Quantum Mechanical Aspects of SU(3) Skyrme Model in Collective Coordinate Quantization
Oct, 198761 pages
Published in:
- Phys.Rev.D 37 (1988) 3663
Report number:
- EPHOU87-012
Citations per year
Abstract: (APS)
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)Y, which is parametrized by a set of seven real parameters qb’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,q̇). From the starting Skyrme Lagrangian with time derivatives, two kinds of terms with order ħ2 appear: one is independent of qb’s and gives a new contribution to the Skyrmion mass, and the other depends on qb’s through vielbeins in the qb-manifold. The former term plays a role to stabilize the rotating chiral soliton; while, the latter disappears in L(q,q̇) 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.- Skyrme model
- SYMMETRY: SU(3)
- QUANTUM MECHANICS
- QUANTIZATION: HAMILTONIAN FORMALISM
- FIELD EQUATIONS: SOLUTION
- FIELD THEORY: EFFECTIVE LAGRANGIANS
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