Quantum-mechanical aspects of SU(3) Skyrme model in collective-coordinate quantization

Journal Article · Wed Jun 15 04:00:00 EDT 1988 · Phys. Rev. D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.37.3663· OSTI ID:6933369

Fujii, K; Sato, K; Toyota, N

We extend the quantization procedure on a curved space, applied already to the SU(2) Skyrme model, to the SU(3) case, and examine its quantum-mechanical structures in the framework of the collective-coordinate formalism. We assume existence of an SU(2) classical solution of the hedgehog type, which is embedded in the SU(3) solution. Then we have to treat the coset manifold SU(3)/U(1)/sub Y/, which is parametrized by a set of seven real parameters q/sup b/'s. The Wess-Zumino-Witten term is taken to be the symmetrized form of the well-known topological contribution to the effective Lagrangian L(q,q-italic-dot). From the starting Skyrme Lagrangian with time derivatives, two kinds of terms with order (h/2..pi..)/sup 2/ appear: one is independent of q/sup b/'s and gives a new contribution to the Skyrmion mass, and the other depends on q/sup b/'s through vielbeins in the q/sup b/-manifold. The former term plays a role to stabilize the rotating chiral soliton; while, the latter disappears in L(q,q-italic-dot) when expressed in terms of the covariant kinetic term, leaving a new mass contribution with negative sign. A comment is given concerning the Hamilton equations of motion and the quantum Euler-Lagrange equation.

• Research Organization: Department of Physics, Faculty of Sciences, Hokkaido University, Sapporo 060, Japan
• OSTI ID: 6933369
• Journal Information: Phys. Rev. D; (United States), Journal Name: Phys. Rev. D; (United States) Vol. 37:12; ISSN PRVDA
• Country of Publication: United States
• Language: English

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71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BARYON NUMBER
COMPOSITE MODELS
DIFFERENTIAL EQUATIONS
EQUATIONS
EQUATIONS OF MOTION
HAMILTONIANS
LIE GROUPS
MASS
MATHEMATICAL MODELS
MATHEMATICAL OPERATORS
MATHEMATICAL SPACE
MECHANICS
MINKOWSKI SPACE
NUCLEON-NUCLEON POTENTIAL
PARTIAL DIFFERENTIAL EQUATIONS
PARTICLE MODELS
POTENTIALS
QUANTIZATION
QUANTUM MECHANICS
QUANTUM OPERATORS
QUASI PARTICLES
SKYRME POTENTIAL
SOLITONS
SPACE
SPACE-TIME
SU GROUPS
SU-3 GROUPS
SYMMETRY GROUPS
U GROUPS
U-1 GROUPS