Dynamical group approach to conformal field theory

TL;DR

This paper introduces a group-theoretical method for describing the S-matrix in quantum field theories with dynamical symmetry, applying it specifically to scalar Euclidean QFT with conformal symmetry.

Contribution

It presents a novel purely group-theoretical approach to the S-matrix, emphasizing the role of dynamical groups and their representations in quantum field theory.

Findings

The S-matrix acts as an intertwining operator between unitary representations.

Application to scalar Euclidean QFT demonstrates the method's effectiveness.

Highlights the importance of conformal symmetry in the proposed framework.

Abstract

We propose a purely group-theoretical method for describing the S-matrix in quantum field theory with dynamical symmetry. In this approach, the Heisenberg S-matrix in a QFT with dynamical symmetry is an intertwining operator between unitary representations of the underlining dynamical group acting in Hilbert spaces spanned by the 'in' and 'out' states. As application we consider scalar Euclidean QFT with conformal symmetry.