Open AccessEigenvalues of volume and area in the spin network representation
Author(s) -
Dan Shao,
Shao Liang,
Cheng-Gang Shao,
Yihan Chen,
Ma Wei-Chuan
Publication year - 2005
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.54.4549
Subject(s) - eigenvalues and eigenvectors , operator (biology) , grasp , volume (thermodynamics) , representation (politics) , spin (aerodynamics) , action (physics) , identity (music) , physics , mathematics , computer science , mathematical physics , quantum mechanics , thermodynamics , chemistry , acoustics , biochemistry , repressor , politics , transcription factor , political science , law , gene , programming language
By antisymmetrizing the action of grasp and binor identity, it is proved that the spin network states of 3-valent and any-valent are the eigenstates of the volume operator and the area operator, respectively. The formulas 2-32l3p∑ipσpτpρ and 2-1l2p∑jpl(j) for calculating the eigenvalue spectrums of volume and area, respectively, are obtained.