English

Matrix Elements of Thiemann's Hamiltonian Constraint in Loop Quantum Gravity

General Relativity and Quantum Cosmology 2014-11-17 v1

Abstract

We present an explicit computation of matrix elements of the hamiltonian constraint operator in non-perturbative quantum gravity. In particular, we consider the euclidean term of Thiemann's version of the constraint and compute its action on trivalent states, for all its natural orderings. The calculation is performed using graphical techniques from the recoupling theory of colored knots and links. We exhibit the matrix elements of the hamiltonian constraint operator in the spin network basis in compact algebraic form.

Keywords

Cite

@article{arxiv.gr-qc/9703090,
  title  = {Matrix Elements of Thiemann's Hamiltonian Constraint in Loop Quantum Gravity},
  author = {Roumen Borissov and Roberto De Pietri and Carlo Rovelli},
  journal= {arXiv preprint arXiv:gr-qc/9703090},
  year   = {2014}
}

Comments

32 pages, 22 eps figures. LaTeX (Using epsfig.sty,ioplppt.sty and bezier.sty). Submited to Classical and Quantum Gravity

R2 v1 2026-07-22T12:52:57.643Z