N‐Dimensional Total Orbital Angular‐Momentum Operator

1963 ◽  
Vol 4 (7) ◽  
pp. 897-900 ◽  
Author(s):  
Kenneth D. Granzow
1985 ◽  
Vol 63 (7) ◽  
pp. 1719-1722 ◽  
Author(s):  
John Avery

Methods are presented for constructing eigenfunctions of the total orbital angular momentum operator of a many-particle system without the use of the Clebsch–Gordan coefficients. One of the equations derived in this paper is analogous to Dirac's identity for total spin; and through this equation, a connection is established between eigenfunctions of L2 and irreducible representations of the symmetric group Sn.


2001 ◽  
Vol 16 (01) ◽  
pp. 41-51
Author(s):  
D. SINGLETON

The spin of a glueball is usually taken as coming from the spin (and possibly the orbital angular momentum) of its constituent gluons. In light of the difficulties in accounting for the spin of the proton from its constituent quarks, the spin of glueballs is re-examined. The starting point is the fundamental QCD field angular momentum operator written in terms of the chromoelectric and chromomagnetic fields. First, we look at the possible restrictions placed on the structure of glueballs from the requirement that the QCD field angular momentum operator should satisfy the standard commutation relationships. This analysis can be compared to the electromagnetic charge/monopole system, where the requirement that the total field angular momentum obey the angular momentum commutation relationships places restrictions (i.e. the Dirac condition) on the system. Second, we look at the expectation value of the field angular momentum operator under some simplifying assumptions.


1980 ◽  
Vol 58 (12) ◽  
pp. 1724-1728
Author(s):  
William R. Ross

The Slater basis states for N equivalent electrons form the basis for the irreducible representation (1N) of the Lie group U(4l + 2). States which are eigenfunctions of the total spin and total orbital angular momentum form the basis for irreducible representations of SO(3) × SU(2). In this paper the intermediate group Sp(4l + 2) is studied. The basis states for irreducible representations of Sp(4l + 2) are expressed in terms of the Slater basis states.


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