a derivation for the self-consistent Hartree theory in polymer physics within a variational scheme. The applications of these methods are also discussed accordingly.

In this work the problem of describing the dynamics of a continuous chain with rigid constraints is treated using a path integral approach.

In this work we discuss the dynamics of a three-dimensional chain. It turns out that the generalized sigma model presented in Ref. 1 may be easily generalized to three dimensions. The formula of the probability distribution of two topologically entangled chains is provided. The interesting case of a chain which can form only discrete angles with respect to the z–axis is also presented.