Closed Time-Path Green Functions by Stochastic Quantization

Abstract

The Langevin equation and the Gaussian average of the stochastic quantization of Parisi and Wu are continued on the closed time-path, at the same time, the new non-Gaussian source is added into it. After assuming some properties of new source, the closed time-path Green functions are computed by using the adapted Langevin equations. While they are transformed into the physical representation, some important characters of closed time-path Green function, i.e. the normalization and causality, are obtained also.

Interaction solutions for mKP equation with nonlocal symmetry reductions and CTE method

“…It is obvious that once the solutions Φ are solved out with (24e), the fields for G, H, U and W can be solved out directly from (24a)-(24d). The explicit solutions for mKP (1) are immediately obtained by substituting Φ, G, H, U and W and into (23). For instance, it has a trivial solution Φ = ξ + η for the system (24e).…”

“…The integrable properties of this equation such as the Lax pair [17,18], Darboux transformation [19,20] and explicit solutions [21,22] have been obtained. From the mKP equation, a new integrable system is given by means of an asymptotically exact reduction method [23]. The paper is organized as follows.…”