Trouble with boson loops in Skyrmion physics

Journal Article · Tue Oct 15 04:00:00 EDT 1985 · Phys. Rev. D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.32.2190· OSTI ID:5213297

Aitchison, I J.R.; Fraser, C M

The possibility is raised that the O((partialphi)/sup 4/) (stability) terms in the Skyrme Lagrangian may arise as quantum corrections, starting from an underlying bosonic field theory. Specifically, these terms are calculated from a derivative expansion of the one-loop effective action of the linear sigma model, which is the simplest relevant theory. The calculated terms are logarithmically divergent in the chiral limit m/sub ..pi../ /sup 2/..-->..0. This physically incorrect result is traced to a failure of the derivative expansion caused by nonanalyticity of the Green's functions at zero momentum (i.e., unitarity thresholds). The difficulties of handling ''light'' particle loops in the effective-Lagrangian approach to soliton physics are discussed. It is suggested that, in the absence of a systematic procedure for calculating unitarity corrections to effective Lagrangians, it may be more fruitful to settle for an approximate theory, in which the soliton Lagrangian is enlarged to include heavier mesons, and used only at the tree level.

• Research Organization: Department of Theoretical Physics, University of Oxford, 1 Keble Road, Oxford OX1 3NP, England
• OSTI ID: 5213297
• Journal Information: Phys. Rev. D; (United States), Journal Name: Phys. Rev. D; (United States) Vol. 32:8; ISSN PRVDA
• Country of Publication: United States
• Language: English

Related Subjects

645400* -- High Energy Physics-- Field Theory
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
FIELD THEORIES
FUNCTIONS
GREEN FUNCTION
LAGRANGIAN FUNCTION
NONLINEAR PROBLEMS
NUCLEON-NUCLEON POTENTIAL
POTENTIALS
QUANTUM FIELD THEORY
QUASI PARTICLES
SKYRME POTENTIAL
SOLITONS