We study rotating thermal states of a massless quantum fermion field inside a cylinder in Minkowski space-time. Two possible boundary conditions for the fermion field on the cylinder are considered: the spectral and MIT bag boundary conditions. If the radius of the cylinder is sufficiently small, rotating thermal expectation values are finite everywhere inside the cylinder. We also study the Casimir divergences on the boundary. The rotating thermal expectation values and the Casimir divergences have different properties depending on the boundary conditions applied at the cylinder. This is due to the local nature of the MIT bag boundary condition, while the spectral boundary condition is nonlocal.
We outline a proof of the stability of a massless neutral scalar field $ψ$ in the background of a wide class of four dimensional asymptotically flat rotating and ``electrically charged'' solutions of supergravity, and the low energy limit of string theory, known as STU metrics. Despite their complexity, we find it possible to circumvent the difficulties presented by the existence of ergo-regions and the related phenomenon of super-radiance in the original metrics by following a strategy due to Whiting, and passing to an auxiliary metric admitting an everywhere lightlike Killing field and const…
Spectral Zeta Functions for a Cylinder and a Circle
构造了无限长圆柱面上满足Dirichlet和Neumann边界条件的无质量标量场的谱zeta函数$ζ(s)$.这些函数被明确地定义在包含实轴$-1\le$ Re $s \le 0$的闭区间的复平面s的有限域中。从这个出发，谱zeta函数的边界条件上的一个圆圈（边值问题的一个平面上）得到没有任何额外的计算。推导了相应场组态的Casimir能量。
The Lewis solutions describe the exterior gravitational field produced by infinitely long rotating cylinders, and are useful models for global gravitational effects. When the metric parameters are real (Weyl class), the exterior metrics of rotating and static cylinders are locally indistinguishable, but known to globally differ. The significance of this difference, both in terms of physical effects (gravitomagnetism) and of the mathematical invariants that detect the rotation, remain open problems in the literature. In this work we show that, by a rigid coordinate rotation, the Weyl class metr…
We show that any 2D scalar field theory compactified on a cylinder and with a Fourier expandable potential $V$ is equivalent, in the small coupling limit, to a 1D theory involving a massless particle in a potential $V$ and an infinite tower of free massive Kaluza-Klein (KK) modes. Moving slightly away from the deep IR region has the effect of switching on interactions between the zero mode and the KK modes, whose strength is controlled by powers of the coupling, hence making the interactions increasingly suppressed. We take the notable example of Liouville field theory and, starting from its w…
We consider rigidly-rotating thermal states of a massless Klein-Gordon field enclosed within a cylindrical boundary, where Robin boundary conditions (RBCs) are imposed. The connection between the parameter of the RBCs and the energy density and four-velocity expressed in the Landau frame is revealed.
