Particle pair creation from vacuum in the presence of an external field is one of the most remarkable consequences of quantum field theory. We investigate this problem as a mechanism of matter formation in the initial stage of relativistic heavy-ion collisions, especially focusing on its real-time dynamics.

Despite the great success of the perfect fluid description of a quarkgluon plasma (QGP) for relativistic heavy-ion collisions, an understanding of how produced matter reaches thermal and chemical equilibrium is still lacking. In the framework of the Color Glass Condensate, which is an effective theory to describe high-energy nuclei in saturated region, it has been shown that high density gluons which are emitted from colliding nuclei can be interpreted as coherent classical color electromagnetic fields polarized in a longitudinal beam direction. Given this situation, describing how particles emerge from the coherent fields is of prime importance in order to get an understanding of the formation process of QGP.

Because heavy-ion collisions are dynamic systems, a real-time description of pair creation is necessary. We describe the space-time evolution of the quantum state of charged particle fields in the presence of strong electromagnetic fields in terms of the mode functions of charged particles, taking into account the back reaction of the particle production to the background field. The time evolution of momentum distributions of created particles is presented, which show collective motion of plasma oscillation and quantum effects as well, such as the Bose enhancement/Pauli blocking and interference between matter fields.

Getting an understanding of how quarks are produced in a system of heavy-ion collisions is important because chemical equilibrium between light quarks and gluons is expected in QGP state, while the initial state of heavy-ion collisions is considered as a gluon-dominated state. Therefore, we investigate quark pair production under SU(3) color electric fields. By the procedure of Abelianization, we introduced a gauge-invariant parameter characterizing the direction of the color field in color space. We find that although the momentum distribution of each colored quark strongly depends on the color direction of the field, field quantities such as the color current and the total number density of created quarks are rather insensitive to it.

We also examined the role of pair creation for the isotropization of pressure. The initial state with the coherent electric field is quite anisotropic: longitudinal pressure is positive and transverse pressure is negative. At later time, created quarks are accelerated by the field and generate positive longitudinal pressure. Moreover, the field strength is weakened by the back reaction, so that pressure by the field is also weakened. As a result, anisotropy in pressure is moderated. This is a collision-less mechanism of isotropization and may assist thermalization expected in heavy-ion collisions.

Because the formation of color magnetic fields as well as electric fields in a longitudinal beam direction is predicted by the Color Glass Condensate model, We investigated the effects of a magnetic field which is parallel to the electric field. Due to emergence of the Landau levels, scalar particles become effectively heavy under the magnetic field, and thereby their pair creation is suppressed. In contrast, pair creation of spinor particles is enhanced by the magnetic field. This is because (i) spinor particles in the lowest Landau level do not become heavy because of the spin-magnetic field interaction, and (ii) the number of modes degenerating in one Landau level is proportional to the magnetic field strength. This enhanced pair creation makes the time evolution of the system faster through the back reaction. Furthermore, induction of chiral charge in the magnetic field is discussed.

In heavy-ion collisions, electric fields are generated only between two color-charged plates of Lorentz-contracted nuclei receding from each other a velocity close to the speed of light. In an ideal situation where the two nuclei run at exactly the speed of light, the electric fields span only inside the forward light cone. The dynamics of particle production in electric fields of such configuration is studied. A characteristic of this field configuration is its boost invariance in the longitudinal direction. By formulating the field quantization in a curvilinear coordinate, we show that particles are created preserving the boost symmetry of the background and they have the same velocity distribution as the Bjorken flow from a first instant they are created. These particles are quantum-mechanical superpositions of several momentum modes. This fact brings non-trivial rapidity correlations among the particles. We calculate the two-particle correlations between these particles, and find that the correlation is shortrange with respect to the transverse momentum, which originates in the Bose-Einstein/Fermi-Dirac correlation, and is long-range with respect to the longitudinal rapidity. This result is interesting in the context of the near-side ridge phenomena observed in nucleus-nucleus collisions at RHIC and recently observed also in proton-proton collisions at LHC.

本論文は5章からなる。第1章は、イントロダクションであり、本研究に至った着想や歴史的経緯、背景となる現象が述べられている。第2章は、一様な強い電場中における非摂動的なボソン粒子、フェルミ粒子生成を量子論的に定式化し、その上で、場に対するバックリアクションの効果を取り入れた。特に生成粒子分布関数の時間発展に注目し、エネルギーが場から粒子にどのように流れるのか、及び、簡単なモデルを用いてプラズマ振動の典型的なスケールを導出した。第3章では、前章の結果を量子色力学における非可換ゲージ場(グルーオン場)中のクォーク対生成に拡張した。特に、非可換ゲージ場に特有の内部空間における向きと生成されるクォークのカラーの自由度の関係を明らかにし、実空間の向きだけでなく内部空間の向きにも依存した粒子対生成を導出した。また、外場のかけられた向きに負の圧力を持った系が、粒子生成によってどのように正の圧力を持ち、最終的に圧力の等方化に向かうかを初めて定量的に示した。加えて、磁場の効果、カイラル異常項の効果についても解析した。第4章では、現実の相対論的重イオン衝突反応の系に即して、前方光円錐内にのみ電場が生じていると想定し、そのような境界条件の下で、粒子対生成の解析を行った。特に、固有時とラピディティを用いた膨張座標系における量子論的な粒子生成を定式化し、膨張座標系に特有の物理量とその意味を明らかにした。

強い電場中の粒子生成の物理は歴史が長いものの、近年実験的な実現可能性も出てきたことから「強場の物理」として急速に発展してきている。その中で、論文申請者は、相対論的重イオン衝突反応における平衡化の問題を見据え、生成粒子数の時間発展を場の量子論の非摂動的に見事に定式化した。この解析は、今後、相対論的重イオン衝突反応において系の局所熱平衡がどのように起こるかを知る上で、非常に重要な結果である。

なお、本論文の内容は、いずれの章も論文提出者が主体となって計算、解析を行ったもので、論文提出者の寄与が十分であると判断する。

したがって、博士(理学)の学位を授与できると認める。