New length operator for loop quantum gravity

Yongge Ma, Chopin Soo, Jinsong Yang

Research output: Contribution to journalArticlepeer-review

41 Citations (Scopus)


An alternative expression for the length operator in loop quantum gravity is presented. The operator is background independent, symmetric, positive semidefinite, and well defined on the kinematical Hilbert space. The expression for the regularized length operator can moreover be understood both from a simple geometrical perspective as the average of a formula relating the length to area, volume and flux operators, and also consistently as the result of direct substitution of the densitized triad operator with the functional derivative operator into the regularized expression of the length. Both these derivations are discussed, and the origin of an undetermined overall factor in each case is also elucidated.

Original languageEnglish
Article number124026
JournalPhysical Review D - Particles, Fields, Gravitation and Cosmology
Issue number12
Publication statusPublished - 2010 Jun 9

All Science Journal Classification (ASJC) codes

  • Nuclear and High Energy Physics
  • Physics and Astronomy (miscellaneous)


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