We discuss the imaginary-time formalism for field theories in thermal equilibrium in uniformly accelerating frames. We show that under a Wick rotation of Minkowski spacetime, the Rindler event horizon shrinks to a point in a two-dimensional subspace tangential to the acceleration direction and the imaginary time. We demonstrate that the accelerated version of the Kubo-Martin-Schwinger (KMS) condition implies an identification of all spacetime points related by integer-multiple rotations in the tangential subspace about this Euclidean Rindler event-horizon point, with the rotational quanta defined by the thermal acceleration, . In the Wick-rotated Rindler hyperbolic coordinates, the KMS relations reduce to standard (anti-)periodic boundary conditions in terms of the imaginary proper time (rapidity) coordinate. Our findings pave the way to study, using first-principle lattice simulations, the Hawking-Unruh radiation in geometries with event horizons, phase transitions in accelerating Early Universe and early stages of quark-gluon plasma created in relativistic heavy-ion collisions.

中文翻译：

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沿着虚圆的圆周运动的加速度：虚时间形式主义中加速场论的 Kubo-Martin-Schwinger 条件


我们讨论均匀加速框架中热平衡场论的虚时间形式主义。我们证明，在闵可夫斯基时空的威克旋转下，林德勒事件视界收缩到与加速度方向和虚时间相切的二维子空间中的一点。我们证明了 Kubo-Martin-Schwinger (KMS) 条件的加速版本意味着识别与欧几里德 Rindler 事件视界点相关的切向子空间中的整数倍旋转相关的所有时空点，其中旋转量子由热加速度，.在 Wick 旋转 Rindler 双曲坐标中，KMS 关系根据虚本时（快速）坐标简化为标准（反）周期边界条件。我们的发现为使用第一原理晶格模拟研究具有事件视界的几何中的霍金-安鲁辐射、加速早期宇宙中的相变以及相对论重离子碰撞中产生的夸克-胶子等离子体的早期阶段铺平了道路。