A generalized dynamics is postulated in a product space ${\cal R}^{3}\times{\cal S}^{1}$ with ${\cal R}^3$ representing the configuration space of a oneparticle system to which is attached the U(1) fibre bundle represented by themanifold ${\cal S}^{1}$. The manifold ${\cal S}^{1}$ is chosen to correspond tothe action phase, with the action being the principal function corresponding tothe associated classical dynamical system. A Hilbert space representation ofthe flow equation representing the dynamics in the above product space is thenobtained, which is found to yield a probability amplitude formalism in terms ofa generalized set of equations of the Schr\"odinger form which constitutes acovering formalism for both quantum and classical mechanics. Being labelled byan integral index $n$, the equation corresponding to $n=1$ is identified withthe Schr\"odinger equation, while equations corresponding to $n\rightarrowlarge$ yield the classical dynamics through the WKB limit. Equations with lowerindices n=2,3,4,... predict the existence of new modes of non-classicalbehaviour, the observational implications of which are discussed. Somepreliminary experimental results are presented which point to the existence ofthese modes of non-classical behaviour.
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机译：在产品空间$ {\ cal R} ^ {3} \ times {\ cal S} ^ {1} $中假设广义动力学，其中$ {\ cal R} ^ 3 $表示一个单粒子系统的配置空间，并附上由它们$ {\ cal S} ^ {1} $表示的U（1）纤维束。选择流形$ {\ cal S} ^ {1} $来对应于动作阶段，其中动作是与关联的经典动力学系统相对应的主要函数。然后获得了表示上述乘积空间中动力学的流动方程的希尔伯特空间表示，发现它产生了一个广义的薛定ism形式方程组的概率振幅形式，该形式构成了量子和经典形式的加法形式用积分指数$ n $标记，对应于$ n ＝ 1 $的方程式用Schr“ odinger方程识别，而对应于$ n \ rightarrowlarge $的方程式则通过WKB极限产生经典动力学。具有较低索引n = 2,3,4，...的方程预测了非经典行为的新模式的存在，并讨论了其观测意义。给出了一些初步的实验结果，这些结果表明了这些非经典行为的模式的存在。
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