Eigenvalues of volume and area in the spin network representation

Shao Dan; Shao Liang; Shao Chang-Gui; Chen Yi-Han; Ma Wei-Chuan

doi:10.7498/aps.54.4549

Abstract
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.

Keywords:
volume operator /

area operator /

eigenvalue /

spin network
Authors and contacts
Shao Dan²,

Shao Liang³,

Shao Chang-Gui¹,

Chen Yi-Han¹,

Ma Wei-Chuan¹

(1)湖北大学理论物理所，武汉 430062; (2)江汉大学物理系，武汉 430056; (3)武汉科技大学物理系，武汉 430081
References

Cited By

[1]	Wu Ze, Fan Hong-Yi. The invariant eigen-operator method in matrix form and the eigenfrequency of several mesoscopic circuits. Acta Physica Sinica, 2019, 68(22): 220301. doi: 10.7498/aps.68.20190651
[2]	Zhang Ke, Fan Cheng-Yu, Fan Hong-Yi. Invariant eigen-operator calculated vibration mode of lattice in the case of absorbing an atom onto crystal surface. Acta Physica Sinica, 2018, 67(17): 170301. doi: 10.7498/aps.67.20180469
[3]	Yang Hui-Hui, Ning Li-Juan. Approximate time-dependent solution of Fokker-Planck equation with non-linear drift force. Acta Physica Sinica, 2013, 62(18): 180501. doi: 10.7498/aps.62.180501
[4]	Jin Shuo, Xie Bing-Hao, Zhang Hong-Biao. An sus(1,1) ⊕ sud(1,1) algebraic structure of the cuprate superconductors model based on the analogy with atomic nuclei. Acta Physica Sinica, 2012, 61(3): 030304. doi: 10.7498/aps.61.030304
[5]	Shao Dan, Huzio Noda, Shao Chang-Gui, Shao Liang. Evaluation of eigenactions of area and volume operators in loop quantum gravity. Acta Physica Sinica, 2009, 58(4): 2198-2219. doi: 10.7498/aps.58.2198
[6]	Li Ti-Jun. Expressions of coordinate eigen vectors and their integration over non-symmetric coordinate projective operators. Acta Physica Sinica, 2008, 57(7): 3969-3972. doi: 10.7498/aps.57.3969
[7]	Shao Dan, Shao Liang, Shao Chang-Gui, H.Noda. Eigenaction of metric operator on Gaussian weave state and spin-geometry. Acta Physica Sinica, 2007, 56(3): 1271-1291. doi: 10.7498/aps.56.1271
[8]	Shao Liang, Shao Dan, Shao Chang-Gui, Zhang Zu-Quan. Eigenactions and eigenvalues of volume operator on any-valent vertices. Acta Physica Sinica, 2006, 55(11): 5629-5637. doi: 10.7498/aps.55.5629
[9]	Luo Shi-Yu, Shao Ming-Zhu. The tan2x potential and the eigenvalue and eigenfunction for planar channelling radiation. Acta Physica Sinica, 2005, 54(9): 4092-4096. doi: 10.7498/aps.54.4092
[10]	Huang Bo-Wen. A time-dependent damped harmonic oscillator with a force quadratic in velocity. Acta Physica Sinica, 2003, 52(2): 271-275. doi: 10.7498/aps.52.271
[11]	Wang Ji-Suo, Feng Jian, Liu Tang-Kun, Zhan Ming-Sheng. . Acta Physica Sinica, 2002, 51(9): 1983-1988. doi: 10.7498/aps.51.1983
[12]	TAN WEI-HAN, LIU JUAN. PHASE OPERATOR AND PHASE STATES FOR FINITE ENERGY SYSTEM. Acta Physica Sinica, 1997, 46(12): 2348-2358. doi: 10.7498/aps.46.2348
[13]	CHEN JIAN-HUA, CHENG XIANG-AI. . Acta Physica Sinica, 1995, 44(10): 1529-1533. doi: 10.7498/aps.44.1529
[14]	LIN DONG-HAI, WU QIN-YI. A NEW FORMALISM FOR DESCRIBING THE EVOLUTION OF DENSITY OPERATORS. Acta Physica Sinica, 1993, 42(6): 893-904. doi: 10.7498/aps.42.893
[15]	WEI LIAN-FU. EIGENSTATES OF OPERATOR aqN(N≥2). Acta Physica Sinica, 1993, 42(5): 757-761. doi: 10.7498/aps.42.757
[16]	ZHAN YOU-BANG. SQUEEZING PROPERTIES OF EIGENSTATES OF HIGH ORDER POWER OF PHOTON ANNIHILATION OPERATOR. Acta Physica Sinica, 1992, 41(8): 1279-1288. doi: 10.7498/aps.41.1279
[17]	WANG JI-SUO. MATHEMATICAL STRUCTURE OF THE EIGENSTATES OF OPERATOR ak AND THEIR PROPERTIES. Acta Physica Sinica, 1991, 40(4): 547-554. doi: 10.7498/aps.40.547
[18]	LIU AI-ZHUO, PEI FENG-KUI. DENSITY OPERATOR FORMALISM FOR SPIN SYSTEMS WITH PERMUTATION SYMMETRY IN MULTIPLE PULSE AND 2D NMR EXPERIMENTS (Ⅱ)——MULTIPLE QUANTUM PRODUCT OPERATOR FORMALISM. Acta Physica Sinica, 1990, 39(8): 154-161. doi: 10.7498/aps.39.154-2
[19]	PENG SHI-AN, GUO GUANG-CAN. ORTHONORMALIZED EIGENSTATES OF OPERATOR αN AND THEIR PROPERTIES. Acta Physica Sinica, 1990, 39(1): 51-60. doi: 10.7498/aps.39.51
[20]	LIU AI-ZHUO, PEI FENG-KUI. PRODUCT OPERATOR FORMALISM FOR SPIN SYSTEMS WITH MAGNETIC EQUIVALENCE. Acta Physica Sinica, 1988, 37(7): 1072-1082. doi: 10.7498/aps.37.1072

Catalog

Vol. 54, Issue 10 - 2005-05-20

Metrics

Abstract views: 8286
PDF Downloads: 955
Cited By: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

Search

Article

留言板

Eigenvalues of volume and area in the spin network representation

Abstract

Authors and contacts

References

Cited By

Catalog

Metrics

Authors

Referees

About Journal

About

Search

Article

留言板

Eigenvalues of volume and area in the spin network representation

Abstract

Authors and contacts

References

Cited By

Catalog

Metrics

Publishing process

Authors

Referees

About Journal

About