Open AccessEigenactions and eigenvalues of volume operator on any-valent vertices
Author(s) -
Shao Liang,
Dan Shao,
Cheng-Gang Shao,
Zhang Zu-Quan
Publication year - 2006
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.55.5629
Subject(s) - eigenvalues and eigenvectors , operator (biology) , algebraic number , volume (thermodynamics) , vortex , mathematics , pure mathematics , combinatorics , mathematical physics , mathematical analysis , physics , quantum mechanics , biochemistry , chemistry , repressor , transcription factor , gene , thermodynamics
Antisymmetrizing the actions of hand triple contained in volume operator and grasping on the segments rooting through any-valent vortex of spin netwok, and using the binor identity, a proof is given that all these actions are eigenactions with eigenvalue -2. A systematic algebraic method to calculate the eigenvalues of volume operator for any-valent vortices is given, and the general and algebraic expressions of volume eigenvalues for 3-, 4-, 5-, 6- valent vertices are obtained.