The Linear Sigma-Model in the 1/N-Expansion via Dynamical Boson Mappings and Applications to $\pi \pi$-Scattering

Abstract

We present a non-perturbative method for the study of the O(N+1)-version of the linear sigma-model. Using boson-mapping techniques, in close analogy to those well-known for fermionic systems, we obtain a systematic 1/N-expansion for the Hamiltonian which is symmetry-conserving order by order. The leading order for the Hamiltonian is evaluated explicitly and we apply the method to $\pi \pi$-scattering, in deriving the T-matrix to leading order.

28 pages, Latex, (with minor corrections to some misprints in the appendix of the old version)

References in corpus (4)

• S-Wave Pion-Pion Correlations in Dense Nuclear Matter
• A Non-Perturbative Treatment of the Pion in the Linear Sigma-Model
• The Cutoff $\lambda {\varphi }^4$ O(N) Model in the Large N Limit
• Equation of State of an Interacting Pion Gas with Realistic $\pi$--$\pi$ Interactions

Cited by in corpus (9)

• Vector and axial-vector correlators in a chirally symmetric model
• Dropping Sigma-Meson Mass and In-Medium S-Wave pion-pion Correlations
• Medium Modification of The Pion-Pion Interaction at Finite Density
• Two-pion production processes, chiral symmetry and NN interaction in the medium
• Single Boson Images Via an Extended Holstein Primakoff Mapping
• The Octet of Goldstone-Bosons in the SU(3) Linear sigma Model in the QRPA
• Generalized Random Phase Approximation and Gauge Theories
• Symmetry conserving non-perturbative s-wave renormalization of the pion in hot and baryon dense medium
• Symmetry Conserving Dynamical Mappings