On the analytic properties of chiral solitons in the presence of the $\omega$--meson

Abstract

A thorough study is performed of the analytical properties of the fermion determinant for the case that the time components of (axial) vector fields do not vanish. For this purpose the non--Hermitian Euclidean Dirac Hamiltonian is generalized to the whole complex plane. The Laurent series are proven to reduce to Taylor series for the corresponding eigenvalues and --functions as long as field configurations are assumed for which level crossings do not occur. The condition that no level crossings appears determines the radius convergence. However, the need for regularization prohibits the derivation of an analytic energy functional because real and imaginary parts of the eigenvalues are treated differently. Consistency conditions for a Minkowski energy functional are extracted from global gauge invariance and the current field identity for the baryon current. Various treatments of the Nambu--Jona--Lasinio soliton are examined with respect to these conditions. Motivated by the studies of the Laurent series for the energy functional the Euclidean action is expanded in terms of the $\omega$--field. It is argued that for this expansion the proper--time regularization scheme has to be imposed on the operator level rather than on an expression in terms of the one--particle eigenenergies. The latter treatment is plagued by the inexact assumption that the Euclidean Dirac Hamiltonian and its Hermitian conjugate can be diagonalized simultaneously. It is then evident that approaches relying on counting powers of the $\omega$--field in the one--particle eigenenergies are

UNITU-THEP-13/1994, 34 LaTeX pages, 5 figures appended as postscript file

References in corpus (9)

• QCD Phenomenology based on a Chiral Effective Lagrangian
• Baryons as Chiral Solitons in the Nambu--Jona-Lasinio Model
• Analysis of Data on Polarized Lepton-Nucleon Scattering
• Rotational Corrections to Axial Currents in Semibosonized SU(3) Nambu--Jona-Lasinio Model
• Anomalies, VMD and the Enjl Model
• $1/N_C$ Corrections to $g_A$ in the Light of PCAC$
• The Chiral Soliton of the Nambu Jona-Lasinio Model with Vector and Axial Vector Mesons
• Strange and Non-Strange Meson Fluctuations off the Nambu--Jona-Lasinio Soliton
• The Nambu-Jona-Lasinio Chiral Soliton with Constrained Baryon Number

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• Baryons as Chiral Solitons in the Nambu--Jona-Lasinio Model
• On the strange vector form factors of the nucleon in the NJL soliton model
• Hadron Structure Functions in a Chiral Quark Model: Regularization, Scaling and Sum Rules
• Estimate of Quantum corrections to the Mass of the Chiral Soliton in the Nambu--Jona--Lasinio Model
• Chiral anomaly and nucleon properties in the Nambu--Jona-Lasinio model with vector mesons
• Nucleon Properties in the Polyakov Quark Meson Model
• The impossible regularization of the Nambu Jona-Lasinio model with vector interactions
• Topologically non--trivial chiral transformations: The chiral invariant elimination of the axial vector meson