ABC formula and R-operation for quantum processes with unstable states

Abstract

For a wide class of Hamiltonians used in quantum field theory and statistical physics, we obtain an explicit formula describing the behavior of the vacuum expectation of the evolution operator on large, but finite, time intervals. This formula also holds for processes with unstable states.

On nonergodic property of Bose gas with weak pair interaction

“…We will prove in the section 10 below that there exist divergences in the theory. Note that the structure of R-operation for the processes at large times for some class of systems has been considered at [10] Let T be a tree. Let us give a definition of its right subtree.…”

“…The accurate consideration for the quantum case can be found in section 10. Suppose that our system is ergodic, i.e.…”

Nonequlibrium Renormalization Theory III

“…To solve this problem we use the R-operation method [1,2,3]. The methods of R-operation for studying the large time behavior of quantum systems have been used in [4]. The philosophical consequences of our statement have been discussed in our first paper on this topic.…”