Algebraic analysis of physical and spurious states in Dyson boson mapping

Journal Article · Sun Feb 01 04:00:00 EST 1987 · Phys. Rev. C; (United States)

DOI:https://doi.org/10.1103/PhysRevC.35.807· OSTI ID:6924904

Park, P

Dyson boson mapping of a system of 2n fermions distributed among k single-particle states uses a space generated by two-index ideal bosons. We define a unitary group U(k) to classify this ideal-boson space. The physical subspace is shown to correspond to the antisymmetric irreducible representation (1/sup 2//sup n/). This classification enables one to introduce a ''Majorana'' operator S which is a linear combination of one- and two-body Casimir operators of U(k). A zero eigenvalue of S characterizes the physical subspace while positive eigenvalues identify all other irreducible representations that occur. The Hermitian boson image of the Hamiltonian does not connect physical and spurious states because it is a function of the generators of U(k). All the nonphysical eigenvalues and eigenstates of a physical boson Hamiltonian (Dyson boson image of a physical fermion Hamiltonian) which could be Hermitian or non-Hermitian, can be removed without affecting the physical eigenvalues and eigenvectors, by adding a suitable multiple of S to the Hamiltonian.

• Research Organization: Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, Pennsylvania 15260
• OSTI ID: 6924904
• Journal Information: Phys. Rev. C; (United States), Journal Name: Phys. Rev. C; (United States) Vol. 35:2; ISSN PRVCA
• Country of Publication: United States
• Language: English

Related Subjects

645201* -- High Energy Physics-- Particle Interactions & Properties-Theoretical-- General & Scattering Theory
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BOSON EXPANSION
BOSONS
DYSON REPRESENTATION
EIGENVALUES
EIGENVECTORS
FERMIONS
HAMILTONIANS
LIE GROUPS
MAPPING
MATHEMATICAL OPERATORS
MATRIX ELEMENTS
QUANTUM OPERATORS
SU GROUPS
SU-3 GROUPS
SYMMETRY GROUPS