Instanton trajectory defined

The basis functions ( ) (z) used to define the instanton trajectory is... 

The boundary conditions formulated in Eqs. (65, 67, 68) contain all the physical requirements for the instanton trajectory. Now we need to figure out the boundary conditions for the functions g 1, 2 that are consistent with Eqs. (65, 67, 68). We will show below that the function 2 — 0 in the superconducting region. Thus, at r Tj the Green function g has the same boundary conditions with those defined by Eq. (65) for function gk... 

The main idea of improvement is to find a direction in the space of trajectories along which the classical action. Equation (6.109), decreases. In order to do so, we use z(t) to define the r-dependent functions < [z(t)] that form the basis of expansion in the vicinity of qo[z(r)]. Namely, we look for a better instanton trajectory in the form... 

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