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Algebraic Theory of Molecules$
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F. Iachello and R. D. Levine

Print publication date: 1995

Print ISBN-13: 9780195080919

Published to Oxford Scholarship Online: November 2020

DOI: 10.1093/oso/9780195080919.001.0001

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Four-Body Algebraic Theory

Four-Body Algebraic Theory

Chapter 5 Four-Body Algebraic Theory
Algebraic Theory of Molecules

F. Iachello

R. D. Levine

Oxford University Press

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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