Algebraic analysis of physical and spurious states in Dyson boson mapping

P. Park
Phys. Rev. C 35, 807 – Published 1 February 1987
PDFExport Citation

Abstract

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 [12n]. 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.

  • Received 3 September 1986

DOI:https://doi.org/10.1103/PhysRevC.35.807

©1987 American Physical Society

Authors & Affiliations

P. Park

  • Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, Pennsylvania 15260

Comments & Replies

Comment on ‘‘Algebraic analysis of physical and spurious states in Dyson boson mapping’’

F. J. W. Hahne, H. B. Geyer, and C. A. Engelbrecht
Phys. Rev. C 37, 885 (1988)

References (Subscription Required)

Click to Expand
Issue

Vol. 35, Iss. 2 — February 1987

Reuse & Permissions
Access Options

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review C

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×