Matrix elements of Lorentzian Hamiltonian constraint in loop quantum gravity

Journal article
(Original article)


Publication Details

Author(s): Liegener K, Alesci E, Zipfel A
Journal: Physical Review D
Publication year: 2013
Volume: 88
Journal issue: 8
ISSN: 1550-7998


Abstract


The Hamiltonian constraint is the key element of the canonical formulation of loop quantum gravity (LQG) coding its dynamics. In Ashtekar-Barbero variables it naturally splits into the so-called Euclidean and Lorentzian parts. However, due to the high complexity of this operator, only the matrix elements of the Euclidean part have been considered so far. Here we evaluate the action of the full constraint, including the Lorentzian part. The computation requires heavy use of SU(2) recoupling theory and several tricky identities among n-j symbols are used to find the final result: these identities, together with the graphical calculus used to derive them, also simplify the Euclidean constraint and are of general interest in LQG computations. © 2013 American Physical Society.



FAU Authors / FAU Editors

Alesci, Emanuele Dr.
Lehrstuhl für Theoretische Physik
Liegener, Klaus
Lehrstuhl für Theoretische Physik
Zipfel, Antonia
Lehrstuhl für Theoretische Physik


How to cite

APA:
Liegener, K., Alesci, E., & Zipfel, A. (2013). Matrix elements of Lorentzian Hamiltonian constraint in loop quantum gravity. Physical Review D, 88(8). https://dx.doi.org/10.1103/PhysRevD.88.084043

MLA:
Liegener, Klaus, Emanuele Alesci, and Antonia Zipfel. "Matrix elements of Lorentzian Hamiltonian constraint in loop quantum gravity." Physical Review D 88.8 (2013).

BibTeX: 

Last updated on 2018-19-04 at 03:57