非平衡態物理往往受到環境影響，例如雜訊的二點關聯函數與布朗運動中的均方位移相關。有效且有效率地描述開放系統是有效場論中的一個重要課題。此外，大多數有效場論和非平衡場論的研究都局限於特定的初始條件。在本論文中，我們提出了一種Schwinger-Keldysh路徑積分，能有系統地分開時間演化和初始條件，使得此方法可用於研究真空態以外的初始條件。我們利用此方法分別研究了量子阻尼振子和相對論性純量場與環境相互作用的動力學。對於阻尼振子，我們證明了該方法給出的結果與文獻[1]一致，且微擾的單點函數與高溫極限下的經典熱單點函數相同。利用這一方法，我們提供了重整化在開放系統微擾相對論性純量場論中的初步見解。更進一步，我們發現，在1-loop的計算中出現了長期增長，這導致微擾理論在特定時間尺度之外失效，並且其有效性可以在動態重正化群的框架內得到提升。這些計算將有助於我們未來研究和理解開放系統的有效理論。;The environment plays a role in the physics far from equilibrium, such as the two-point correlation function of noise is associated with mean squared displacement in Brownian motion. Describe an open system effectively and efficiently is an imperative issue in effective field theory. Moreover, most studies of effective field theory and non-equilibrium field theory restrict to specific choices of initial states. In this thesis, a Schwinger-Keldysh path integral is developed that systematically separates the time evolution and the initial conditions to include the initial conditions beyond the vacuum state. We employ this formalism to study the real-time dynamics of a quantum damped oscillator and a relativistic scalar field interacting with the environment, respectively. For the damped oscillator, we demonstrate that the formalism gives results consistent with Ref. [1] and the perturbed one-point function coincides with the classical thermal one-point function in the high temperature limit. Exploiting this formalism, we provide an insight of renormalisation up to one-loop order in the perturbative relativistic scalar field theory of open systems. Furthermore, it is found that the secular growth appears at the one-loop order, which leads to the breakdown of perturbation theory beyond a specific time scale, and the validity could be improved within the framework of dynamical renormalisation group. These computations could help us study and understand the effective theory of open systems in the future.
