作为巡游真空的红外发散
Infrared Divergences as Itinerant Vacua
AI总结：
研究提出红外发散是巡游真空的标志，其源于经典序参量演化时量子真空在不等价态间连续变化。核心方法是实时闭时路径有效作用的精确分离，应用于多领域，揭示同一机制存在于多种现象中。
AI中文摘要：
红外发散通常被视为需消除、正则化或隐藏于修饰渐近态的病态。本文提出互补性建设性观点：红外发散是巡游真空的标志，即量子真空随经典序参量演化在一族不等价态中连续游走。其技术核心是实时闭时路径有效作用的精确分离，应用于四个领域揭示同一机制。最后概述了基于真空流形上希尔伯特空间丛的几何表述。
英文摘要：
Infrared divergences (IRDs) are usually treated as pathologies to be cancelled, regularized, or hidden in dressed asymptotic states. This paper develops a complementary and constructive viewpoint: an IRD is the signature of an \emph{itinerant vacuum} -- a quantum vacuum that wanders continuously through a family of inequivalent states as a classical order parameter evolves. Each value of the order parameter carries its own coherent vacuum, so moving the order parameter means traversing a succession of orthogonal vacua. The IRD is the field-theoretic cost of this wandering, and the $1/f$ noise, gravitational memory, and non-Gaussian fluctuations that emerge from it are its observable classical remnants. The technical core is an exact separation in the real-time closed-time-path (CTP) effective action. The infrared-divergent imaginary part of the influence functional must not be left as a divergent coefficient in a deterministic equation of motion; it is instead converted, by a Hubbard--Stratonovich identity, into a classical stochastic source. This step is an algebraic identity of the generating functional and requires no prior coarse graining or decoherence assumption: the retarded kernel encodes the memory of past vacuum transitions, while the noise kernel encodes the quantum uncertainty of the next one. We apply this construction to four parallel arenas -- soft QED, scalar fields in de Sitter space, soft gravitons, and non-equilibrium phase transitions -- and show that the same itinerant-vacuum mechanism underlies $1/f$ current noise, the primordial power spectrum, gravitational memory, and order-parameter dynamics. A geometric formulation in terms of a Hilbert-space bundle over the vacuum manifold is outlined as an outlook.
