Structure of Extended Loop Wave Function in Quantum Gravity and Operator Formalism

TL;DR

This paper explores the structure of extended loop wave functions in quantum gravity using operator formalism, revealing their classification by family number and a hierarchical constraint structure.

Contribution

It introduces a classification scheme for extended loop wave functions based on family number and analyzes the hierarchical constraints in quantum gravity.

Findings

Extended loop wave functions are characterized by family number.

Classification by partition of the family number is established.

Hierarchical structure of constraints in quantum gravity is identified.

Abstract

The structure of extended loop wave function is investigated in terms of the operator formalism. It is found that the extended loop wave function is characterized by the family number and classified by the partition of the family number. It is pointed out that the constraints to the extended loop function in quantum gravity exhibit a hierarchy structure.