Dilatation operator or Hamiltonian?

TL;DR

This paper explores the conditions under which the Hamiltonian in field theory can be substituted with the dilatation operator, examining the implications for theoretical physics.

Contribution

It provides a detailed analysis of the circumstances allowing the replacement of the Hamiltonian with the dilatation operator in field theories.

Findings

Identifies specific scenarios where the dilatation operator can substitute the Hamiltonian.

Clarifies the theoretical implications of using the dilatation operator in place of the Hamiltonian.

Enhances understanding of symmetry and scale transformations in field theory.

Abstract

We analyze the situation when the Hamiltonian in field theory can be replaced by the dilatation operator.