The rules of canonical quantization normally offer good results, but sometimes they fail, e.g., leading to quantum triviality ($=$ free) for certain examples that are classically nontrivial ($\ne$ free). A new procedure, called Enhanced Quantization, relates classical models with their quantum partners differently and leads to satisfactory results for all systems. This paper features enhanced quantization procedures and provides highlights of two examples, a rotationally symmetric model and an ultralocal scalar model, for which canonical quantization fails while enhanced quantization succeeds.
Quantization of the one-dimensional free harmonic oscillator as an example of the application of the node theorem and the MacDonald-Hylleraas-Undheim theorem
Quantum and Classical Fields in the Finite-Dimensional Formalism
M. Navarro（和独立的I. V. Kanatchikov）的有限维量子场论公式被应用于Klein-Gordon场和Dirac场，得到两个场的量子运动方程。在这样做的过程中出现了几个问题。解决这些困难使我们提出了一个新的经典规范形式主义，这反过来又使我们新的，改进的量子化规则。我们表明，新的经典运动方程和规则的量化克服了几个已知的不满意的功能，以前的形式主义。我们认为，新的形式主义是一个普遍的改进，相对于以前的。此外，我们表明，量子场论的狄拉克和克莱因-戈登场描述粒子额外的，谐振子样的自由度。我们认为，这些自由度应该引起的形式主义的多粒子的解释。
Department of Physics, Cornell University（康奈尔大学物理系）；Institute of Natural Sciences, Shanghai Jiao Tong University（上海交通大学自然科学研究院）；School of Mathematical Sciences, Shanghai Jiao Tong University（上海交通大学数学科学学院）；Ministry of Education Key Laboratory in Scientific and Engineering Computing, Shanghai Jiao Tong University（上海交通大学教育部科学与工程计算重点实验室）；Global College, Shanghai Jiao Tong University（上海交通大学全球学院）；School of Electrical and Computer Engineering, Cornell University（康奈尔大学电气与计算机工程学院）
