Boson realizations of Lie algebras with applications to nuclear physics
- Department of Physics, University of Pennsylvania, Philadelphia, PA (USA)
- Department of Physics, University of Notre Dame, Notre Dame, IN (USA)
The concept of boson realization (or mapping) of Lie algebras appeared first in nuclear physics in 1962 as the idea of expanding bilinear forms in fermion creation and annihilation operators in Taylor series of boson operators, with the object of converting the study of nuclear vibrational motion into a problem of coupled oscillators. The physical situations of interest are quite diverse, depending, for instance, on whether excitations for fixed- or variable-particle number are being studied, on how total angular momentum is decomposed into orbital and spin parts, and on whether isotopic spin and other intrinsic degrees of freedom enter. As a consequence, all of the semisimple algebras other than the exceptional ones have proved to be of interest at one time or another, and all are studied in this review. Though the salient historical facts are presented in the introduction, in the body of the review the progression is (generally) from the simplest algebras to the more complex ones. With a sufficiently broad view of the physics requirements, the mathematical problem is the realization of an arbitrary representation of a Lie algebra in a subspace of a suitably chosen Hilbert space of bosons (Heisenberg-Weyl algebra). Indeed, if one includes the study of odd nuclei, one is forced to consider the mappings to spaces that are direct-product spaces of bosons and (quasi)fermions. Though all the methods that have been used for these problems are reviewed, emphasis is placed on a relatively new algebraic method that has emerged over the past decade. Many of the classic results are rederived, and some new results are obtained for odd systems.
- OSTI ID:
- 5662923
- Journal Information:
- Reviews of Modern Physics; (USA), Journal Name: Reviews of Modern Physics; (USA) Vol. 63:2; ISSN 0034-6861; ISSN RMPHA
- Country of Publication:
- United States
- Language:
- English
Similar Records
Boson realization of sp(4). I. The matrix formulation
On the boson--quasifermion realization of the particle--hole SO(2. cap omega. +1) algebra
Related Subjects
Moments
Spin
& Models
73 NUCLEAR PHYSICS AND RADIATION PHYSICS
BANACH SPACE
BOSON EXPANSION
DOCUMENT TYPES
ENERGY LEVELS
HAMILTONIANS
HIGH SPIN STATES
HILBERT SPACE
LIE GROUPS
MATHEMATICAL MODELS
MATHEMATICAL OPERATORS
MATHEMATICAL SPACE
NUCLEAR MODELS
QUANTUM NUMBERS
QUANTUM OPERATORS
REVIEWS
SENIORITY NUMBER
SPACE
SU GROUPS
SU-2 GROUPS
SYMMETRY GROUPS