8 pages, o figures; talk given by the first author at the 5th International Symposium on Quantum Theory and Symmetries (QTS5) held in Vallodolid, Spain, July 2007; published in a special issue of the Journal of Physics A, Ed. by M. Gadella, J. M. Izquierdo, S. Kuru, J. Negro, M. del Olmo
The Pais-Uhlenbeck model is a quantum theory described by a higher-derivative field equation. It has been believed for many years that this model possesses ghost states (quantum states of negative norm) and therefore that this model is a physically unacceptable quantum theory. The existence of such ghost states was believed to be attributable to the field equation having more than two derivatives. This paper shows that the Pais-Uhlenbeck model does not possess any ghost states at all and that it is a perfectly acceptable quantum theory. The supposed ghost states in this model arise if the Hamiltonian of the model is (incorrectly) treated as being Dirac Hermitian (invariant under combined matrix transposition and complex conjugation). However, the Hamiltonian is {\it not} Dirac Hermitian, but rather it is PT symmetric. When it is quantized correctly according to the rules of PT quantum mechanics, the energy spectrum is real and bounded below and all of the quantum states have positive norm.
Ghost-free vector superfield actions in supersymmetric higher-derivative theories
在四维${\cal N}=1$整体超对称理论中，我们系统地构造了阿贝尔向量超多重态的无重影高阶导数作用。在给出一个简单的例子，说明了一个天真的引入一个较高的导数项引起的鬼，我们讨论了可能的积木的鬼自由行动，并明确表明，他们的玻色子部分没有鬼模式和辅助字段$\boldsymbol{D}$不传播。高阶导数项在作用中产生更高的辅助场$\boldsymbol{D}$的幂，因此D项运动方程一般允许多个解。我们确认著名的超对称Dirac Born Infeld作用属于这一类。我们进一步给出另一个例子，其中标准的二次动力学项（麦克斯韦项）是由一个四次项的场强校正。我们还讨论了可能的耦合到物质场和变形的D项潜力。
Lagrangian Formulation of an Infinite Derivative Real Scalar Field Theory in the Framework of the Covariant Kempf-Mangano Algebra in a $(D+1)$-dimensional Minkowski Space-time
2017年，G. P. de Brito及其同事提出了$(D+1)$维Minkowski时空中Kempf-Mangano代数的协变推广[A. Kempf和G. Mangano，Phys. Rev. D \textbf{55}，7909（1997）; G. P. de Brito，P. I. C. Caneda，Y. M. P. Gomes，J. T. Guaitolini Junior和V. Nikoofard，Adv. High Energy Phys. \textbf{2017}，4768341（2017）]。从协变Kempf-Mangano代数的观点出发，对实标量场理论进行重构，得到描述自由空间中两个玻色粒子（一个普通粒子和一个幽灵粒子）的无限导数Klein-Gordon波动方程.我们表明，在低能量（大距离）限制我们的无限导数标量场理论的行为就像一个Pais-Uhlenbeck振荡器的空间均匀的场配置$ϕ(t,\vec{\textbf{x}})=ϕ(t)$。我们的计算表明，在四维Minkowski时空中存在一个特征长度尺度$δ$，其上限接近于核尺度，即，$δ_{max}\sim δ_{nuclear\ scale}\sim 10^{-15}\, m$。最后，从协变Kempf-Mangano代数的角度证明了具有非局部形状因子${\cal K}(x-y)= -\frac{\squ…
