Roles of Asymptotic Condition and S-Matrix as Micro-Macro Duality in QFT

TL;DR

This paper explores how asymptotic conditions and the S-matrix in quantum field theory underpin the emergence of independence and the reconstruction of interacting fields from free fields, highlighting a micro-macro duality framework.

Contribution

It introduces a novel perspective linking asymptotic conditions and the S-matrix to micro-macro duality in QFT, using cocycles of K-T operators to reconstruct interactions.

Findings

Asymptotic conditions relate to independence in quantum fields.

The S-matrix acts as a bridge between free and interacting fields.

A new duality framework connects micro-objects and macro-objects in QFT.

Abstract

Various versions of "independence" are actively inverstigated in quantum probability. In the context of relativistic QFT, we show here that the physical origin of "independence" can be sought in the asymptotic condition through which asymptotic fields and states exhibiting the independence emerge from the non-independent interacting Heisenberg fields in a kind of "central limit". From the algebraic viewpoint, this condition is equivalent to the on-shell condition to pick up free one-particle modes, which also reduces to Einstein's famous formula $E=mc^{2}$. A scenario to reconstruct interacting Heisenberg fields as Micro-objects from these "independent" =free Macro-objects intertwined by an S-matrix as a measurable quantity is formulated according to the Micro-Macro Duality associated with a new notion of a \textit{cocycle of K-T operators}.