Four-Body Algebraic Theory
Four-Body Algebraic Theory
In tetratomic molecules, there are three independent vector coordinates, rl, r2, and r3, which we can think of as three bonds. The general algebraic theory tells us that a quantization of these coordinates (and associated momenta) leads to the algebra . . .G = U1(4) ⊗ U2(4) ⊗ U3(4). . . . . . .(5.1). . . As in the previous case of two bonds, discussed in Chapter 4, we introduce boson operators for each bond . . .σ †1, π†1μ , μ = 0, ±1 ,. . . . . .σ †2, π†2μ , μ = 0, ±1 ,. . . . . .σ †3, π†3μ , μ = 0, ±1 ,. . . . . .(5.2). . . together with the corresponding annihilation operators σ1, π1μ, σ2, π2μ, σ3, π3μ. The elements of the algebras Ui(4) are the same as in Table 2.1, except that a bond index i = 1, 2, 3 is attached to them.
Keywords: Amat-Nielsen couplings, Casimir operators, Fermi coupling, Majorana couplings, Raccah coefficient, Wigner, coupling scheme, interbond coupling, recoupling coefficients, vibrational l-doubling
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