Quantum fluctuation energies over a spatially inhomogeneous field background in a chiral soliton model

Abstract

Based on chiral soliton models, the quantum fluctuation energies of quarks over a spatially inhomogeneous meson field background have been thoroughly studied. We have used a systematic calculation scheme initiated by Schwinger, in which the loop quantum fluctuation energies are evaluated by a nontrivial level summation over the eigenvalue spectrum of the effective Hamiltonian of the system. The effective Hamiltonian can be constructed by one loop effective action of fluctuations of quarks over a static chiral soliton field background. The corresponding Dirac equation is obtained. In a static and spatially spherical case and by the hedgehog ansatz the radial part and the angular part of the grand spin of the wave function for the Dirac equation can be separated. Due to the soliton background the eigenvalue spectrum are distorted. The scattering phase shift can be determined by solve the radial equations at different momentum. The density of states in momentum space can be derived. The effective Hamiltonian has been diagonalized in a Hilbert space where the eigenfunctions are labeled by the parity, grand spin and energy. The renormalization scheme can be carried out by a Born subtraction of the phase shift and the compensating Feynman diagram renormalization. Finally the finite quantum fluctuation energies over chiral soliton background at different parities and grand spins have been numerically evaluated, compared and discussed.

25 pages,9 figures

References in corpus (11)

• Inhomogeneous chiral condensates
• Inhomogeneous phases in the Nambu-Jona-Lasino and quark-meson model
• Inhomogeneous confining-deconfining phases in rotating plasmas
• Inhomogeneous chiral condensation under rotation in the holographic QCD
• Magnetohydrodynamic simulations of self-consistent rotating neutron stars with mixed poloidal and toroidal magnetic fields
• Competition of inhomogeneous chiral phases and two-flavor color superconductivity in the NJL model
• Structure formation during phase transitions in strongly interacting matter
• Spontaneous symmetry breaking via inhomogeneities and the differential surface tension
• Thermal phonon fluctuations and stability of the magnetic dual chiral density wave phase in dense QCD
• Quantum fluctuation in an inhomogeneous background and its influence on the phase transition in a finite volume system
• The nucleon properties in finite temperature and density with Gaussian fluctuations