Soliton quantization and internal symmetry

Journal Article · Fri Apr 01 04:00:00 EST 1994 · Physical Review, D (Particles Fields); (United States)

DOI:https://doi.org/10.1103/PhysRevD.49.3598· OSTI ID:5019664

Dorey, N ^[1]; Hughes, J ^[2]; Mattis, M P ^[1]

---

1. Theoretical Division, T-8 MS B285, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)
2. Physics Department, Michigan State University, East Lansing, Michigan 48823 (United States)

We apply the method of collective coordinate quantization to a model of solitons in two spacetime dimensions with a global U(1) symmetry. In particular we consider the dynamics of the charged states associated with rotational excitations of the soliton in the internal space and their interactions with the quanta of the background field (mesons). By solving a system of coupled saddle-point equations we effectively sum all tree graphs contributing to the one-point Green's function of the meson field in the background of a rotating soliton. We find that the resulting one-point function evaluated between soliton states of definite U(1) charge exhibits a pole on the meson mass shell and we extract the corresponding [ital S]-matrix element for the decay of an excited state via the emission of a single meson using the standard Lehmann-Symanzik-Zimmermann reduction formula. This [ital S]-matrix element has a natural interpretation in terms of an effective Lagrangian for the charged soliton states with an explicit Yukawa coupling to the meson field. We calculate the leading-order semiclassical decay width of the excited soliton states and discuss the consequences of these results for the hadronic decay of the [Delta] resonance in the Skyrme model.

• OSTI ID: 5019664
• Journal Information: Physical Review, D (Particles Fields); (United States), Journal Name: Physical Review, D (Particles Fields); (United States) Vol. 49:7; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

662110* -- General Theory of Particles & Fields-- Theory of Fields & Strings-- (1992-)
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
CALCULATION METHODS
ENERGY LEVELS
EXCITED STATES
FUNCTIONS
GREEN FUNCTION
LIE GROUPS
MATRICES
NUCLEAR POTENTIAL
POTENTIALS
QUANTIZATION
QUASI PARTICLES
ROTATIONAL STATES
S MATRIX
SADDLE-POINT METHOD
SOLITONS
SPACE-TIME
SYMMETRY
SYMMETRY GROUPS
U GROUPS
U-1 GROUPS
YUKAWA POTENTIAL