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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:
Chapter 5 Four-Body Algebraic Theory
Source:
Algebraic Theory of Molecules
Author(s):

F. Iachello

R. D. Levine

Publisher:
Oxford University Press
DOI:10.1093/oso/9780195080919.003.0008

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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