Study on the spontaneous generation of ferromagnetic phase and the emergence of strong magnetic field in high density quark matter

1)分析了手征凝聚相、色超导相和铁磁相三相共存和/或跃迁的机制：利用推广的Nambu-Jona Lasinio(NJL)模型，通过计算高密度极化二味夸克物质的热力学势，主要研究了手征凝聚相在色超导夸克物质内部产生铁磁相，手征凝聚相、色超导相和铁磁性相三相共存和/或跃迁的机制。2)计算自旋极化夸克物质的能量密度的理论研究：2)用拉格朗日形式证明了库仑规范QCD中能量发散的消除和库仑规范QCD的可重整化。2.2)热算符…更能代表热量子场系统中的散射幅度。2)建立了基于Tsallis统计的量子统计力学的量子场论，并将其应用于“中性”夸克物质。结果在YITP研讨会、日美联合物理会议和JPS会议上公布，并发表在《物理评论D》和《理论物理进展》上。3)分析通过硬热环恢复的改进梯形Dyson-Schwinger方程获得规范不变解的可能性，以基本理论为基础理解热和/或密度相关相变的机制：3.1)协变规范内解的规范相关尺寸的研究。3.2)对得到满足Ward-Takahashi恒等式的解的过程进行了理论研究，并对得到“规范不变量”解进行了数值研究。结果在YITP研讨会、日美联合物理会议、JPS会议和两个国际研讨会上公布，并发表在研究中心公报(奈良大学)和两个国际研讨会的论文集上。4)基于费米液体理论和玻尔兹曼方程的夸克物质中铁磁相的产生和强磁场的出现的研究正在进行中。较少

1) Analysis of the mechanism of co-exsistence and/or transition among the 3-phases, i.e., the chiral condensed, the color superconducting and the ferromagnetic phases: In terms of the extended Nambu-Jona Lasinio (NJL) model, by evaluating the thermodynamic potential of the high density polarized 2-flavor quark matter, we studied, mainly focussing on the generation of the ferromagnetic phase inside the color superconducting quark matter associated with chiral condensates, the mechanism of co-exsistence and/or transition among the 3-phases, i.e., the chiral condensed, the color superconducting and the ferromagnetic phases. Results are presented at the YITP workshop and at the Japan-US Joint Physics Meeting.2) Theoretical study toward the calculation of the energy density of the spin-polarized quark matter :2.1) Proof, in the Lagrangian formalism, of the cancellation of energy-divergences in the Coulomb-gauge QCD and of the renormalizability of the Coulomb-gauge QCD.2.2) Thermal operator … More representation of the scattering amplitudes in the thermal quantum field system. 2.3) Construction of quantum field theory of quantum statistical mechanics on the basis of Tsallis statistics, and its application to the "neutral" quark matter. Results are presented at the YITP workshop, the Japan-US Joint Physics Meeting and the JPS meeting, and published in Physical Review D and Progress of Theoretical Physics.3) Analysis of the possibility of obtaining the gauge-invariant solution through the Hard-Thermal-Loop resummed improved ladder Dyson-Schwinger equation toward understanding the mechanism of thermal and/or density dependent phase transition based on the fundamental theory QCD :3.1) Study of the size of gauge-dependence of the solution inside the covariant gauge. 3.2) Theoretical study on the procedure to get a solution that satisfy the Ward-Takahashi identity, and numerical study to get a "gauge invariant" solution. Results arepresented at the YITP workshop, the Japan-US Joint Physics Meeting, the JPS meeting and two international workshops, and published in Bulletin of Research Center (Nara University) and the proceedings of the two international workshops.4) Study on the generation of the ferromagnetic phase and the emergence of strong magnetic field in the quark matter based on the Fermi liquid theory, and based on the Boltzmann equation, are now underway. Less