Spin Algebra

However, all three particles in this equation are fermions with intrinsic spins S = jh. Therefore, we cannot balance the angular momentum in the reaction as written. The spins of the proton and the electron can be coupled to 0 or 1 ft and can also have relative angular momenta with any integral value from the emission process. This simple spin algebra will never yield the half-integral value on the left-hand side of the equation. Another fermion must be present among the products. 

E. ElBaz and B. Castel. Graphical Methods of Spin Algebras in... 

In 1957, Bardeen, Cooper and Schriffer proposed a microscopic theory of superconductivity [2], This theory was isotropic (s-wave pairing). In 1958, Bogoliubov [3] and Valatin [4] introduced a transformation that made the treatment of superconductivity simpler (quasi-particle transformation). Still in 1958, Anderson [5] addressed the same problem by introducing the algebra of SU(2) to describe the properties of the system (quasi-spin algebra). In the same year, Bohr, Mottelson and Pines applied BCS theory to... 

Graphical Methods of Spin Algebras. In most problems of chemical interest, the molecular hamiltonian can be taken to be spin-free and can be written172 173 in terms of the generators of the unitary group, U(n), where n is the number of basis functions... 

The matrix elements of the generators, Sab, can be evaluated using the graphical methods of spin algebra.174-176 The particle-hole formalism introduced by Flores and Moshinsky177 and recently discussed by Paldus and Boyle178 is most suitable for such developments. 

E. El Baz and B. Castel, Graphical Methods of Spin Algebras , Dekker, New York, 1972. 178 S. Wilson, in Proceedings of Daresbury Study Weekend , November 1979, ed. M. F. 

For the doubly reduced complexes, the spin algebra is only... 

As in ordinary spin algebra, the vector operator T obeys the angular momentum commutation relations. 

Actually, the components of the bosonized SB spin operator act as generators of rotations in spin space, i.e., Si(pi ) satisfies the spin algebra. Since and commute with the SB t-J Hamiltonian, the constraints in Eq. 5 and Eq. 6 can be ensured by introducing the time-independent Lagrange multipliers and = consequence, the... 

Note that additional constraints do not exist. Especially, if the constraint xpj = 0 is added [25] the spin algebra is not satisfied. 

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