Speaker
Description
In recent years, the search for new ground states or new phase boundaries in quark/nuclear matter has attracted widespread theoretical interest in high-energy nuclear physics [1, 2]. The study of inhomogeneous phases is a key research topic in this field. Numerous studies have investigated possible inhomogeneous phases in QCD systems, such as the chiral density wave (CDW) phase, the chiral soliton lattice (CSL) phase, and the baronic phase, a mixture of quark and baryon states [3, 4, 5].
These inhomogeneous phases are theoretically caused by a spatially inhomogeneous background field generated by strong coupling in a semiclassical approximation, which is calculated based on mean-field calculations. Quantum fluctuations are a crucial physical effect in quark matter systems, but they are not systematically considered or rigorously calculated in conventional semiclassical calculations. We aim to systematically and rigorously calculate the quantum fluctuation effects of quark matter systems in the presence of an inhomogeneous field and, in the future, apply this approach to the study of thermodynamic properties and phase transitions in inhomogeneous phases of quark matter.
In this paper, we use the chiral soliton model (linear sigma model) to investigate this problem [6, 7]. We first solve the chiral soliton solution using the mean-field approximation and the hedgehog approximation. We then use the corresponding meson fields σ(r) and π(r) as an inhomogeneous background field to calculate the single-loop quantum fluctuation energy of the system in this inhomogeneous field. Due to the distortion of the energy continuum and the divergence of the integral, we need to employ a self-consistent and unconventional renormalization scheme in this inhomogeneous field [8, 9, 10].
We first perform a Born subtraction on the scattering phase shift in the energy integral caused by the energy spectrum distortion. Then, we add a compensating Feynman diagram and introduce the corresponding renormalization cancellation term to achieve energy renormalization. Specifically, we constructed a wave function basis with a definite parity, angular quantum number, and energy under the background of an inhomogeneous field, diagonalized the system Hamiltonian, and obtained the energy discrete spectrum and continuous spectrum corresponding to the quantum fluctuations as well as the corresponding eigenwave function. Combined with the self-consistent renormalization treatment, we obtained a finite system energy quantum fluctuation correction with a definite parity and angular quantum number under the background of an inhomogeneous field.
Keywords: Quantum fluctuations, chiral soliton model, inhomogeneous background field, non-perturbative field theory calculation method
References
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| Academic Status | I am a Ph.D. student |
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