SU(3) normal mode theory

Rosensteel, G.; Dankova, Ts.

doi:10.1103/physrevc.64.064303

Cited by 10 publications

(6 citation statements)

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“…Thus, no extra work is required to derive the non-integral orbit results. Although the energy functions are formally the same in our weak and strong su(2) mean field models, the weak su(2) Hamiltonian operator must break su(2) dynamical symmetry, and it is not equal to the LMG Hamiltonian ĤLMG that acts in an irreducible su (2)…”

Section: Lmg Critiquementioning

confidence: 99%

“…The representation σ of rot(3) acts on the Fock space of all antisymmetrized many-particle wavefunctions. The Hermitian operators in the image of the unitary representation σ are the one-body angular momentum operators, Li = ε ij k α x αj p αk , and the one-body quadrupole moment operators, Q(2) μ = α r 2 α Y (2) μ ( α ), where summations are over the particle index α [23,24].…”

Section: Representation Of the Matrix Lie Groupmentioning

confidence: 99%

“…This physical requirement, when viewed as a qualitative statement, is the same for a typical group theoretical model based on representation theory and for AMFT. But the general physical concept is rendered precise in two different ways: (1) in a representationbased theory, the physical states are vectors in one irreducible representation of a strong dynamical Lie group; (2) in AMFT the densities of physical states must be points on one co-adjoint orbit O of a weak dynamical Lie group.…”

Section: Representation Of the Matrix Lie Groupmentioning

confidence: 99%

“…The resulting simplification is a modified Lax equation, equation (67), in which the mean field Hamiltonian is replaced by the mean field Routhian, defined on a two-dimensional phase space, equation (66). The two new su(3) topics in this paper, compared to the presentation in [1][2][3][4], are a different energy function and a subsection about Marsden-Weinstein reduction.…”

Section: Su(3) Elliott Theorymentioning

confidence: 99%

“…In addition to its compliance with Ockham's Razor, the idempotent density matrix theory has the further advantage of a natural generalization which eliminates completely the independent particle ansatz. This theoretical extension, which is the main subject of this paper, enlarges the domain of applicability of HF and creates a new class of mean field theories [1][2][3][4][5][6][7][8][9][10].…”

Section: Introductionmentioning

confidence: 99%

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Mean field theory for U(n) dynamical groups

Rosensteel¹

2011

J. Phys. A: Math. Theor.

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Algebraic mean field theory (AMFT) is a many-body physics modeling tool which firstly, is a generalization of Hartree–Fock mean field theory, and secondly, an application of the orbit method from Lie representation theory. The AMFT ansatz is that the physical system enjoys a dynamical group, which may be either a strong or a weak dynamical Lie group G. When G is a strong dynamical group, the quantum states are, by definition, vectors in one irreducible unitary representation (irrep) space, and AMFT is equivalent to the Kirillov orbit method for deducing properties of a representation from a direct geometrical analysis of the associated integral co-adjoint orbit. AMFT can be the only tractable method for analyzing some complex many-body systems when the dimension of the irrep space of the strong dynamical group is very large or infinite. When G is a weak dynamical group, the quantum states are not vectors in one irrep space, but AMFT applies if the densities of the states lie on one non-integral co-adjoint orbit. The computational simplicity of AMFT is the same for both strong and weak dynamical groups. This paper formulates AMFT explicitly for unitary Lie algebras, and applies the general method to the Lipkin–Meshkov–Glick (2) model and the Elliott (3) model. When the energy in the (3) theory is a rotational scalar function, Marsden–Weinstein reduction simplifies AMFT dynamics to a two-dimensional phase space.

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Section: Lmg Critiquementioning

confidence: 99%